Timing Risk

one_liner: The failure mode where a technically sound product, technology, or policy fails not from its own defects but because the surrounding environment is not yet — or is no longer — ready to absorb it, treating environmental readiness as a risk factor independent of execution.

core_idea:
Timing risk is the failure mode in which a technically sound product, technology, policy, or business model fails not because of intrinsic defects but because the surrounding environment — market demand, infrastructure, regulation, capital availability, user behaviour, or institutional readiness — is not yet in a state that can absorb and sustain it, or is no longer in that state. The idea is in active use in venture capital, product development, public-policy innovation, and technology commercialisation; the canonical case file includes General Magic (1990–2002), the Apple Newton, electronic medical records initiatives of the 1990s, ride-sharing before smartphone adoption, and synchronous video calling before broadband penetration.

The mechanism has two symmetric failure branches. *Too early*: the intervention lands before the receptive substrate has formed — the necessary infrastructure does not yet exist, regulatory frameworks have not been built, user habits have not been established, complementary technologies are unavailable, or financing for the sector has not yet developed. The intervention may be technically correct and commercially well-executed and still fail, because its success depends on a set of environmental preconditions that will only emerge later. Some of the cost of early entry is absorbed as a subsidy to those who enter later once the substrate has been pre-conditioned. *Too late*: the readiness window has closed — the niche has been filled by incumbents, the regulatory moment has passed, user attention has migrated, or capital has already concentrated in established players. A substantively equivalent intervention that would have succeeded during the window fails after it.

The diagnostic move the concept enables is to separate the intervention's internal quality (execution, technology, team, product design) from the *environmental readiness* as an independent risk factor. This separation matters for post-hoc attribution (a failure was timing, not execution) and for prospective strategy: timing risk is partially manageable through *substrate-shaping* (acting on the environment to bring the readiness window forward), *signal-early* approaches (building awareness before the window opens), *optionality preservation* (remaining capable of entering once conditions ripen), and *explicit staging* (placing small early bets that expire if the window does not open, reserving larger bets for when it does).

scope_of_application:
Timing risk lives within innovation and venture contexts; it operates wherever a technically sound intervention must be absorbed by an environment with its own readiness dynamics, framed in venture terms (capital runway, adoption window, exit window). Its reach is across the substantive application areas of innovation, not cross-substrate travel — the developmental-critical-period and policy-window analogues each have a richer native concept and belong to the broader `opportunity_window` pattern, not "timing risk."

- **Venture capital** — the native home: environmental readiness is priced as an independent risk factor against capital runway and burn rate, and the too-early/too-late branch governs whether to be the subsidizing pioneer, the fast follower, or the patient holder of optionality.
- **Product development and technology commercialization** — the canonical case file (General Magic, the Apple Newton, ride-sharing before smartphones, video calling before broadband) where sound products met unformed infrastructure, habits, or complements.
- **Consumer products and B2B platforms** — adoption-window analysis separating product quality from whether the market, integrations, and user habits are ready to absorb the offering.
- **Public-policy innovation** — reform initiatives whose success rides on a readiness window (institutional capacity, regulatory clarity, public appetite) rather than on the policy's intrinsic design.
- **Education reform and health-tech adoption** — sector-specific instances (electronic medical records in the 1990s) where reimbursement codes, infrastructure, and institutional readiness gate an otherwise sound intervention.
- **Timing-management strategy** — the in-domain play menu read off the readiness gap: substrate-shaping to pull the window forward, signal-early, optionality preservation, and staged bets that expire if the window stays shut.

structural_signature:
**Sig role-phrases:**

- **the intervention** — the technically sound product, technology, policy, or business model being released, held distinct from its quality
- **the receptive substrate** — the surrounding conditions that must be ready to absorb it (infrastructure, regulation, complementary technologies, user habits, capital, attention)
- **the readiness window** — the interval during which the substrate can accept the intervention, with its own opening and closing dynamics
- **the release moment** — when the intervention actually lands relative to that window
- **the too-early branch** — release before the substrate has formed, where a correct, well-executed intervention fails for want of preconditions that emerge only later
- **the too-late branch** — release after the window has closed, the niche filled by incumbents, attention migrated, or capital concentrated
- **the readiness-versus-quality separation** — the diagnostic that treats environmental readiness as a risk factor independent of execution, routing attribution to timing or to internal quality
- **the subsidy-to-the-later-winner sequence** — the order-of-events inference that a too-early pioneer can absorb the cost of pre-conditioning the substrate, creating the readiness a later entrant exploits
- **the timing-management menu** — the plays that follow from the located readiness gap: substrate-shaping, signal-early, optionality preservation, and staged bets that expire if the window stays shut

what_it_is_not:
- **Not a defect in the intervention.** Timing risk is the failure mode where a *technically sound* product, technology, or policy meets an unready environment — the binding constraint is the missing substrate (infrastructure, regulation, complements, habits, capital), not execution, team, or design. A genuinely defective intervention is outside its scope, and invoking timing to excuse an execution failure is the category error the concept exists to prevent.
- **Not only "too early."** The mechanism is symmetric: *too early* (the receptive substrate has not yet formed) and *too late* (the window has closed — the niche filled, attention migrated, capital concentrated in incumbents). Reading it as merely "ahead of its time" misses the mirror branch, where a substantively equivalent intervention that would have won during the window fails after it.
- **Not pure bad luck.** Environmental readiness is treated as a *partly manageable* variable, not a fixed backdrop: substrate-shaping pulls the window forward, signaling-early earns recognition when it opens, optionality preservation holds the capability to enter when it ripens, staged bets expire if it stays shut. "When" becomes a lever — "be earlier" and "be later" are options alongside "be better."
- **Not "risk" in the broad probabilistic sense.** The "risk" in timing risk is the *venture* sense — a hazard against capital runway — not exposure to a known outcome distribution. It is one specific source of variance among many; the general probabilistic notion of `risk` subsumes it rather than defining it.
- **Not the general opportunity-window pattern.** The substrate-spanning structure — an intervention meeting a receptive window with its own opening and closing dynamics — is the `opportunity_window` / readiness-window pattern, and each field already has a *richer* native concept for it (developmental critical period, Kingdon's policy window, adaptive radiation, resonance). The venture framing (adoption window, burn-rate-aware staging, readiness) that makes this *timing risk* does not travel; importing it into, say, developmental biology would lose more than it gained.

clarity:
Naming timing risk separates two things that failure post-mortems in venture and product development chronically merge: *what the intervention is* — its technology, execution, team, design — and *when it lands* relative to the readiness of the environment that must absorb it. Without the concept, a failed product invites only internal explanations — the team under-executed, the design was wrong, the company ran out of money — and a founder or investor reaches for fixes aimed at quality when the binding constraint was that the infrastructure, regulation, complementary technologies, user habits, or sector financing simply had not yet formed. By treating environmental readiness as an *independent risk factor*, timing risk lets the analyst ask the sharp diagnostic question — *was the receptive substrate present at the moment of release?* — and route attribution accordingly: if yes, the failure was internal; if no, the failure was timing, and no amount of better building would have saved it. That same separation guards the symmetric error of crediting a success to brilliant execution when it was really the arrival of a ripe window that incumbents had pre-conditioned.

The concept also makes legible a class of strategic moves that "build a better product" alone obscures. Once *when* is a manipulable variable rather than a fixed backdrop, "be earlier" and "be later" become recognizable options alongside "be better" — and so do the finer plays the diagnostic opens up: shaping the substrate to pull the readiness window forward, signaling early to be recognized when it opens, preserving optionality to enter the moment conditions ripen, and staging small bets that expire if the window stays shut while reserving larger commitments for when it opens. The clarity is in converting "the market wasn't there" from a lament into a question with a location — which precondition was missing, and is it the kind one can wait out, accelerate, or hedge — letting a practitioner act on timing deliberately instead of discovering it only in the post-mortem.

manages_complexity:
The sprawl timing risk tames is the open-ended catalog of failure stories that venture and product post-mortems generate: we ran out of money, the market wasn't there, the regulator wasn't ready, users didn't care, a rival got there first, the technology was too clunky. Confronting a failed venture, an analyst faces all of these at once, each pointing toward a different lesson and a different fix, with no principled way to know which mattered. Timing risk collapses that catalog by routing it through a single binary: *was the receptive substrate present at the moment of release?* If yes, the failure is internal and attribution flows to execution, technology, team, design; if no, the failure is timing and no amount of better building would have changed it. The dozens of bespoke narratives reduce to one question with two answers, and the analyst tracks one variable — environmental readiness, held apart from intervention quality — rather than re-deriving each failure from its full circumstantial detail. The same binary, run forward, guards the mirror error of crediting a success to brilliant execution when it was a ripe window that did the work.

Beyond the diagnostic, the concept compresses the strategy space the same way. Once *when* is a manipulable parameter rather than a fixed backdrop, the entire menu of responses organizes around a small branch structure keyed to which precondition is missing and whether it can be waited out, accelerated, or hedged: substrate-shaping to pull the window forward, signal-early to be recognized when it opens, optionality preservation to enter the moment it ripens, staged bets that expire if it stays shut. The analyst no longer evaluates an unbounded space of "how could this product be better" but reads the move off the readiness gap — locate the absent precondition, classify it, and the appropriate play follows. A high-dimensional tangle of why-it-failed and what-to-do-next folds onto one tracked quantity (substrate readiness) and one decision tree (present / absent-but-shapable / absent-and-unripe), which is what lets a practitioner act on timing deliberately instead of discovering it only in the post-mortem.

abstract_reasoning:
Timing risk licenses a focused set of moves in venture and innovation analysis, all generated by treating environmental readiness as a risk factor independent of the intervention's internal quality.

