Cross-Boundary Subsidy

one_liner: An asymmetric, sustained flow of a sustaining resource across a boundary holds a recipient above its endogenous capacity, creating donor-coupling vulnerability mistaken for autonomy.

core_idea:
Cross-boundary subsidy is the structural pattern of an *asymmetric, sustained, directional flow of a sustaining resource across a system boundary*, holding the recipient system above the abundance, productivity, or fitness level its in-system production could support, and creating a donor-coupling vulnerability that recipient-side observers routinely misread as recipient autonomy. The recipient looks different than it would on its own endogenous resources, and because the recipient's own mechanisms are visible while the off-system donor is not, the recipient is taken to be self-sufficient when it is structurally dependent.

The pattern carries five structural commitments. A *donor system* with surplus production. A *boundary* across which the flow passes — geographic, institutional, sectoral, disciplinary. A *delivery mechanism* — passive transport, active carriers, financial transfer, knowledge spillover — that sustains the flow at non-trivial magnitude. A *recipient system* whose abundance, structure, or fitness is *materially shaped* by the subsidy. And a *coupling vulnerability* — donor-side disturbance propagates to the recipient with a characteristic lag as predictable stress, even though the recipient appears self-sufficient. Two structural facts follow from the shape. First, the recipient's steady state is a function of the donor's surplus production, so any donor-side change propagates to the recipient with a lag set by the transport mechanism and the recipient's storage. Second, the recipient's *adaptive trajectory* — the slow shaping of community structure, business model, fiscal commitments, or research agenda — calibrates to the inflow as if it were endogenous, which makes withdrawal disproportionately destructive because the recipient has lost the structural capacity to operate at its in-system productivity. When such a system is observed at steady state, three quantities govern its fragility: the flow magnitude, the donor's reliability, and the recipient's *adaptive distance* from its endogenous capacity, the last being the dominant predictor of vulnerability to interruption.

structural_signature:
*the surplus-producing donor system* — *the boundary the flow crosses* — *the delivery mechanism sustaining the flow* — *the recipient whose steady state is materially shaped by the inflow* — *the asymmetry and persistence of the flow* — *the recipient's adaptive drift from endogenous capacity* — *the lagged donor-coupling vulnerability mistaken for autonomy*

A configuration exhibits cross-boundary subsidy when each of the following holds:

- **A donor system with surplus.** A system off to one side produces more of some sustaining resource than it consumes, leaving a surplus available to flow elsewhere.
- **A boundary.** A divide — geographic, institutional, sectoral, disciplinary — separates donor from recipient, so the flow is genuinely cross-boundary rather than internal redistribution.
- **A delivery mechanism.** A transport, carrier, transfer, or spillover process moves the resource across the boundary and sustains it at non-trivial magnitude over time.
- **A materially shaped recipient.** A recipient system whose abundance, structure, or fitness is held above what its own in-system production could support, so its observed steady state is a function of the donor's surplus.
- **Asymmetry and persistence.** The flow is directional (donor to recipient, not reciprocal) and sustained rather than incidental — these two properties distinguish a subsidy from a one-off transfer or a balanced exchange.
- **Adaptive drift.** Over time the recipient reorganises around the inflow — community structure, business model, fiscal commitments, research agenda calibrate to it as if endogenous — increasing its adaptive distance from in-system capacity.
- **Coupling vulnerability.** Donor-side disturbance propagates to the recipient with a characteristic lag as predictable stress, even though the recipient's visible in-system mechanisms make it appear self-sufficient.

The components compose so that apparent autonomy is the warning sign: the more self-sufficient the recipient looks, the more its visible mechanisms have masked the off-system dependence, and the further its adaptive drift has carried it from the capacity it would need to survive withdrawal.

what_it_is_not:
- **Not `arbitrage_generalized`.** Arbitrage *exploits and
  closes* a spread, predicting convergence; cross-boundary
  subsidy *sustains* a spread because donor surplus keeps
  replenishing it, predicting recipient fragility on
  withdrawal. Same cross-boundary flow, opposite dynamics.
- **Not `free_riding`.** A free rider extracts an
  under-priced benefit *against* the provider's interest;
  the donor here supplies surplus by its own dynamics,
  often indifferent to the recipient. The recipient is not
  cheating a commons but adapting to an external gift.
- **Not `externality`.** An externality is an *incidental*
  side effect spilling across a boundary; a subsidy is a
  *directional, sustained, recipient-shaping* flow. The
  defining additions are persistence and adaptive drift,
  absent from a one-off spillover.
- **Not `scarcity`.** Scarcity is a shortage of a resource;
  this prime is about an *abundance* the recipient does not
  itself produce. The danger is not too little but a
  sustaining surplus from off-system that masks a deficit.
- **Not `systemic_fragmentation`.** Fragmentation concerns
  loss of internal cohesion; subsidy concerns a recipient
  held together *by* an external flow. The recipient looks
  more integrated, not less, while being more dependent.
- **Common misclassification.** Reading a thriving
  recipient's apparent self-sufficiency as endogenous
  capacity. When a system performs above what its in-system
  production could support, the visible internal mechanisms
  invite attribution-to-the-visible; catch it by hunting
  for the off-system donor whose surplus the recipient has
  silently calibrated to.