*Diagnostic (attribute a failure to timing or execution by testing substrate readiness at the moment of release).* The central move is to take a failed (or successful) intervention and infer whether the binding factor was internal or environmental, by asking a single counterfactual: *was the receptive substrate present at the moment of release?* A failure where the substrate was present is attributed to execution, technology, team, or design; a failure where the substrate was absent — infrastructure, regulation, complementary technologies, user habits, or sector financing not yet formed — is attributed to timing, with the inference that no amount of better building would have changed the outcome. The reasoning runs from the observed failure plus the state of the environment at launch to a located cause, and it cuts both ways: the same test guards against crediting a success to brilliant execution when a ripe window (often pre-conditioned by earlier entrants) did the work. The diagnostic further refines *which branch of timing* by reading the signature: a sound product that found no infrastructure or habits to rest on indicts *too early*; a sound product that found the niche filled, attention migrated, or capital concentrated in incumbents indicts *too late*.

*Boundary-drawing (separate the intervention from its moment, and timing risk from internal risk).* The construct draws a boundary that post-mortems chronically erase: between *what the intervention is* and *when it lands* relative to the environment that must absorb it. The move "the product failed, so the product was deficient" is ruled out of bounds until readiness has been checked — environmental mismatch is a distinct, partly independent risk factor, and conflating it with quality misroutes both attribution and remedy. The framing also bounds what timing risk can explain: it is the failure mode where a *technically sound* intervention meets an unready environment, so a genuinely defective intervention is outside its scope, and invoking timing to excuse an execution failure is itself a category error the boundary guards against.

*Interventionist (convert "when" into a manipulable variable and select the play from the readiness gap).* Once timing is a parameter rather than a fixed backdrop, the concept licenses an interventionist menu that "build a better product" obscures, and predicts the appropriate move from *which precondition is missing and whether it can be waited out, accelerated, or hedged*. Substrate-shaping acts on the environment to pull the readiness window forward (predicted to help when the missing precondition is one the entrant can influence); signal-early builds awareness so the entrant is recognized when the window opens; optionality preservation keeps the capability to enter the moment conditions ripen; staged betting places small commitments that expire if the window stays shut while reserving larger ones for when it opens. Each is a coupled prediction — *act on this missing precondition in this way, and the timing exposure is reduced thus* — and the selection among them is read off the located readiness gap rather than chosen blind.

*Predictive sequencing (the too-early entrant subsidizes the later winner).* The concept supplies a characteristic order-of-events inference: an entrant who lands before the substrate forms may absorb the cost of pre-conditioning the environment — building awareness, proving the concept, pressing regulators — as a subsidy to whoever enters once the window has opened. The analyst predicts not just that a too-early venture fails, but that its failure can *create* the readiness a substantively identical later venture exploits, so the sequence (early entrant pre-conditions, window opens, later entrant succeeds) is itself a forecastable pattern. This turns "the market wasn't there" from a terminal lament into a position in a temporal sequence, letting the practitioner reason about whether to be the subsidizing pioneer, the fast follower, or the patient holder of optionality.

knowledge_transfer:
Within innovation and venture contexts timing risk transfers *as mechanism* across substantive domains, and this is its native strength. The same diagnostic (was the receptive substrate present at the moment of release? — route attribution to execution if yes, to timing if no) and the same intervention family carry intact across consumer products, B2B platforms, public services, education reform, and health-tech adoption: *seed early* (small bets before the window opens, accepting some waste), *signal early* (build awareness to be recognized when it opens), *wait visibly* / *preserve optionality* (hold the capability to enter the moment conditions ripen), *shape the substrate* (act on the environment to pull the window forward), and *abandon at fit failure* (notice when a window has closed). The diagnostics carry with the vocabulary — the too-early/too-late branch signature, the separation of intervention quality from environmental readiness, the too-early-entrant-subsidizes-the-later-winner sequence — wherever a sound intervention must be absorbed by an environment with its own readiness dynamics, framed in venture terms (capital runway, burn rate, adoption window, exit window).

Beyond innovation the honest reading is the **shared-abstract-mechanism** case (B), with an unusually sharp twist worth stating plainly: the cross-domain reach is real, but at each landing there is a *richer native concept* that carries more substrate-specific structure than "timing risk" does, so the named concept should *not* be exported. The genuine recurring pattern is *an intervention meeting a receptive window with specific opening and closing dynamics* — a candidate `opportunity_window` / `readiness_window` prime — and that pattern appears as real co-instances across biology (developmental critical periods), evolution (adaptive radiations into newly opened niches), epidemiology (R₀ crossing one), politics (Kingdon's policy windows, reform windows after crises), physics (resonance), and complexity theory (Kauffman's adjacent possible). But each of those already has its own well-established framing — *critical period*, *adaptive radiation*, *policy window*, *resonance* — that encodes more about its substrate's window dynamics than the venture concept does. Importing "timing risk" into developmental biology would *lose more than it gained*. So the cross-domain lesson should be carried by the broader readiness-window pattern (and, at each landing, by that field's native concept), not by "timing risk," which is best read as one domain-shaped instance pointing at the general window pattern.

The home-bound cargo is exactly the venture/innovation framing that makes the strip-the-jargon test fail to pass cleanly: the "risk" in "timing risk" is the venture sense (a hazard against capital runway), not the broad probabilistic sense; "adoption window" is diffusion-of-innovations language; "readiness" is product-management vocabulary; and the intervention menu (burn-rate-aware staged betting, signaling to acquirers and partners) is venture machinery. Strip those and what remains is the substrate-neutral move — read the environment's receptivity as a separate variable with opening and closing dynamics — which is the `opportunity_window` parent, not anything specifically "timing risk." So an off-domain invocation borrows the readiness-window *shape* (which belongs to the parent and to each field's native concept) while carrying venture baggage that does not fit, and should be marked as such. One discipline travels genuinely well wherever the window pattern is recognized and is the concept's sharpest lesson: treat *when* an intervention lands as a manipulable variable rather than a fixed backdrop — so "be earlier" and "be later" become options alongside "be better," and a too-early pioneer may *create* the readiness a later entrant exploits. That habit — separate the intervention from its moment, locate the missing precondition, and ask whether it can be waited out, accelerated, or hedged — generalizes even where the venture vocabulary does not. Mechanism within innovation/venture, parent-pattern (`opportunity_window` / readiness window, plus each field's richer native concept) recurrence beyond — the profile *Structural Core vs. Domain Accent* makes precise.


Tobin's q

one_liner: The ratio of a firm's market value to the replacement cost of its physical assets, read against a threshold of one to signal whether capital should flow in (build) or out (divest) — because building beats buying only when the market prices assembled capital above the cost of reproducing it.

status: draft

core_idea: Tobin's q (James Tobin, 1969) is the ratio of a firm's market value to the replacement cost of its underlying physical assets — the price the market places on assembled capital divided by what it would cost to rebuild that capital from scratch. When q exceeds one, the market values the firm's capital stock above its reproduction cost, which creates a direct incentive to invest: building a new unit of capital costs less than the market will pay for it. When q falls below one, the reverse holds — the market values existing capital below replacement cost, so the firm has an incentive to disinvest or becomes an attractive acquisition target (it is cheaper to buy the assembled capital on the secondary market than to build new capacity). The mechanism is arbitrage across markets: the primary market for newly produced capital goods and the secondary market for ownership claims on existing capital cannot remain far apart without triggering capital flows to close the gap. Frank Hayashi (1982) established the conditions — constant returns to scale, perfect competition, convex adjustment costs — under which the observable average q (market value over book replacement cost) equals the theoretically load-bearing marginal q (the shadow price of an additional unit of investment), licensing the use of price-to-book ratios as the empirical investment trigger. The full q-theory of investment thus converts the diffuse question of whether a firm or sector should be expanding its capital stock into a testable numerical threshold, with the ratio's departure from unity both signalling the direction of the investment distortion and quantifying how large it is.

scope_of_application:
Because Tobin's q is a constructed ratio rather than a causal mechanism, it is not bounded by a single domain but applies wherever its one precondition holds: a market value placed on an assembled stock of capital *and* a physical replacement cost for reproducing that stock. The habitats below are genuine literal uses of the identical ratio, computed the same way and read against the same unity threshold; the loose "Tobin's q for brand/human capital/ecosystems" usages, where the reproduction-cost denominator loses its referent, are the borrowed-shape analogues carried by `marginal_cost_marginal_benefit`, not part of this map.

- **Corporate investment / capital budgeting** — the home turf; q is the firm-level investment trigger, q > 1 saying build and q < 1 saying divest, with Hayashi's average-equals-marginal conditions travelling as the licensing checklist.
- **Macroeconomic investment theory** — aggregate q is the microfounded account of investment that displaced accelerator and user-cost models, converting net capital flows into a reading off one economy-wide ratio.
- **Mergers and acquisitions** — the secondary-market-versus-reproduction-cost arbitrage *is* the M&A logic: low-q firms are buy-rather-than-build asset targets, high-q firms acquire by issuing richly valued equity.
- **Housing economics** — the analog ratio of house price to construction cost is the same construct on a different asset; a sustained housing q above one is read as the building-side primary market being blocked, and even localizes the obstruction (zoning, permits).
- **Asset-pricing / efficient-markets tests** — cross-sectional deviations of q from unity across firms or sectors serve as a mispricing diagnostic, testing whether markets price assembled capital at reproduction cost.

structural_signature:
**Sig role-phrases:**

- **the market-value numerator** — the price the market places on the firm's assembled stock of physical capital
- **the replacement-cost denominator** — what it would cost to reproduce that same capital stock from scratch in the primary capital-goods market
- **the unity threshold** — the value q = 1 at which assembled-capital valuation and reproduction cost coincide, partitioning into invest (q > 1) and divest-or-be-acquired (q < 1)
- **the cross-market arbitrage it encodes** — the flow between the primary market for newly produced capital and the secondary market for ownership claims that the ratio's departure from one is supposed to trigger and eventually close
- **the magnitude reading** — the distance of q from unity, taken to quantify how large the investment distortion is, not merely its sign
- **the average-vs-marginal coincidence conditions** — Hayashi's constant returns, perfect competition, and convex adjustment costs, the engineered guarantee licensing the observable average q to stand in for the decision-relevant marginal q
- **the reproduction-cost precondition (its limitation)** — q means what it should only where a genuine physical cost of rebuilding the asset exists; absent a primary production market it degrades to a market-value-over-baseline figure wearing q's name

what_it_is_not:
- **Not a causal mechanism.** q is a *ratio* — market value over replacement cost — not a force that drives investment. It does not *make* capital flow; it *reads off* whether the underlying arbitrage (build when reproduction is cheaper than purchase) favors expansion. The thing that moves capital is the cross-market price gap; q is the gauge that measures it.
- **Not the price-to-book ratio it is usually computed as.** The decision-relevant quantity is *marginal* q — the shadow price of one additional unit of investment — not the observable *average* q (market value over book replacement cost). They coincide only under Hayashi's conditions (constant returns, perfect competition, convex adjustment costs); treating an observed price-to-book number as the investment trigger outside those conditions is an unlicensed leap, not a measurement of what governs the decision.
- **Not a verdict that the firm is over- or under-valued in an absolute sense.** q above one does not say a stock is "expensive"; it says the market prices *assembled capital* above what it would cost to *reproduce* that capital, which is a statement about the gap between two markets, not about whether the equity is a good buy at today's price.
- **Not a law that q always returns to one.** Arbitrage closes the gap only when the primary production market can respond; a q held far from unity by something blocking that market — building-side restrictions in housing, for instance — is a standing wedge, not a temporary disequilibrium awaiting reversion. The convergence is conditional on the arbitrage being free to operate.
- **Not applicable wherever a market value can be written over some baseline.** q means what it should only where a genuine *physical reproduction cost* exists — a primary market in which the asset can be produced at the quoted cost. A "Tobin's q" for brand value, human capital, or a person's worth borrows the shape but loses the denominator's referent: there is no cost of rebuilding the thing from scratch, so the predictive arbitrage is absent and the number is q's name on a different quantity.

clarity:
Naming the ratio q makes the investment decision legible as a single, comparable number, dissolving a confusion that older accelerator and user-cost models left tangled: whether a firm "should expand" was a fuzzy verdict assembled from interest rates, expected demand, depreciation schedules, and tax treatment, with no principled way to say how far from optimal current capital was. q collapses that bundle into one observable threshold and gives the question a sign and a magnitude — above unity, build; below, divest or be acquired — so a corporate-finance analyst can ask the sharper question directly: is the market pricing this firm's assembled capital above or below what it would cost to reproduce, and by how much?

The construct's enduring force is that it sharpens a distinction practitioners routinely blur — *average* q (market value over book replacement cost, which anyone can compute) versus *marginal* q (the shadow price of one additional unit of investment, which is what the theory says actually governs the decision). Before Hayashi, treating an observed price-to-book ratio as an investment trigger was an unlicensed leap; naming the two q's and the conditions (constant returns, perfect competition, convex adjustment costs) under which they coincide tells the analyst exactly when the observable proxy is load-bearing and when it is not. It also separates two readings of a q far from one that survey practice conflates: a genuine investment signal (capital genuinely mispriced relative to reproduction cost, inviting flows to close the gap) versus a standing wedge held open by something outside the arbitrage — in housing, a sustained q above one localizes the problem not to "high prices" but specifically to building-side restrictions blocking the primary market from responding.

manages_complexity:
The investment determinants a corporate-finance analyst would otherwise have to assemble separately are many and heterogeneous: the level and term structure of interest rates, expected demand growth, depreciation schedules, the corporate tax code's treatment of capital and its allowances, the cost of capital goods, and the firm's idiosyncratic productivity and growth prospects. Each enters the expand-or-contract decision through a different channel, and the older accelerator and user-cost models required modeling each channel explicitly and then somehow netting them against one another to reach a verdict — with no principled summary of how far from optimal the current capital stock actually sat. Tobin's q collapses that sprawl into a single sufficient statistic. Because the market value in the numerator is itself the price at which all those determinants are already capitalized — every expectation about future demand, every tax consideration, every discount-rate movement is impounded into what investors will pay for the assembled capital — the analyst no longer tracks the determinants one by one. They track one ratio: market value over replacement cost. The qualitative outcome reads off a single threshold at unity. q above one says the market prices this capital above its reproduction cost, so capital should flow in (build, expand); q below one says it prices the capital below replacement cost, so capital should flow out (divest, or the firm becomes a buy-rather-than-build acquisition target); and the distance of q from one quantifies how large the distortion is, not merely its sign. What had been an open-ended diffuse judgment becomes a one-number reading with a sign and a magnitude.

The compression carries one explicit branch the analyst must hold, the one Hayashi's conditions govern. The observable quantity is *average* q — total market value over book replacement cost, computable from public data — while the quantity the theory says actually governs the decision is *marginal* q, the shadow price of one additional unit of investment. Under constant returns to scale, perfect competition, and convex adjustment costs the two coincide, and the observable proxy is load-bearing; outside those conditions they diverge, and reading an observed price-to-book ratio as the investment trigger is an unlicensed leap. So the analyst tracks not just the ratio but whether the firm's setting satisfies the coincidence conditions — a small, named checklist that tells them when the cheap observable number can be trusted to stand in for the expensive theoretical one. And a persistent q far from unity forks again: it is either a genuine mispricing inviting arbitrage flows that should close it, or a standing wedge held open by something outside the arbitrage that blocks those flows — in housing, a sustained q above one localizes the cause not to vague "high prices" but specifically to building-side restrictions choking off the primary market's response. The whole bundle of investment macroeconomics, M&A targeting, and construction analysis thus reduces to: compute one ratio, check whether its setting licenses the proxy, and read the direction, the magnitude, and (when q stays stuck) the location of the obstruction off its relation to one.

abstract_reasoning:
Tobin's q licenses a tight set of moves in corporate-finance and investment analysis, all flowing from reading one ratio — market value over replacement cost — against the threshold of unity, and from the cross-market arbitrage that threshold encodes.

*Diagnostic (read the direction and size of the investment distortion off q's distance from one).* The foundational move is to infer, from a single observable, whether a firm's or sector's capital is mispriced relative to what it would cost to rebuild — and in which direction. q above one is read as the market pricing assembled capital above its reproduction cost, so capital is *under-supplied* relative to its valuation; q below one is read as capital priced below replacement cost, so it is *over-supplied*. The reasoning runs from the ratio to a signed verdict with a magnitude: the distance of q from unity quantifies how large the distortion is, not merely its sign, so the analyst reads both *whether* and *how much* capital is out of line. The diagnostic also localizes a *persistent* wedge: a q stuck far from one is read not as vague "high (or low) prices" but as either a genuine mispricing inviting flows to close it or a standing obstruction blocking those flows — in housing, a sustained q above one points specifically at building-side restrictions choking the primary market, not at prices in general.

*Interventionist (predict capital flows and corporate actions from the threshold crossing).* Because q encodes an arbitrage between the primary market for new capital goods and the secondary market for claims on existing capital, it yields coupled predictions about what agents will do. q above one predicts investment inflow — building a new unit costs less than the market will pay for assembled capital, so firms expand and entrants rush in; q below one predicts disinvestment, or that the firm becomes a *buy-rather-than-build* acquisition target, since assembled capital can be bought on the secondary market more cheaply than new capacity can be constructed. The move is "observe q's position relative to one, predict the direction capital flows to close the gap," and it extends to M&A targeting (low-q firms as asset-arbitrage targets, high-q firms acquiring by issuing richly valued equity) and to construction (new building responds to housing q above one unless something blocks it). The same logic supports comparative statics: a tax change or cost-of-capital shock is traced through its effect on q, and the predicted investment response read off the resulting shift relative to unity.

*Boundary-drawing (when the observable average q may stand in for the decision-relevant marginal q).* The sharpest discipline the construct imposes is the distinction between *average* q (total market value over book replacement cost, computable from public data) and *marginal* q (the shadow price of one additional unit of investment, which the theory says actually governs the decision). Treating an observed price-to-book ratio as the investment trigger is licensed only under specific conditions — constant returns to scale, perfect competition, convex adjustment costs — under which the two coincide; outside them the proxy diverges from the load-bearing quantity and the inference is an unlicensed leap. The analyst must therefore check whether the firm's setting satisfies the coincidence conditions before trusting the cheap observable to stand for the expensive theoretical one. This boundary tells the practitioner exactly when q is decision-relevant and when it is merely suggestive, and it is what separates a rigorous q-theoretic investment call from a naive price-to-book heuristic.