broad_use:
- **Ecology**: cross-ecosystem subsidies — marine-derived nutrients from salmon to riparian forests, seabird guano to islands, kelp wrack to beaches, stream-emerging insects to riparian birds; recipient community structure is shaped by the donor flow, and closure of the flow (dam, overfishing, guano-mining) collapses the recipient.<!-- FACT-D61-101 -->[^polis-etal-1997]
- **Remittance economics**: migrant remittances constituting large fractions of recipient-country GDP; household consumption and fiscal capacity are shaped by donor-country labour conditions, and host-country recessions propagate as balance-of-payments stress.<!-- FACT-D61-102 -->[^worldbank-mdb40-2024]
- **Platform and multi-product business**: two-sided platform subsidies where advertisers fund users or one side funds the other; loss-leader pricing; "free" or below-cost goods sustained by donor-side surplus.<!-- FACT-D61-103 -->[^rochet-tirole-2003]
- **Venture-funded ecosystems**: startup-ecosystem dependence on venture capital that prices growth above margin; recipient business models look self-sustaining but are structurally subsidised, and capital-cycle contraction propagates as ecosystem-wide stress.<!-- FACT-D61-104 -->[^hoffman-yeh-2018]
- **Knowledge ecosystems**: foundational disciplines subsidising applied ones whose problems outrun their in-discipline productivity (mathematics to physics, statistics to empirical social science); the recipient research agenda is shaped by donor capacity.<!-- FACT-D61-105 -->[^wigner-1960]
- **Aid and infrastructure**: development aid shaping recipient fiscal capacity and service provision; cloud providers subsidising compute below a startup's marginal cost, sustaining models that would not survive at rental rates.<!-- FACT-D61-106 -->[^brautigam-knack-2004]

clarity: The label distinguishes a *directed, sustained, recipient-shaping* flow from incidental boundary-crossing of effects. Naive accounts treat the recipient as autonomous because its in-system mechanisms are the visible ones — salmon spawning is in-river behaviour, remittance-funded consumption is in-country economy, a startup's business model is the startup's own — and so attribute the recipient's apparent functioning entirely to itself. The cross-boundary-subsidy lens names the *off-system donor* and the *flow* as load-bearing components of that functioning, relocating part of the explanation outside the recipient's visible boundary. The clarifying separation is between what the recipient produces endogenously and what the inflow supplies, and between the recipient's apparent fitness and the flow magnitude that actually sustains it. Once that separation is named, the recipient's risk register acquires the donor as a primary line item, and the diagnostic question shifts from "why is this system thriving?" to "what off-system surplus is holding it above its endogenous capacity, and how reliable is that surplus?"

manages_complexity: The pattern reduces a heterogeneous set of "puzzlingly thriving recipient" diagnoses — across ecology, economics, business, aid, and knowledge production — to one structural question with a compact, portable intervention catalogue. *Identify the donor* when a system looks puzzlingly successful relative to its in-system productivity. *Identify the boundary* across which the subsidy passes, since protecting that boundary is often the cheapest conservation, policy, or business-continuity move. *Treat donor-coupling as a latent risk* on the recipient's register even when the donor looks remote. *Plan for the interruption-and-stress failure mode* rather than for recipient-internal failure. *Diversify subsidies* across multiple donors where possible. And *track flow magnitude directly* as the leading indicator of recipient health, in preference to recipient-apparent fitness. The compression is that an ecologist, a development economist, and a platform strategist run the same six-move audit under different vocabularies, so a diagnosis learned in one substrate transfers as a checklist in the next. Complexity moves from a per-substrate puzzle about recipient internals to a single boundary-and-flow analysis whose key quantity — the recipient's adaptive distance from endogenous capacity — predicts the severity of the failure that matters most.

abstract_reasoning: The prime trains a reasoner to model a thriving system as a steady state driven partly by an external sustaining flux, and then to ask three questions: how large is the flow, how reliable is the donor, and how far has the recipient's structure drifted from what its endogenous production alone could support? The non-obvious move is to treat the recipient's *adaptive trajectory* as the source of fragility rather than the inflow itself: a subsidy is not dangerous because it exists but because the recipient slowly reorganises around it, losing the capacity to operate without it, so that withdrawal is disproportionately destructive relative to the flow's marginal contribution. The prime also licenses a sharp contrast with arbitrage, its natural complement: arbitrage *exploits and closes* a spread, predicting convergence, whereas cross-boundary subsidy *sustains* a spread because the donor's surplus keeps replenishing it, predicting recipient-side fragility. Recognising which of the two is operating is the difference between expecting a gap to close and expecting a recipient to collapse when the flow stops. The reasoning generalises across any substrate with a boundary, a directional sustaining flux, and a recipient that can adapt to it, because all the structure requires is asymmetry, persistence, and recipient reorganisation.