*Sufficient-statistic reasoning (let the market price aggregate the determinants).* The construct licenses a characteristic compression move: rather than modeling interest rates, expected demand, depreciation, and tax treatment separately and netting them, the analyst reasons that the market value in the numerator has *already* capitalized all of them, so q serves as a sufficient statistic for the whole bundle. The inference is that whatever moves the optimal investment decision must show up in q, so tracking the single ratio captures the net effect of the heterogeneous determinants — provided the average-equals-marginal conditions hold. This is the reasoning that let q-theory displace accelerator and user-cost models: it replaces an explicit multi-channel calculation with a reading off one price ratio that the market has done the aggregation for.

knowledge_transfer:
Tobin's q is a *constructed ratio* — a measure, not a causal mechanism — so the "mechanism within, metaphor beyond" frame does not quite fit it. What governs its travel is a precondition: the construct is computable, and means what it is supposed to mean, exactly where its two ingredients both exist and are commensurable — a *market value* placed on some assembled stock of capital, and a *replacement cost* for reproducing that same stock from scratch. Wherever both are well-defined, q transfers *literally*: the ratio is built the same way and the unity threshold reads the same way, because the underlying arbitrage (you build when reproduction is cheaper than purchase, you buy or divest when it is dearer) is a real cross-market flow, not an analogy. The boundary to police is therefore not mechanism-versus-metaphor but *instrument-reach versus over-reading* — whether the two ingredients are genuinely present and genuinely comparable, or whether the number is being computed past the point where its inputs mean what they should.

Within economics and finance the construct travels broadly and as itself, because the precondition recurs across subfields with the same capital-arbitrage content intact. In **corporate investment and macroeconomic investment theory** — the home turf — q is the firm-level and aggregate investment trigger, and the average-versus-marginal distinction and Hayashi's coincidence conditions travel with it as part of the apparatus. In **mergers and acquisitions** the same ratio identifies low-q firms as buy-rather-than-build asset-arbitrage targets and high-q firms as acquirers paying in richly valued equity — the secondary-market-versus-reproduction-cost arbitrage is literally the M&A logic. In **housing economics** the analog ratio of house price to construction cost is *the* same construct on a different asset: a sustained housing q above one is read, with no loss of mechanism, as the primary (building) market being blocked from responding — and the construct even localizes the obstruction (building-side restrictions: zoning, permits) rather than vaguely flagging "high prices." In **asset-pricing tests** cross-sectional deviations of q from one serve as a mispricing diagnostic. Across all of these the inputs remain a true market valuation and a true reproduction cost, so the same arbitrage interpretation, the same direction-and-magnitude reading, and the same proxy-licensing checklist carry without translation. This is instrument transfer in the strict sense: the same statistic, computed the same way, meaning the same thing, wherever capital is priced in two markets at once.

Beyond the substrate where a *physical reproduction cost* exists, the transfer changes character, and honesty requires marking the shift. Whenever someone speaks of a "Tobin's q" for human capital, brand value, a labor market, an ecosystem, or a person's worth, the denominator quietly loses its referent: there is no well-defined cost of *rebuilding from scratch* the thing being valued, so the ratio is no longer the same construct but a *borrowed shape* — a market-value-over-some-baseline figure wearing q's name. That is the over-reading boundary: the number can still be written down, but the arbitrage that gave q its predictive force (capital flowing to close a gap between a primary production market and a secondary ownership market) is absent, because there is no primary market in which the asset can be *produced* at the quoted cost. At that point what remains and genuinely recurs across domains is not Tobin's q but the more general pattern it instantiates — *compare the marginal value of a thing to the marginal cost of producing one more of it, and let flows close the gap*. That comparison really does travel as mechanism: in evolutionary biology the fitness gradient (marginal fitness value of a trait against its marginal cost) is a clean co-instance, and in any allocation problem a price-signal-driven flow toward higher value-to-cost activities recurs. But that traveling content belongs to the parent patterns — a marginal-value-to-cost comparison, an arbitrage-driven flow, a price signal guiding allocation — and the cross-domain lesson should be carried under those, not under "Tobin's q," whose finance-specific cargo (equity-market valuation, physical-capital replacement cost, the average-versus-marginal coincidence conditions) does not and should not travel. The general comparison is the prime; q is its corporate-finance instrument, literal wherever a reproduction cost exists and metaphor the moment it does not — a split traced in full in *Structural Core vs. Domain Accent*.


Tonality

slug: tonality

one_liner: Organize a musical system around one referential pitch — the tonic — so every note is heard not absolutely but as a position in a hierarchy of stability, with a codified grammar of directed pulls that encodes tension as distance from the center and resolution as return to it.

origin_domain: music

core_idea: Tonality is the organization of a musical system around a single referential pitch class — the *tonic* — such that every other pitch and chord is heard relative to it, positioned within a hierarchy of stability that radiates outward from the tonic center and systematically encodes tension as distance from that center and resolution as return to it. No pitch in a tonal piece is heard absolutely: each is heard as a *position within this hierarchy*, carrying a functional role (tonic, dominant, subdominant, leading-tone, secondary dominant) that predicts how it will behave — whether it will sound like rest or motion, whether it will urge resolution and in which direction, and how chromatic alteration will sharpen or weaken its pull. The structural commitment is a *codified grammar of stability and directed motion*, not merely the presence of a center: the dominant (fifth scale degree) creates strong tension that resolves to the tonic; the leading tone (seventh scale degree) creates a particularly intense upward pull one semitone to the tonic; the subdominant creates a softer pre-dominant tension resolved most characteristically via the dominant; and the cadential progressions (V→I, ii→V→I, IV→I) are the syntactic punctuation by which tonal closure is achieved and confirmed. Modulation — the orderly relocation of the tonic to a new pitch class, typically achieved through pivot chords that are functional in both the old and new key — allows large-scale dramatic structure: a tonal piece's large-scale formal organization is a tonal narrative, moving away from and returning to the home key. Empirical work in music cognition — Krumhansl's probe-tone experiments, EEG studies measuring mismatch responses to unexpected tonal events — confirms that listeners internalize the tonal hierarchy and respond measurably to its violations, even without theoretical training. Common-practice Western art music from roughly 1650 to 1900 operates almost exclusively within tonal syntax; the late nineteenth century's increasing chromaticism (Wagner, Liszt, Reger) strains but does not break it; the twentieth century's experiments with atonality and post-tonality (Schoenberg, Webern, Bartók) are defined partly by their departure from, or selective engagement with, the tonal grammar that preceded them.

scope_of_application:
Tonality lives across the tonal-harmony subfields of music and musicology; its reach is within that domain, since the load-bearing tension grammar (directed functional pulls, cadential syntax, modulation-by-pivot) does not cross — a brand's "tonal center" or a taxonomy's "root" is metaphor carried by anchoring, hierarchy, and attractor primes (see *Knowledge Transfer*), not the system itself.

- **Common-practice harmony (c. 1650–1900)** — the home: the entire architecture of sonatas, fugues, symphonies, and operas, whose large-scale structure is tonal before it is anything else.
- **Functional and Schenkerian analysis** — Roman-numeral analysis, voice-leading reduction, and harmonic-rhythm analysis, all presupposing and operating on the tonal hierarchy.
- **Composition pedagogy** — counterpoint, figured-bass realisation, and progression-writing taught as moves within the tonal grammar.
- **Popular and jazz music** — tonal centers, key changes, and functional progressions, even under extended harmony and modal mixture.
- **Music cognition and perception** — Krumhansl's probe-tone profiles and EEG mismatch responses showing untrained listeners internalise the tonal hierarchy and react to its violations.

structural_signature:
**Sig role-phrases:**

- **the tonic** — the single privileged referential pitch class to which the system refers and tends to return
- **the stability hierarchy** — the ranking that positions every other pitch and chord by distance from the tonic, encoding tension as distance and resolution as return
- **the functional roles** — the closed vocabulary (tonic, dominant, subdominant, leading-tone, secondary dominant) prescribing how chords are heard to act on each other
- **the directed pulls** — the codified resolution-tendencies that make tonality more than mere centrality: the dominant's pull to tonic, the leading-tone's intense upward semitone urge, the subdominant's softer pre-dominant tension
- **the cadential syntax** — the progressions (V→I, ii→V→I, IV→I) that punctuate, confirm closure, and discharge tension
- **the internalised expectation** — the hierarchy listeners demonstrably internalise (probe-tone profiles, EEG mismatch), making confirmation and breach analysable material
- **the modulation mechanism** — the orderly relocation of the tonic through pivot chords functional in both keys, rendering large-scale form as a tonal narrative of departure and return
- **the centrality-versus-grammar boundary** — the load-bearing distinction that a bare tonic is not tonality; only the tension grammar makes a leading tone *sound* as though it must resolve

what_it_is_not:
- **Not merely "having a center."** A bare tonic is not tonality. The load-bearing content is the *codified grammar of directed motion* — the dominant's pull to tonic, the leading-tone's intense semitone urge, the subdominant's pre-dominant tension, the cadential syntax (V→I, ii→V→I) — and it is precisely that tension grammar, not the presence of a privileged pitch, that makes a leading tone *sound* as though it must resolve.
- **Not absolute pitch-hearing.** In a tonal piece no pitch is heard in isolation; each is heard as a *position within a hierarchy of stability* radiating from the tonic, carrying a functional role that predicts whether it rests or moves and which way it pulls. Tonality is the relational re-coordination of pitch, not a fact about individual notes.
- **Not broken by chromaticism.** Late-nineteenth-century chromaticism (Wagner, Liszt, Reger) *strains* the grammar — weakening the pulls, obscuring the center — but does not break it; the functional tendencies remain operative. Heavy chromatic alteration is reasoned about as tension within tonality, not as its abandonment, which is the distinct condition of atonal and post-tonal practice.
- **Not a substrate-neutral "organised around a center."** When a brand strategist invokes a "tonal center" or a UX designer a "tonic emphasis," these are *metaphors borrowed from music*: the part that makes tonality *tonality* — the directed-pull grammar, the cadential punctuation, the circle-of-fifths key relations, modulation-by-pivot — does not cross. What survives the strip is *centrality*, already carried more accurately by `anchoring`, `frame_of_reference`, `hierarchy`, and `attractor_selection_and_basin_control` (with the directed-tension dynamic by an emergent `tension_and_release`).

clarity:
Naming a passage as "in a key" discharges an enormous amount of structure at once: it predicts which pitches will sound consonant and which dissonant, which chords will read as rest and which as motion, where the music is likely to cadence, and how a given chromatic alteration will function — as a borrowed chord, a secondary dominant, a modulation, or a mere non-chord tone. Its core clarifying move is to separate the *referential pitch* from the moment-to-moment pitches, so that no note is heard absolutely; each is heard as a *position within a hierarchy of stability*. That conversion turns the bare question "what is the next chord?" into the sharper one a tonal analyst actually asks: "how is the next chord *positioned* — what is its function, and which way does it pull?"

The concept's decisive distinction is between mere centrality and a *codified grammar of directed motion* — and getting this right is what keeps tonality from collapsing into "having a tonic." A center alone does not yield the leading-tone's intense semitone urge upward, the dominant's strong pull to tonic, the subdominant's softer pre-dominant tension, or the cadential syntax (V→I, ii→V→I) by which closure is achieved and confirmed; it is precisely this tension grammar that makes a leading tone *sound* like it must resolve. By the same grammar the concept makes large-scale form legible as a tonal narrative: modulation, the orderly relocation of the tonic through pivot chords functional in both keys, lets a movement depart from and return to a home key, so that a piece's architecture can be read as motion through tonal space. And because the hierarchy is something listeners demonstrably internalize — registering its violations even without theoretical training — the practitioner can treat expectation and its breach as analyzable material, asking not just whether a progression is "correct" but how strongly it confirms or thwarts the pull the key sets up.

manages_complexity:
A common-practice movement presents the analyst with hundreds of distinct pitches and dozens of chords unfolding in time, and without an organizing principle each is a separate object to be evaluated on its own — whether it is consonant or dissonant, whether it rests or moves, where it is headed — a combinatorial sprawl that would have to be re-derived chord by chord across the whole piece. Naming the passage as *in a key* discharges that sprawl in one stroke by re-coordinating every pitch to a single referential center: no note is heard absolutely, each is heard as a *position within a hierarchy of stability* radiating from the tonic. That single re-coordination does an enormous amount of compression at once — fixing the key predicts which pitches will sound consonant and which dissonant, which chords read as rest and which as motion, where the music is likely to cadence, and how a chromatic alteration will function (borrowed chord, secondary dominant, modulation, or mere non-chord tone) — so the open question "what is this chord" collapses to the bounded one "what is this chord's *function*, and which way does it pull." The analyst stops tracking absolute pitch content and tracks instead each event's position in the stability hierarchy, reading its behavior off that position.

The deeper compression is that tonality supplies not just a center but a *codified grammar* of directed motion, and that grammar reduces the qualitative behavior of any pitch or chord to its functional role — a small, closed vocabulary the analyst can read off. The dominant carries strong tension resolving to the tonic; the leading tone carries a particularly intense upward semitone pull; the subdominant a softer pre-dominant tension discharged characteristically through the dominant; the cadential progressions (V→I, ii→V→I, IV→I) are the punctuation that confirms closure. Knowing a chord's function fixes how it will sound and where it must go without separate analysis of its constituent pitches, so the role is the parameter and the resolution-tendency is read off it. The same grammar compresses the piece's *large-scale* structure, where the dimensionality would otherwise be greatest: rather than tracking a long succession of local events, the analyst tracks the location of the tonic over time, and modulation — the orderly relocation of the tonic through pivot chords functional in both keys — renders the whole architecture as a tonal narrative of departure from and return to a home key. A movement's form collapses to motion through tonal space. And because the hierarchy is one listeners demonstrably internalize, registering its violations even untrained, the analyst gains a further trackable quantity: not merely whether a progression is correct but how strongly it confirms or thwarts the pull the key has set up, so expectation and its breach become analyzable material read off the same grammar. Hundreds of pitches and chords, and an entire multi-section form, thus reduce to a single referential center, a closed inventory of functional roles, and the location of the tonic over time — from which consonance, motion, closure, and large-scale shape can be read off rather than re-derived event by event.

abstract_reasoning:
Tonality's foundational move is to hear every pitch *relationally* and to reason from position rather than from absolute identity. Once a key is fixed, the analyst does not ask what a chord is in isolation but how it is positioned within the hierarchy of stability radiating from the tonic, and from that position predicts its behavior: whether it will sound like rest or motion, whether it will urge resolution and in which direction. The inference runs from functional role to resolution-tendency — a dominant is read as strong tension that will discharge to the tonic, a leading tone as a particularly intense pull one semitone upward to the tonic, a subdominant as a softer pre-dominant tension most characteristically released through the dominant. The reasoning is predictive in the strong sense that knowing a chord's function fixes where it must go *without* separately analyzing its constituent pitches, so "what is the next chord?" becomes "what is its function, and which way does it pull?"

A second diagnostic move reads ambiguous or chromatic material by *how it functions* rather than by what notes it contains. Faced with a chromatic alteration, the analyst reasons among a closed set of functional possibilities — is this a borrowed chord, a secondary dominant, the pivot of a modulation, or a mere non-chord tone? — and the choice is settled by which reading coheres with the surrounding tonal syntax and where the alteration pulls. The same logic scales up to large-scale form: rather than tracking a long succession of local events, the analyst tracks the location of the tonic over time, reasoning that an orderly relocation of the center through a pivot chord functional in both keys is a modulation, so that a movement's architecture can be inferred as a tonal narrative of departure from and return to a home key. Form is read as motion through tonal space, an inference from the trajectory of one tracked quantity.

The interventionist and predictive reasoning exploits the fact that the hierarchy is *internalized by listeners*, which converts expectation into analyzable material. Because untrained listeners demonstrably register tonal events and their violations — the probe-tone profiles and the measured mismatch responses to unexpected cadences are the evidence — the composer can reason forward from the pull the key sets up to a predicted listener response, and the analyst can ask not merely whether a progression is "correct" but how strongly it *confirms* or *thwarts* the expectation the key has established. A deceptive resolution, a withheld cadence, an arrival in an unexpected key are reasoned about as calculated breaches of a prediction the tonal grammar made on the listener's behalf, each with a foreseeable effect. The reasoning treats the listener's anticipation as a quantity the music acts upon, not an incidental side effect.

The decisive boundary the concept draws — and the discrimination its reasoning most depends on — is between *mere centrality* and a *codified grammar of directed motion*. The analyst must not infer tonality from the bare presence of a tonic, because a center alone yields none of the leading-tone's semitone urge, the dominant's pull, the subdominant's pre-dominant tension, or the cadential syntax (V→I, ii→V→I, IV→I) that confirms closure; it is precisely the tension grammar that makes a leading tone *sound* as though it must resolve. So the moves — relational hearing, function-to-behavior prediction, the reading of expectation and its breach — have force only inside that grammar, where functional roles and directed resolutions are defined. This also fixes the regime: common-practice Western art music operates almost entirely within tonal syntax, late-nineteenth-century chromaticism is reasoned about as *straining but not breaking* the grammar (the pulls weakened, the center obscured, yet still operative), and twentieth-century atonal and post-tonal practice is understood by its *departure from or selective engagement with* that grammar — so the analyst applies tonal reasoning where the functional pulls are in play and recognizes its limits exactly where the grammar is abandoned and there is no hierarchy of stability for a pitch to be heard against.

knowledge_transfer:
*Within the home domain — tonal harmony — tonality transfers as mechanism, the relational-hearing move and the function-to-resolution grammar carrying across the repertoire and its analytic and pedagogical disciplines.* The tension grammar (a referential tonic, a hierarchy of stability radiating from it, functional roles whose pulls predict resolution, cadential syntax confirming closure) and its full apparatus apply intact across **common-practice harmony** (the entire architecture of sonatas, fugues, symphonies, and operas, whose large-scale structure is tonal before it is anything else), **functional and Schenkerian analysis** (Roman-numeral, voice-leading reduction, harmonic-rhythm analysis all presupposing the hierarchy), **composition pedagogy** (counterpoint, figured-bass realisation, progression-writing taught as moves within the grammar), **popular and jazz music** (tonal centers, key changes, and functional progressions even under extended harmony and modal mixture), and **music cognition** (Krumhansl's probe-tone profiles and EEG mismatch responses showing untrained listeners internalise the hierarchy). Across all of these the same relational hearing reasons from a chord's *function* to where it must go, the same closed-vocabulary diagnostic reads chromatic material (borrowed chord, secondary dominant, modulation pivot, non-chord tone), the same tonic-over-time tracking renders form as a tonal narrative, and the same internalised-expectation fact makes deceptive resolutions and withheld cadences analysable as calculated breaches. Within tonal music this is mechanism, not analogy — the functional pulls are literally in play across the whole common-practice and tonal-popular substrate.