knowledge_transfer: The diagnostic ports across substrates intact. An ecologist who has learned to identify trophic subsidies recognises the same structural move in remittance economies, platform business models, and venture-funded startup ecosystems; the role mappings transfer directly — *donor* ↔ salmon run / migrant labour / advertiser side / venture capital / foundational discipline; *boundary* ↔ river mouth / national border / platform side / funding round / disciplinary divide; *delivery mechanism* ↔ nutrient transport / wire transfer / cross-subsidy / capital round / knowledge spillover; *coupling vulnerability* ↔ forest-productivity decline / balance-of-payments stress / ecosystem cascade. The intervention catalogue — identify the donor, protect the boundary, treat coupling as latent risk, plan the interruption response, diversify donors, track flow magnitude — is invariant, and the only substrate-specific work is identifying what the donor produces, what crosses the boundary, and what the recipient has lost the capacity to do for itself. The transferred and non-obvious prediction is that the recipient's apparent autonomy is the warning sign: the more self-sufficient a subsidised system looks, the more its in-system mechanisms have masked an external dependence, and the further its adaptive trajectory has likely drifted from endogenous capacity, so a donor-side disturbance that looks remote will propagate as a predictable, lagged cascade. The pairing with arbitrage is itself a transferable diagnostic — when a sustained cross-boundary flow is observed, the analyst asks whether it is closing a spread (arbitrage, expect convergence) or replenishing one (subsidy, expect fragility on withdrawal) — and getting that question right is what separates predicting a market correction from predicting an ecosystem collapse.<!-- FACT-D61-107 -->[^unverified-107]

formal_abstract: The salmon-to-riparian-forest subsidy is the prime's canonical ecological instance, and it admits a clean steady-state reading. The *donor system* is the marine ecosystem, which produces surplus biomass that salmon accumulate at sea.<!-- FACT-D61-108 -->[^polis-etal-1997] The *boundary* is the river mouth and the streambank; the *delivery mechanism* is the spawning run plus the bears, eagles, and decomposition that carry marine-derived nitrogen into the soil. The *recipient* is the riparian forest, whose tree growth rate, foliar nitrogen, and even community composition are measurably elevated above what the watershed's own nutrient cycling could support.<!-- FACT-D61-109 -->[^helfield-naiman-2001] The *asymmetry and persistence* are evident: nutrients flow sea-to-forest, run after run, decade after decade. The *adaptive drift* is the load-bearing piece — over centuries the forest community reorganises around the annual marine pulse, so its standing structure presupposes the subsidy. The *coupling vulnerability* then makes the prediction sharp: dam a river or overfish the run, and the forest does not merely lose a marginal input, it loses a flux its structure had calibrated to, and riparian productivity declines with a lag set by soil-nitrogen storage.<!-- FACT-D61-110 -->[^polis-etal-1997] The diagnostic quantities are the prime's three — flow magnitude (run size), donor reliability (ocean conditions, fishing pressure), and the forest's adaptive distance from its endogenous nutrient budget, the last being the dominant predictor of how badly closure hurts. **Mapped back:** the salmon run is the donor, the riverbank the boundary, the spawning-and-scavenging chain the delivery mechanism, and the forest's drift from its own nutrient capacity is exactly the adaptive distance the prime names as the key fragility variable.

applied_industry: Two industry instances share the skeleton. First, a venture-funded startup ecosystem: the *donor* is the venture-capital pool, the *boundary* is the funding round, the *delivery mechanism* is below-margin pricing of growth (paying to acquire users faster than unit economics support).<!-- FACT-D61-111 -->[^hoffman-yeh-2018] The *recipient* is the startup, whose headcount, customer base, and operating tempo are held above what its own revenue could sustain. The *adaptive drift* is the company building a cost structure, a hiring plan, and customer expectations calibrated to subsidised burn; the *coupling vulnerability* is that a capital-cycle contraction — rising rates, a funding winter — propagates as ecosystem-wide layoffs with a lag set by runway. The apparent autonomy ("our growth proves product-market fit") is the warning sign the prime flags: the more self-sustaining the model looks, the more its visible mechanisms mask the off-system capital dependence. Second, a remittance-dependent economy: the *donor* is the migrant-labour host country, the *boundary* is the national border, the *delivery mechanism* is wire transfers that can exceed a tenth of recipient-country GDP.<!-- FACT-D61-112 -->[^worldbank-mdb40-2024] Household consumption and government fiscal capacity drift to presuppose the inflow, so a host-country recession propagates as balance-of-payments stress that the recipient cannot offset domestically. The intervention catalogue is identical across both: identify the donor, protect or diversify the channel, treat donor-coupling as a primary risk-register line, and track flow magnitude directly rather than trusting recipient-apparent health. **Mapped back:** VC and migrant labour are donors; funding rounds and borders are boundaries; the recipients' drift from endogenous capacity (revenue, domestic income) is the adaptive distance, and the diagnostic pairing — is this flow closing a spread (arbitrage) or replenishing one (subsidy)? — correctly predicts fragility-on-withdrawal in both.