*Beyond the home domain the honest verdict is (A) metaphor: the shallow "organised around a center" reading drops the entire load-bearing grammar, and what genuinely recurs elsewhere is a more general centrality pattern already named in the catalogue.* When a brand strategist speaks of a "tonal center," a taxonomy of a "root concept," or a UX designer of a "tonic emphasis," these are *metaphors borrowed from music* — domain-borrowings, not independent occurrences of the structural pattern — because the part that makes tonality *tonality* does not cross. Strip the music vocabulary and what survives is "a system with a privileged center plus distance-graded tension toward it plus a return tendency"; but it is precisely the *tension grammar* — the dominant's pull to tonic, the leading-tone's intense semitone urge, the subdominant's pre-dominant tension, the cadential syntax (V→I, ii→V→I), the circle-of-fifths distance metric — that distinguishes tonality from mere centrality, and none of that survives the strip. A brand "centered on its pillar" or a tree "with a root" has the privileged node but none of the directed-pull grammar, so what remains is *centrality*, not tonality. That residual is already carried, more accurately, by the catalogue's own primes: `frame_of_reference` (which coordinate system is privileged), `anchoring` (which reference point judgments gravitate toward), `hierarchy` (which node sits at the apex), and `attractor_selection_and_basin_control` (the tonic as an attractor with a surrounding basin) — with the tension-and-release dynamic itself flagged as an emergent cross-domain pattern (`tension_and_release`) that tonality *realises* in music, and which should fill that slot rather than tonality being promoted to it. The home-bound cargo that cannot peel away is the entire functional grammar: the codified stability gradations, the directed resolutions, the cadential punctuation, the circle-of-fifths key relations, the modulation-by-pivot mechanism. So the right statement of reach is: the privileged-center pattern recurs widely but is carried by `anchoring` / `frame_of_reference` / `hierarchy` / `attractor_selection` (and the directed-tension dynamic by an emergent `tension_and_release`); "tonality," as named, is the music-domain instantiation whose load-bearing tension grammar does not transfer, so its use outside music is metaphor for the broader centrality pattern (see *Structural Core vs. Domain Accent*).


Topic Facet

one_liner: Isolate what a resource is about as a single independently selectable axis in a faceted classification, so topical queries combine with place, time, and form filters at query time instead of being fused in advance into precoordinated compound headings.

core_idea: A topic facet is the design decision to isolate *what* a resource is about — its subject matter — as a single independently selectable axis within a faceted classification system, so that topical queries can be combined with place, time, form, or audience filters without those dimensions being fused in advance into compound headings. The mechanism is axis decomposition: instead of precoordinating "Cooking — Italy — 19th century" into one indivisible string, the system assigns each resource a topical value from a controlled vocabulary (Cooking), a geographic value (Italy), and a chronological value (19th century) as three separate facets. A user can then query any combination — "this topic, any place" or "any topic, this period" — by selecting values on independent axes, and the catalog constructs the conjunction at query time rather than at indexing time. OCLC FAST operationalizes this by decomposing Library of Congress Subject Headings into five facets, of which topic is one; e-commerce filter panels and digital library interfaces follow the same structural pattern. The design criterion is genuine orthogonality: the topic axis must vary independently of the other axes so that no topical value presupposes a particular place, form, or period, and no cross-axis pairing is foreclosed by the vocabulary structure.

scope_of_application:
The topic facet lives across the classification-and-retrieval family — one substrate, retrieval-oriented descriptive systems; the substrate-spanning orthogonal-decomposition lesson (separation of variables, basis selection, parametric design) belongs to the `paradigmatic_vs_syntagmatic_relations` parent, not to the subject axis itself.

- **Library cataloging** — OCLC FAST and faceted-LCSH split traditional precoordinated headings into topic, place, time, and form facets, each with its own controlled value list.
- **Faceted search interfaces** — e-commerce filter panels and digital-library catalogs separate category/topic from brand, price, format, and the rest, forming the conjunction at query time.
- **Web content taxonomies** — news sites and Wikipedia categories separate subject topic from format (image, list, biography) and from geography.

structural_signature:
**Sig role-phrases:**

- **the designated topic axis** — *what a resource is about* isolated as one description dimension, separated from place, time, form, and audience
- **the controlled topical vocabulary** — the (often hierarchical) value list from which a resource's subject value is drawn
- **the per-resource subject selection** — each resource assigned one (sometimes several) topical values rather than fused into a precoordinated compound heading
- **the designed orthogonality** — the load-bearing precondition: the topic axis must vary independently, no topical value presupposing a place, period, or form
- **the independent retrievability** — queries constrain topic without constraining the other axes and vice versa, the conjunction formed at query time
- **the sum-not-product economy** — separating the axis keeps the enumerated vocabulary additive in the axes rather than multiplicative across the cross-product
- **the cross-facet leak** — the characteristic failure: a topic term that smuggles in a region or era, making its axis non-orthogonal and its pairings unreachable or doubly-counted

what_it_is_not:
- **Not "the subject" as a whole.** The topic facet is *one axis among several* — pure aboutness — not the indexing system's organizing trunk. A precoordinated string like "Cooking — Italy — 19th century" reads as "the subject," but most of it is place and period riding along; the facet isolates the topical value (Cooking) from the descriptive machinery that merely co-occurs with it.
- **Not any subject term whatever.** A topical value that quietly presupposes a region or an era is a *cross-facet leak*, not a legitimate facet value — its axis is no longer orthogonal, and its pairings become unreachable or doubly-counted. Genuine orthogonality (no topical value presupposing a place, period, or form) is the load-bearing precondition, so a leaking term is a defect, not an accepted feature of the heading.
- **Not the general form/content distinction.** `form_and_content` is the broad expression-versus-aboutness relation; the topic facet is the narrow operationalization of the *content* half as one retrievable axis inside a controlled-vocabulary system. The facet presupposes a controlled topical vocabulary, per-resource subject selection, and a faceted interface — apparatus the general distinction does not carry.
- **Not the whole faceted vocabulary.** It is a *single* designated axis (subject/aboutness) within a faceted system, not the faceting design itself; its only distinctive content beyond the parent is the choice of *which* axis. Treating "topic facet" as the entire orthogonal-decomposition apparatus overstates it — the structure that gives it force is `paradigmatic_vs_syntagmatic_relations`, the parent.
- **Not a catalog that pre-mints every topic-place-period combination.** Giving topic its own axis collapses the cross-product into a sum: the catalog forms the conjunction *at query time*, so "this topic, any place" is a single selection with the other axes left free, and combinations need never have been anticipated at indexing time. Expecting a stored compound heading for each pairing mistakes the design for the precoordinated explosion it replaces.

clarity:
Naming the topic facet makes one design choice in subject access stand out as a choice rather than a given: subject matter is *one axis among several*, not the indexing system's organizing trunk. Without the label, a cataloger working in a precoordinated tradition treats "Cooking — Italy — 19th century" as a single subject heading and reads the whole string as "the subject," so the question of whether topical access could be separated from place or period never surfaces — the dimensions are fused before anyone asks whether they should be. Isolating *topic* as a designated facet dissolves that fusion and lets a designer ask the sharper question: which of the dimensions a precoordinated heading welds together are genuinely about *aboutness*, and which are place, time, form, or audience riding along? It separates the topical value (Cooking) from the descriptive machinery that merely co-occurs with it.

It also sharpens the distinction between *precoordination* and *postcoordination* at exactly the point where it bites. Once topic is its own axis with its own controlled value list, the system can construct "this topic, any place" or "any topic, this period" as a conjunction at query time, and the combinatorial cost of enumerating compound headings in advance disappears as a cataloging burden. The crisp design test the facet supplies is orthogonality: does the topical vocabulary vary independently of the other axes, so that no topical value presupposes a particular place, form, or period and no cross-axis pairing is foreclosed? A topic term that quietly implies a region or an era is a leak across facets, and naming the topic facet is what makes that leak visible as a defect rather than an accepted feature of the heading.

manages_complexity: A precoordinated subject vocabulary faces a combinatorial sprawl: every topic that could co-occur with every place, every period, and every form has to be anticipated and minted as its own compound heading, so the heading list grows as the product of the dimensions and a cataloger must either pre-enumerate "Cooking — Italy — 19th century," "Cooking — France — 18th century," "Architecture — Italy — 19th century," and so on across the whole cross-product, or leave the un-minted combinations unreachable. Recognizing topic as one independently selectable facet collapses that product into a sum. Instead of tracking a heading space whose size is the multiplied cardinality of all the axes, the designer tracks each axis separately — a topical value list, a geographic value list, a chronological value list — and lets the catalog form the conjunction at query time. The quantities that determine the system's behavior shrink to a handful the designer can hold at once: how many axes there are, the size of each axis's controlled vocabulary, and one structural property per axis — does it vary independently of the others, or does some topical value smuggle in a place or a period? From those, the qualitative outcomes read straight off. If the axes are genuinely orthogonal, every cross-axis pairing is automatically reachable without being pre-minted, the catalog's enumerated vocabulary stays linear in the axes rather than multiplicative, and a query like "this topic, any place" is a single selection on one axis with the rest left free. If a facet leaks — a topic term that presupposes a region or an era — that one parameter flips and predicts the failure: the affected pairings become unreachable or doubly-counted, and the conjunction the user wanted cannot be constructed cleanly. The analyst no longer reasons case by case about which compound headings exist; they reason about a few axis-level properties and derive the retrieval behavior of the entire combination space.

abstract_reasoning:
Designating topic as a facet licenses a tight set of reasoning moves about a classification system's behavior, all turning on the orthogonality of the topic axis against the others.

*Diagnostic — infer a cross-facet leak from a retrieval failure.* When a user query like "this topic, any place" comes back with too few hits, or when certain topic-place pairings are systematically empty while the resources demonstrably exist, the cataloger reasons backward to a contaminated vocabulary: a topical value that silently presupposes a region or an era. The surface signature is an unreachable or doubly-counted pairing; the hidden cause inferred from it is that the topic term is not pure aboutness but carries place, period, or form riding along, so the axis it lives on is not actually independent. The classic instance is the precoordinated heading read as "the subject": from the observation that "Cooking — Italy — 19th century" cannot be queried for "Cooking, any place" without enumerating every minted variant, one infers the dimensions were fused before indexing, not separable at query time. A topic value that never co-occurs with more than one value of another facet is the fingerprint of a leak.