Cross Cutting Relationship

type: prime

one_liner: Reading relative temporal order from intersection geometry — a feature that interrupts or overprints another must be younger than the one it cuts.

status: draft

core_idea:
The cross-cutting relationship is the structural inference pattern by
which the *geometry of intersection* between two features encodes their
relative *temporal order*: a feature that interrupts, displaces, or
overprints another must be younger than the feature it cuts.<!-- FACT-D61-126 -->[^hutton-1795] The
geological formulation is canonical, but the inference shape is general:
any medium that preserves a record of operations such that later
operations interrupt or overprint earlier ones supports the same
inference. From a static snapshot of the present geometry, the analyst can
reconstruct partial temporal order without ever observing the events
unfold.

The structural commitment has three parts: a *substrate* that preserves
an inscribed record — rock, document, codebase, magnetic medium,
palimpsest; an *intersection geometry* where a later feature crosses,
interrupts, or overprints an earlier one; and an *inference rule* that
reads geometry as relative chronology. Two consequences follow that are
load-bearing for how the pattern is used. The inference is *partial* — it
orders only those features that actually intersect, not every feature in
the substrate — and it is *robust* under quite weak assumptions about
substrate persistence. The rule is also intrinsically *acyclic*: a
consistent reading yields a directed acyclic graph of ages, so a detected
cycle signals either later reworking of the substrate or a misread of the
geometry. Because the rule reasons from spatial relationships alone, it
extracts time from space, recovering chronology that no surviving log or
direct observation could supply.

structural_signature:
*the record-preserving substrate* — *the intersection geometry between two features* — *the inference rule reading geometry as relative chronology* — *the partial-order output* — *the acyclicity invariant* — *the substrate-preservation precondition*

A configuration exhibits the cross-cutting inference when each of the following holds:

- **A record-preserving substrate.** A medium — rock, document, codebase,
  magnetic tape, palimpsest, planetary surface — preserves an inscribed record
  of operations such that later operations physically interrupt or overprint
  earlier ones.
- **An intersection geometry.** Two features actually cross, interrupt,
  displace, or overprint one another; the geometry of their intersection is
  observable in a static snapshot.
- **An inference rule.** The interrupting/overprinting feature must be *younger*
  than the feature it cuts — geometry is read directly as relative temporal
  order, extracting time from space without observing the events unfold.
- **A partial order.** The rule orders only those features that intersect, not
  every feature in the substrate, yielding a partial order that can be combined
  with independent dating to build a fuller chronology.
- **An acyclicity invariant.** A consistent reading yields a directed acyclic
  graph of ages; a detected cycle signals later reworking of the substrate or a
  misread of the geometry, so the rule doubles as a consistency check.
- **A preservation precondition.** The inference holds only if the medium
  preserves the geometry; an erasing or homogenising substrate (a mixed fluid,
  a wiped tape, a redacted document) voids the reading — so applying the rule
  also audits whether the record can be trusted.

Composed, these reduce a dating problem to enumerate-intersections-then-apply
the acyclic rule, recovering chronology that no surviving log could supply, with
non-intersecting features requiring a complementary rule (superposition, ring
count) instead.

what_it_is_not:
- **Not `interpretation`.** Interpretation extracts meaning from a sign;
  cross-cutting extracts *relative temporal order* from intersection geometry
  alone — a mechanical inference, not a hermeneutic reading.
- **Not `provenance`.** Provenance traces an object's chain of custody or
  origin from records; cross-cutting recovers order *from the geometry itself*,
  precisely when no record survives.
- **Not `causality`.** It orders *which came first* without claiming the cutter
  *caused* the cut feature; it is constitutively silent on mechanism — order is
  not cause.
- **Not `comparison`.** Comparison weighs features against a criterion;
  cross-cutting reads a directed precedence (younger-cuts-older) off a specific
  intersection, not a similarity judgement.
- **Not `abductive_reasoning`.** Abduction infers the best explanation for an
  observation; cross-cutting applies a *deductive* geometric rule — the cutter
  is younger — that needs no inference to the best account.
- **Not `layered_accumulation` / superposition.** Superposition orders
  *stacked* layers by deposition order; cross-cutting orders *intersecting*
  features, and the two are complementary rules covering different geometries.
- **Common misclassification.** Reading the cross-cutting partial order as a
  *total* chronology, assuming non-intersecting features are simultaneous. The
  rule orders only what actually intersects; the gaps need a complementary
  method.

broad_use:
The pattern is the canonical relative-dating tool in structural geology
and stratigraphy: a dike cutting a fault is younger than the fault, an
unconformity truncating folded strata is younger than the folding, and
combined with superposition these relations build the relative-time
scaffold onto which absolute dates are hung.<!-- FACT-D61-127 -->[^hutton-1795] Archaeology reads the same
logic in stratigraphic excavation — a pit cut into a floor postdates the
floor, a wall foundation crossing an earlier trench postdates the trench
— formalised in the Harris matrix.<!-- FACT-D61-128 -->[^harris-1979] In software engineering and code
archaeology a patch that modifies a line is later than the line, and git
blame, three-way merge, and file-history walks operationalise the
inference.<!-- FACT-D61-129 -->[^git-blame-docs] In document forensics and palaeography corrections, marginal
glosses fitting around an earlier stain, and palimpsest readings recover
order from overprinting.<!-- FACT-D61-130 -->[^netz-noel-2007] In conflict and forensic reconstruction
overlapping footprints, blood spatter, and intersecting bullet holes let
the investigator order events from a static scene. In network and
infrastructure archaeology a new road cut across an older field pattern,
or a fibre line trenched across an older corridor, carries the same
inference. And in cosmology and planetary chronology, crater-on-crater
intersections plus crater counts produce relative-age maps on surfaces
with no other dating.<!-- FACT-D61-131 -->[^fassett-2016]

clarity:
Naming the cross-cutting inference rule separates the question *how do we
know which came first?* from the question *what happened?* The former is
a geometric question answerable from a snapshot; the latter requires
direct observation or independent evidence. The vocabulary makes explicit
that an inference about temporal order can be extracted from purely
spatial information, given the right substrate. It also clarifies a
frequent confusion in legacy-system analysis: a component "crossing"
another — a function call that bypasses a layer, a wire running across a
panel, a road cutting a property line — often encodes a temporal fact
about which was emplaced later, and that fact is recoverable without
consulting the change log, often precisely when the log is lost or
unreliable. The pattern tells the analyst when the geometry is itself the
record.

manages_complexity:
The pattern compresses a class of dating problems into a uniform
analytical operation: identify the substrate, enumerate intersections,
apply the inference rule. The result is a *partial order* over features,
which is frequently more usable than a guess at absolute dates and can be
combined with independent dating constraints to yield a full chronology.
The compression is dramatic in practice. A field mapper can produce a
stratigraphic sequence spanning vast intervals from a single afternoon's
outcrop work, using cross-cutting plus superposition; a code archaeologist
recovers partial order from intersection-of-edits without reading every
diff. By reducing the dating task to enumeration of intersections and a
single acyclic rule, the pattern turns an open-ended historical question
into a bounded, mechanical procedure.

abstract_reasoning:
The pattern supports inference about *what can and cannot be ordered* from
geometric evidence alone. Features that do not intersect cannot be ordered
by cross-cutting and require a different rule — superposition, fossil
content, ring count; features that do intersect get ordered. It supports
*consistency checking*: if A cuts B, B cuts C, and C cuts A, then the
substrate has been reworked since some of these relations were emplaced,
or the analyst has misread the geometry, because the rule is acyclic by
construction. It further supports inference *about the substrate itself*:
the rule works only if the medium preserves the geometry, so a substrate
that erases or homogenises — a well-mixed fluid, a wiped tape, a redacted
document — loses the relative-time record. Cross-cutting is therefore
informative about a substrate's preservation properties as much as about
chronology, and the act of applying it doubles as an audit of whether the
record can be trusted at all.

knowledge_transfer:
Because the residue — substrate plus intersection geometry plus acyclic
partial order — is medium-neutral, the rule transfers historically and
intact. The inference moved from geology into archaeology with the
formal codification of Harris-matrix stratigraphy, which made explicit the
partial-order graph implicit in field practice; the archaeologists
imported the geological rule rather than inventing a parallel one.<!-- FACT-D61-132 -->[^harris-1979] It
moved into planetary science as crater-counting chronology, the
cross-cutting rule applied to impact geometry and calibrated against
returned sample ages.<!-- FACT-D61-133 -->[^fassett-2016] It moved into software code archaeology, where
diff-overprints-line yields a partial order and merge-conflict detection
is consistency-checking on the inferred order. It moved into forensic
analysis, where glass-fracture analysis uses cross-cutting — later
fractures terminate at earlier ones — to reconstruct event sequences from
a static crime scene.<!-- FACT-D61-134 -->[^swgmat-glass-2005] In each port the intervention vocabulary is the
same: construct the partial order, run the consistency (acyclicity)
check, and audit the substrate for preservation. The transfer also carries
its own boundary: the rule orders only intersecting features, so a
receiving domain must be told that non-intersecting features need a
complementary rule, and that an erasing or homogenising substrate voids
the inference entirely. A practitioner who has used cross-cutting in one
medium arrives at a new one already equipped to ask which features
intersect, whether the inferred order is acyclic, and whether the
substrate has preserved the geometry faithfully enough to trust the
reading — three questions that travel without metaphor from rock to code
to crater to manuscript.