*Interventionist — predict the retrieval consequence of an axis edit.* The facet design supplies a small repertoire of moves with forecastable effects. Splitting a fused heading into a topical value plus a geographic plus a chronological value predicts that every cross-axis pairing becomes reachable by conjunction at query time without being pre-minted, so previously unreachable combinations light up. Tightening a topic value that leaked place back into a pure-aboutness term predicts that the affected pairings stop collapsing and the "any place" query recovers its full result set. Coarsening or refining the granularity of the topical value list predicts a shift in recall versus precision on topical queries while leaving the other axes' behavior untouched — the orthogonality is precisely what guarantees the edit stays local to the one axis. Each move is a claim about the combination space that can be checked by re-running the conjunction.

*Boundary-drawing — decide when the facet decomposition is the right design.* The topic facet earns its keep only where the topical vocabulary genuinely varies independently of place, time, and form and where the cross-product of dimensions is large enough that precoordinating compound headings is infeasible. Where a topical value is inherently bound to one region or era — where the "aboutness" cannot be cleanly separated from where or when — the axis is not orthogonal and faceting it buys nothing the fused heading did not already provide. So the move is to test, before committing: does any topical value presuppose a value on another axis? If yes, the dimension is not a clean facet and the decomposition will leak; if no, postcoordination dominates precoordination and the facet should be split off.

*Predictive — read the whole combination space off the axis properties.* Given orthogonal axes, the system's retrieval behavior follows without case-by-case enumeration: every pairing of a topical value with any value on another axis is automatically constructable, the enumerated vocabulary stays additive in the axes rather than multiplicative, and any "this topic, free on the rest" query resolves to a single selection. Flip the independence property on one axis and the prediction inverts for exactly the pairings that axis touches. The order of operations the facet asserts is the load-bearing claim: the catalog forms the conjunction *at query time*, so combinations need never have been anticipated at indexing time — a topic value plus the freedom to leave the other axes unconstrained is sufficient to reach anything the orthogonal structure permits.

knowledge_transfer:
Within the classification-and-retrieval family the topic facet transfers *as mechanism*. The orthogonality test (does any topical value presuppose a place, period, or form?), the cross-facet-leak diagnostic, and the precoordination-versus-postcoordination reasoning carry intact across every subfield that gives subject matter its own axis. In **library cataloging**, OCLC FAST and faceted-LCSH split traditional precoordinated headings into topic, place, time, and form facets, each with its own value list. In **faceted search interfaces**, e-commerce filter panels and digital-library catalogs separate category/topic from brand, price, format, and the rest. In **web content taxonomies**, news sites and Wikipedia categories separate subject topic from format and geography. A designer who learns to read "this topic, any place" as a single selection on one orthogonal axis — and to diagnose a systematically empty topic-place pairing as a leaked topic term carrying place along — carries that reasoning without translation across all of these, because they are one substrate: retrieval-oriented descriptive systems.

Beyond that substrate the case is **(B): the topic facet contributes no portable mechanism of its own — it is wholly a specialization, and the parent is what travels.** The structure that gives the topic facet its force, *decompose a description into orthogonal independently combinable axes so a description is a per-axis selection rather than one fused label*, is exactly `paradigmatic_vs_syntagmatic_relations` (selection-axis versus combination-axis), the same parent that powers separation of variables in mathematics, basis selection in linear algebra, principal-component decomposition in statistics, and parametric design in engineering. The topic facet inherits everything from that parent and adds only the choice of *which* axis (subject/aboutness) and the catalog machinery around it: a controlled topical vocabulary, per-resource subject selection, and a faceted-retrieval interface. So what a reader could carry into physics or software architecture is the general orthogonality lesson, which belongs to the parent prime, not to "topic facet." Near-neighbor `form_and_content` is the broader expression-versus-aboutness distinction; the topic facet is the narrow operationalization of the *content* half as one retrievable axis inside a controlled-vocabulary system. Invoking "a topic facet" for any aboutness-versus-everything-else split outside cataloging renames the parts and borrows the parent's orthogonality while dropping the classification apparatus — the cross-domain lift is the parent's, and the named LIS axis should be reserved for the retrieval substrate where its vocabulary and interface do real work (see *Structural Core vs. Domain Accent*).


Topoi

slug: topoi

one_liner: The pre-formed argument templates of rhetorical invention — a finite catalogue of move-forms (definition, a fortiori, cause-and-effect, sign, precedent) whose form is fixed and content variable — so finding arguments becomes an auditable search through a known library rather than creation ex nihilo.

core_idea: Topoi (Greek "places"; Latin *loci communes*, "commonplaces") are the pre-formed argument templates that constitute the apparatus of rhetorical invention: a systematically organized catalogue of argument-generating moves — definition, division, similarity, contrast, comparison of degree (*a fortiori*), cause and effect, past-fact-predicts-future-fact, argument from sign, argument from precedent — each a structural slot whose content varies by subject matter but whose form is invariant across disputes. The defining structural commitment is that finding arguments is a *search* through a known library of templates, not creation ex nihilo: the rhetor applies each topos to the present case, asking whether it generates something defensible, and the catalogue both bounds the search (defining what counts as an argument-type) and guarantees coverage (a rhetor who has worked all applicable topoi has not missed a class of available moves). In Aristotle's *Rhetoric* and *Topics*, topoi are divided into *koinoi* (common topoi applicable across all subjects) and *idioi* (special topoi specific to a domain such as deliberative or forensic speech); Cicero in *Topica* and *De Inventione* adapted and extended the system into the Latin rhetorical tradition that shaped medieval and Renaissance pedagogy. The topos functions as a *generative template*: a slot with a recognizable inferential form — "if X holds in the harder case, it holds in the easier" — that the rhetor fills with the particular terms of the dispute at hand to produce a candidate argument that can then be evaluated, refined, or discarded before commitment to arrangement and style.

scope_of_application:
The topoi live across the argument-discovery subfields of rhetoric and its argument-theoretic descendants; the apparatus was built to be portable across *disputes*, but its reach stays within the single substrate of argument — beyond it the searchable-template move belongs to its parent primes (`design_patterns`, `system_archetypes`), not to "topoi" as named.

- **Classical rhetorical invention** — the home turf: Aristotle's *Rhetoric* and *Topics* catalogue of *koinoi* and *idioi*, Cicero's *loci* in *De Inventione* and *Topica*, Quintilian's *Institutio Oratoria*, and the whole ancient-through-Renaissance pedagogy of *inventio* as a taught search through stock argument-forms.
- **Modern argumentation theory** — the catalogue reappears as Perelman and Olbrechts-Tyteca's argumentation schemes in the *New Rhetoric*, and most explicitly as Walton's named schemes (argument from expert opinion, popular opinion, sign, analogy, cause) — a topos-library with the coverage check made explicit via attached critical questions.
- **Legal reasoning** — Viehweg's *topical jurisprudence* treats legal argument as a canvass of recognized *loci*, and the practical brief-builder works a checklist of admissible argument-types against the case at hand.
- **Composition and writing pedagogy** — textbook "ways of developing a topic" (compare/contrast, cause/effect, classification, definition) are the topoi rebranded as paragraph-generation moves for student writers.
- **Computational argumentation** — argument-mining and dialogue systems literally encode argumentation schemes as templates a program searches over, instantiates, and probes with the schemes' critical questions.

structural_signature:
**Sig role-phrases:**

- **the catalogue** — a known, finite, taught library of named argument-types that bounds and enumerates the space of available moves
- **the topos** — an individual generative template: a fixed inferential form (definition, *a fortiori*, sign, precedent, cause/effect) with variable content slots
- **the instantiation** — pouring the present dispute's particular terms into a topos's slots to yield a candidate argument
- **the search** — running the case against each admissible topos in turn as a checklist, tracking which are worked and which remain
- **the coverage guarantee** — because the library furnishes the denominator, canvassing every applicable topos certifies no whole *class* of move was overlooked
- **the genre gate** — the koinoi/idioi split that, before generation, fixes which topoi the deliberative/forensic/epideictic register even admits
- **the phase boundary** — invention marked off from arrangement (*dispositio*) and wording (*elocutio*), so a failed speech localizes to which topos went unworked
- **the catalogue's growth** — recognition and naming of new schemes (Walton, Perelman) that extend the library as new argument-types are identified

what_it_is_not:
- **Not a recipe that mechanically outputs finished arguments.** A topos yields a *candidate* — a claim that must still be tested, refined, or discarded — not a settled argument. Running the *a fortiori* slot tells the rhetor an argument of that form is available here; whether it is any good remains to be judged. The catalogue automates the *finding*, not the *vetting*.
- **Not a guarantee that what it generates is sound.** The coverage assurance is about *move-types*, not validity: canvassing every applicable topos certifies that no whole class of available argument was overlooked, not that any instantiated argument is true or persuasive. A complete search can still surface only weak arguments — completeness of the slot-list and quality of the fills are independent.
- **Not stylistic ornament or the "commonplace" as cliché.** Though *loci communes* gives English "commonplace," topoi are not hackneyed phrases, set-piece passages, or decorative figures. They belong to *inventio* — the discovery of what to argue — not to *elocutio*; their content is an inferential form, not a turn of wording.
- **Not a constraint that narrows what a rhetor may say.** The catalogue is generative, not restrictive: it expands the search by naming move-types the rhetor might not have thought to try, rather than fencing invention inside an approved list. A topos that yields nothing for the present case is simply set aside, costing nothing.
- **Not invention from nothing dressed up as method.** The whole commitment is the reverse — argument-discovery is *structured retrieval* from a known library, not creation ex nihilo. What looks like native inventive fluency is recast as recognizing the case as one where a stored template applies and instantiating it.

clarity:
Naming the topoi makes legible that *invention is a tractable, teachable discipline rather than an unanalyzable gift*. Before the catalogue, the question "how does one find what to say?" has no method behind it — argument-discovery looks like native fluency or inspiration, something a speaker either has or lacks. Reconceived as a search through a known library of argument-types, finding arguments becomes a procedure that can be taught, practiced, and audited: the rhetor runs the dispute against definition, division, comparison of degree, cause and effect, sign, precedent, and the rest, and what once read as creative facility is exposed as *structured retrieval* — recognizing the present case as one where a known template applies and instantiating it. The sharp question the catalogue licenses is no longer "am I clever enough to think of an argument?" but "which topoi have I not yet worked?" — and because the library bounds the space of move-types, a rhetor who has canvassed every applicable topos has positive assurance of not having overlooked a whole *class* of available arguments, an assurance no unsystematized ingenuity can give.