formal_abstract:
A geological outcrop showing an igneous dike crossing a faulted sandstone is
the prime's canonical case, and it demonstrates the full inference from a static
snapshot. The *record-preserving substrate* is the rock, which holds an
inscribed record of past events. The *intersection geometry* is direct: a fault
displaces the sandstone beds, and a vertical dike of intruded magma cuts
straight across both the beds and the fault without itself being offset. The
*inference rule* reads this geometry as relative chronology — the sandstone was
deposited first, the faulting that displaced its beds came next, and the dike,
which interrupts the fault plane, must be *youngest*, because a feature that
cuts another postdates it.<!-- FACT-D61-135 -->[^hutton-1795] This yields a *partial order* (sandstone → fault →
dike) that orders only the features that actually intersect; an unrelated
mineral vein elsewhere in the outcrop is left unordered until it too is found to
cut or be cut by something. The *acyclicity invariant* doubles as a
consistency check: if mapping produced "dike cuts fault, fault cuts dike," the
geologist would conclude the substrate had been reworked or the geometry
misread. And the *preservation precondition* matters — had the rock been
melted and recrystallised, the geometry would be erased and the reading voided.
The procedure is mechanical: enumerate intersections, apply the rule, build the
graph.

**Mapped back:** The rock is the substrate, the dike-cuts-fault geometry is the
intersection, "the cutter is younger" is the inference rule, sandstone → fault →
dike is the partial order, and the no-cycle check is the acyclicity invariant.

applied_industry:
Code archaeology with version control instantiates the same prime in a
software-engineering substrate, recovering history when the change log is the
record. The *record-preserving substrate* is the source file together with its
commit history; the *intersection geometry* is the overprinting of edits — a
later commit modifies a line that an earlier commit introduced, physically
overwriting it. The *inference rule* is identical to the geological one: the
edit that overprints a line is *younger* than the line it replaces, so `git
blame` reads the present text and attributes each surviving line to the last
operation that touched it, reconstructing relative order without any developer
watching the edits happen.<!-- FACT-D61-136 -->[^git-blame-docs] The *partial order* is genuine — two edits to
unrelated files are not ordered by cross-cutting and need an independent
timestamp — and *merge-conflict detection is the acyclicity consistency check*:
a three-way merge flags exactly the cases where two branches overprint the same
region in incompatible order, the software analogue of a detected cycle
signalling that the geometry cannot be consistently read.<!-- FACT-D61-137 -->[^git-merge-strategies-docs] The *preservation
precondition* shows up as a squashed or rewritten history that erases
intermediate edits, voiding the fine-grained reading. A structurally identical
applied instance is archaeological stratigraphy formalised as the Harris matrix,
where a pit cut into a floor postdates the floor and the excavator builds the
same intersection-derived partial-order graph.

**Mapped back:** The source file and its history are the substrate, an edit
overprinting a line is the intersection, "the overprinting edit is younger" is
the inference rule, `git blame` output is the partial order, and merge-conflict
detection is the acyclicity check.


Cross-Dimensional Leakage

one_liner: A single shared variance source contaminates multiple supposedly-independent output dimensions, inflating their apparent correlations above the true cross-dimensional signal.

core_idea:
Cross-dimensional leakage is the structural pattern in which a *single shared source of variance* — a channel, instrument, rater, batch, common method, or common shock — contaminates *multiple supposedly-independent output dimensions*, inflating their apparent correlations above the true cross-dimensional signal and biasing any analysis that reads channel-derived covariance as evidence about the underlying sources. The output dimensions appear to measure or generate multiple distinct things, but the measurement or generation channel is silently sharing one source of variance across all of them, so the cross-dimensional correlations are partly an artefact of the channel rather than a property of the underlying sources. Naive analysis treats the inflated correlations as substantive findings; structural analysis treats them as diagnostics for shared-channel variance to be partitioned out.

The pattern admits a factor decomposition: each measured output `y_i` is generated by a true underlying source `t_i` plus a shared channel factor `c` (loading `λ_i` on each output) plus noise. The naive covariance `cov(y_i, y_j)` is inflated by `λ_i · λ_j · var(c)` beyond the true `cov(t_i, t_j)`. The decisive structural fact is that *channel-shared variance has the same statistical signature as substantive cross-dimensional covariance*: from a single channel's data the two are indistinguishable. Resolution therefore requires either an independent second channel (orthogonal measurement) or a strong prior on the factor structure (explicit modelling) — which is exactly why multi-trait/multi-method designs, factor models, multi-batch designs, and randomisation work where naive correlation analysis fails. The structural commitments are: multiple supposedly-independent output dimensions sharing a channel; a single shared-variance source affecting all of them; inflated apparent cross-dimensional covariance; and a naive analysis that reads the channel-derived covariance as a substantive cross-source relation.

structural_signature:
*the multiple supposedly-independent output dimensions* — *the single shared-variance source (channel) feeding all of them* — *the per-dimension loading of the channel onto each output* — *the inflated apparent cross-dimensional covariance* — *the statistical indistinguishability of channel variance from substantive covariance* — *the partitioning move requiring an orthogonal channel or a factor prior*

A configuration exhibits cross-dimensional leakage when each of the following holds:

- **Multiple output dimensions.** Several quantities are measured or generated and treated as if they index distinct underlying sources: traits, survey items, features, genes, economic series, voxels.
- **A shared channel.** A single common source of variance — an instrument, rater, batch, method, or common shock — feeds into all of those output dimensions rather than into one in isolation.
- **Per-dimension loadings.** The channel couples to each output with its own strength, so each measured output decomposes into a true source term, a channel term scaled by its loading, and noise.
- **Inflated cross-covariance.** The apparent covariance between any two outputs is lifted above the true cross-source covariance by the product of their channel loadings times the channel variance — an artefact of the shared channel, not a property of the sources.
- **Statistical indistinguishability.** From a single channel's data, channel-injected covariance and substantive cross-source covariance have the same signature and cannot be told apart; the contamination is structural, so it does not average out with more same-channel data.
- **The partitioning requirement.** Resolution requires either an independent second channel (orthogonal crossing) or a strong factor prior (explicit modelling), after which the residual cross-dimensional structure reveals whether the pattern was artefact or substance.

The components compose so that a tight cross-dimensional correlation observed through one channel is exactly what shared-channel variance produces, making inflated correlation a trigger for suspicion rather than a finding — and making channel-crossing, not larger samples, the only remedy.

what_it_is_not:
- **Not `escape_and_leakage`.** That prime is about
  confined material crossing a boundary out of its region;
  this is about *shared variance* contaminating multiple
  output dimensions through a common measurement channel.
  The shared "channel" metaphor is coincidental, not the
  same structure.
- **Not `confounding`.** A confound is a *real third cause*
  acting on the constructs themselves; here the shared
  variance is introduced by *how* the dimensions are
  measured (instrument, rater, batch), not by what drives
  them. They have the same statistical signature but live
  at different layers.
- **Not `correlation`.** Correlation is the bare statistical
  relation; this prime is a *specific generative story* for
  why an observed correlation is inflated above the true
  cross-source signal — a diagnosis, not a measure.
- **Not `synergy_and_antagonism`.** That concerns genuine
  interaction between sources; cross-dimensional leakage
  produces *apparent* relations that are channel artefact,
  vanishing under channel-crossing rather than reflecting
  any real interaction.
- **Not stochastic noise.** Random error averages out with
  sample size; channel-shared variance is structural, has a
  mean structure, and does not diminish with more
  same-channel data — the defining contrast.
- **Common misclassification.** Reading a tight
  cross-dimensional correlation measured through one channel
  as a substantive finding. The collect-more-data reflex
  treats it as stochastic; catch it by asking what single
  channel feeds all the dimensions and whether an orthogonal
  channel has ever confirmed the relation.

broad_use:
- **Social cognition**: the halo effect — a single overall impression of a person contaminates ratings of distinct traits (intelligence, warmth, competence).<!-- FACT-D61-151 -->[^thorndike-1920]
- **Measurement and instrumentation**: a single instrument's drift, calibration error, or operator effect contaminates multiple measured quantities; multi-trait/multi-method matrix designs were built to separate trait from method variance.<!-- FACT-D61-152 -->[^campbell-fiske-1959]
- **Survey methodology**: common-method bias — one questionnaire rated at one sitting by one respondent inflates cross-item correlations beyond what the true cross-construct relations imply.<!-- FACT-D61-153 -->[^podsakoff-etal-2003]
- **Machine learning**: a confounding feature correlated with the target inflates the apparent importance of other features that co-vary with it; importance diagnostics partially reveal but cannot fully resolve this without experimental decoupling.
- **Genomics**: batch effects — assay-batch variance contaminates apparent biological signal across many genes at once; correction methods were built specifically to partition this leakage.<!-- FACT-D61-154 -->[^leek-etal-2010]
- **Macroeconometrics**: a common shock (oil prices, monetary policy) contaminates apparent cross-sectoral or cross-country relations; factor models partition out the common component.<!-- FACT-D61-155 -->[^stock-watson-2002]
- **Reputation and neuroimaging**: an organisation's reputation halo contaminates ratings of unrelated products; scanner drift and physiological noise inflate apparent functional connectivity across voxel time series.<!-- FACT-D61-156 -->[^power-etal-2012]

clarity: The label distinguishes the *channel-level* shared-variance contamination from the substrate-level vocabulary — halo, common method, batch effect, common shock — that names each instance separately and so obscures their identity. Naive analyses treat correlations between output dimensions as substantive findings about the underlying constructs; the cross-dimensional-leakage lens reveals an entire layer of shared-channel variance that must be partitioned out before the substantive question can even be posed. The clarifying separation is between covariance that lives in the sources (`cov(t_i, t_j)`) and covariance injected by the shared channel (`λ_i · λ_j · var(c)`), two quantities with the same statistical appearance and very different meanings. Naming the pattern makes the diagnostic question routine across substrates — "what is the shared channel here, and how is it contaminating my apparent cross-dimensional pattern?" — and exposes a recurring inferential trap in which inflated correlations are reported as substantive structure precisely because the channel that produced them was never modelled. Once the channel is named as a separable variable, the analyst can suspect it before crediting the cross-dimensional finding.