The catalogue also sharpens the division of labor within the rhetorical art itself. By locating argument-discovery in *inventio*, the topoi mark it off cleanly from *dispositio* (the arrangement of arguments once found) and *elocutio* (their wording) — so a speech that fails can be diagnosed: did invention miss an available line of argument, or was a sound argument merely misarranged or poorly phrased? The koinoi/idioi distinction sharpens this further, separating the move-forms that travel across every subject from those proper to deliberative, forensic, or epideictic speech, telling the rhetor which slots are even in play before the search begins. Each topos thereby becomes an addressable, nameable unit — a slot with a fixed inferential form and a variable content — rather than an indistinct flash of insight, which is exactly what lets invention be examined, corrected, and improved at all.

manages_complexity:
Confronting a fresh dispute, a rhetor faces what looks like an unbounded space: any subject — a war policy, a murder charge, a funeral oration — could in principle be argued in indefinitely many ways, and the question "what can I say here?" has no obvious edge to start from and no obvious way to know when one has said enough. The topoi compress that open-ended generative problem into a closed, finite traversal. Instead of confronting the infinite particularity of subjects, the rhetor confronts a fixed catalogue of perhaps a few dozen argument-forms — definition, division, similarity, contrast, comparison of degree, cause and effect, sign, precedent, past-fact-predicts-future-fact — and runs the present case against each in turn. The sprawl of possible arguments collapses to a small set of *slots*, and the only thing that varies from dispute to dispute is the content poured into those slots; the inferential forms themselves are invariant. What the rhetor tracks is reduced to two coordinates: which topoi the genre puts in play (the koinoi/idioi split tells you before you start whether the deliberative, forensic, or epideictic register admits this slot at all), and which of the admissible topoi have already been worked. From those two, the qualitative state of invention reads off directly — the search is complete when every applicable slot has been canvassed, incomplete otherwise, with the unworked slots naming exactly where the remaining arguments must lie.

This is what converts an unmeasurable creative act into a bounded, auditable one. Without the catalogue, the analyst of a speech has no handle on whether invention was thorough — completeness is undefined when the space of moves is unenumerated, so a missed argument is indistinguishable from an argument that was never available. The catalogue supplies the denominator. Because it bounds the *types* of move that exist, coverage becomes a checkable quantity: a rhetor who has applied every topos admissible to the genre has positive assurance of not having overlooked a whole class of arguments, and a critic diagnosing a failed speech can localize the breakdown by asking which topos went unworked rather than gesturing at a general want of ingenuity. The branch structure is correspondingly simple. For each topos the case either yields something defensible or it does not; the topos that yields becomes a candidate to refine or discard, the topos that yields nothing is set aside — and the qualitative outcome of the whole invention phase is just the accumulated verdict over that finite list of yes/no probes, read off a catalogue rather than re-derived from the boundless specifics of each new dispute.

abstract_reasoning:
The topoi license a set of moves in rhetorical invention, all flowing from the conception of argument-discovery as a search through a library of templates whose inferential form is fixed and whose content varies. The signature *generative* move is instantiation: the rhetor takes a topos with a recognizable form — "if X holds in the harder case, it holds in the easier" (*a fortiori*), "what this has done elsewhere it will do here" (precedent/sign), "this falls under that definition, so it inherits its consequences" (definition) — and fills its slots with the particular terms of the present dispute to produce a candidate argument. The reasoning runs from an abstract slot to a concrete claim: recognizing the case as one where a known template applies, and pouring the case's content into the template's variable positions to yield something defensible. This is structured *retrieval-and-instantiation*, not invention ex nihilo, and it is what lets a rhetor produce arguments on demand rather than waiting for inspiration.

The *search-and-coverage* move converts that generation into a bounded, auditable procedure. Because the catalogue enumerates the *types* of move that exist, the rhetor runs the dispute against each applicable topos as a checklist — definition, division, comparison of degree, cause and effect, sign, precedent — and tracks which have been worked and which remain, so the unworked slots name exactly where any remaining arguments must lie. The completeness inference is the distinctive payoff: a rhetor who has canvassed every admissible topos has positive assurance of not having overlooked a whole *class* of available moves, an assurance no unsystematized ingenuity can supply, because the library furnishes the denominator against which thoroughness is even definable. The per-topos branch is simple and the verdicts accumulate: for each, the case either yields something defensible (a candidate to refine or discard later) or it does not (set the slot aside), and the state of invention is just the running tally over that finite list of probes.

Two *boundary-drawing* moves frame the search before and around it. The first is genre-gating via the koinoi/idioi split: the rhetor reasons, before generating anything, about which topoi the register even admits — the common topoi that travel across every subject versus the special topoi proper to deliberative, forensic, or epideictic speech — so slots not in play for this genre are excluded from the search at the outset, narrowing the traversal to the admissible set. The second localizes failure within the rhetorical art: because invention is marked off cleanly from arrangement (*dispositio*) and wording (*elocutio*), a speech that fails can be diagnosed by *where* it failed — did invention miss an available line of argument, or was a sound argument merely misarranged or poorly phrased? The analyst reasons from the symptom of a weak speech to the responsible phase, and if the fault is in invention, further to *which topos* went unworked — a precise, addressable diagnosis rather than a gesture at a general want of ingenuity. Each topos being a nameable unit with a fixed form and variable content is exactly what makes invention examinable, correctable, and improvable at all.

knowledge_transfer:
Within rhetoric and its argument-theoretic neighbors the topoi transfer *as mechanism*, and the transfer is unusually clean because the apparatus was built to be portable across disputes in the first place. The same catalogue of move-forms — definition, division, *a fortiori*, cause-and-effect, sign, precedent — that a deliberative orator runs against a war-policy question, a forensic advocate runs against a murder charge and an epideictic speaker against a funeral oration: only the content poured into the slots changes, the inferential forms and the search-and-coverage procedure carrying intact. Across the historical lineage the mechanism survives renaming. Cicero's *loci* in *Topica* and *De Inventione*, Quintilian's treatment in the *Institutio Oratoria*, and the medieval-Renaissance *inventio* pedagogy are the same machine in Latin dress. In modern argumentation theory it reappears under a new vocabulary that is still mechanically the topoi: Perelman and Olbrechts-Tyteca's argumentation schemes in the *New Rhetoric*, and above all Walton's catalogue of named schemes (argument from expert opinion, from popular opinion, from sign, from analogy, from cause), each with its slots and its attached critical questions — a topos-library with the coverage check made explicit. Legal reasoning carries the mechanism into Viehweg's *topical jurisprudence* and the practical brief-builder's canvass of recognized argument-types; computational argumentation carries it into argument-mining and dialogue systems that literally encode the schemes as templates a program searches over. In all of these the diagnostics ("which topos went unworked?"), the interventions (instantiate an unworked slot), the completeness inference (every admissible scheme canvassed ⇒ no class of move overlooked), and the genre-gating logic all transfer without translation, because the substrate is the same throughout: *argument*.

Beyond argument the situation is case (B), a shared abstract mechanism rather than the named concept travelling. What genuinely recurs across software design, UX, systems modeling, and strategy work is the *meta-pattern* the topoi instantiate: maintain a library of named, reusable structural templates, and meet a fresh problem by searching that library for one that applies rather than inventing from nothing. That meta-pattern is real and substrate-spanning — but it already has its own homes in the catalog. The "topoi" of object-oriented software and of interface design are `design_patterns`; the "topoi" of systems dynamics are `system_archetypes`; the strategist's library of frameworks (five forces, SWOT) is the same searchable-template move again. The portable lesson — *to make invention tractable, enumerate and catalogue the move-types so that discovery becomes auditable retrieval* — belongs to that parent, not to "topoi" as named. The topoi's own machinery is home-bound: *what the templates are* (argument from sign, from precedent, *a fortiori*), the koinoi/idioi split keyed to deliberative/forensic/epideictic genres, the partition of the rhetorical art into invention, arrangement, and style — none of these survive extraction into a non-argument domain, where the library is differently populated and the genre and arrangement scaffolding has no referent. So the honest report is the inverse of "mechanism within, metaphor beyond": within argument the named concept itself transfers as mechanism; beyond it, it is not even metaphor but a *re-instantiation of the shared parent in a new substrate*, and the cross-domain lesson should be carried by that parent (a library of named templates searched on demand), with "topoi" reserved for its rhetorical realization. See *Structural Core vs. Domain Accent*.