manages_complexity: The pattern compresses a heterogeneous set of substrate-specific methodologies — multi-trait/multi-method matrices, batch-correction algorithms, factor models, halo correction, common-method-bias adjustment, scanner-drift regression, feature-importance auditing — into one structural problem with one solution shape: *cross the measurement channel with something else, then partition the variance*. The intervention catalogue ports across substrates. *Cross the channel with an independent second channel*: multi-method designs, independent ground truth, repeat measurement with different instrumentation. *Model the shared variance explicitly*: a factor model, a batch covariate, a common-method-bias factor, a fixed effect on channel identity. *Decouple by experimental design*: randomise the channel assignment, balance batches across conditions, blind raters. *Test the residual cross-dimensional structure*: after removing the shared-channel variance, see what survives — if the cross-dimensional pattern collapses, it was channel artefact; if it persists, it is substantive. The compression is that a psychometrician, a genomicist, a macroeconometrician, and an ML practitioner are running the same four-move procedure under different names, so a method mastered in one substrate transfers as a template in the next. Complexity moves from a per-field corrective literature to a single channel-crossing-and-partitioning discipline.

abstract_reasoning: The prime trains a reasoner to read any matrix of cross-dimensional correlations as potentially carrying two superimposed signals — true cross-source covariance and channel-injected covariance — and to recognise that the two are indistinguishable from within a single channel. The governing move is to treat a single channel's correlations as untrustworthy by construction and to seek a second, independent channel (or a strong factor prior) before crediting any cross-dimensional finding. The non-obvious consequence is that more data through the *same* channel does not help: the inflation is structural, not stochastic, so it does not average out with sample size; only an orthogonal channel or an explicit model of the shared factor can separate `λ_i · λ_j · var(c)` from `cov(t_i, t_j)`. The prime also keeps the failure cleanly distinguished from substantive confounding — here the shared variance is introduced by the measurement or generation channel, not by a real third cause acting on the constructs — and from its input-side dual, in which correlated *inputs* collapse per-input identifiability rather than correlated *outputs* inflating cross-output relations. Both arise from shared variance at a layer the naive analysis does not model, and the reasoning move in each is the same: find the unmodelled shared layer and partition it before reading the pattern.

knowledge_transfer: The diagnostic ports across substrates without redesign. A psychometrician who has learned multi-trait/multi-method analysis recognises the identical structural problem in feature-importance auditing, genomics batch effects, and macroeconometric common shocks; a genomicist who has internalised batch correction predicts correctly that survey research will be contaminated by common-method effects and reputation research by halo. The role mappings transfer directly — *output dimensions* ↔ traits / survey items / features / genes / economic series / voxels; *shared channel* ↔ overall impression / single questionnaire / confounding feature / assay batch / common shock / scanner; *channel factor* ↔ halo / method variance / batch variance / common component; *partitioning move* ↔ MTMM crossing / factor model / batch covariate / motion regression. The intervention catalogue — cross the channel, model the shared factor, decouple by design, test the residual structure — is invariant, and the only substrate-specific work is identifying what counts as the channel and what kinds of independent crossing are feasible. The transferred and non-obvious lesson is that inflated correlations should be the trigger for suspicion rather than for discovery: a tight cross-dimensional pattern measured through one channel is exactly what shared-channel variance produces, so the right response is to cross the channel before publishing the relation, not to interpret it. Because the inflation does not diminish with sample size, the prime also corrects a common instinct — collecting more data through the same instrument — by showing that the only remedies are an orthogonal channel or an explicit shared-factor model, both of which a practitioner can import from whichever substrate first taught them the move.

formal_abstract: The multi-trait/multi-method (MTMM) matrix in psychometrics is the prime's purest worked case, because it was engineered specifically to expose and partition the leakage. Suppose a researcher measures three *output dimensions* — anxiety, depression, hostility — each by two *methods* (self-report questionnaire and clinician rating).<!-- FACT-D61-157 -->[^campbell-fiske-1959] Each measured score decomposes as `y_i = t_i + λ_i·c + noise`, where `t_i` is the true construct, `c` is the shared *method channel* (the questionnaire's response style, the clinician's halo), and `λ_i` is the loading. The naive observation is that all three self-report scores correlate tightly — read uncritically, this says the three constructs are nearly the same thing. But the MTMM design crosses the channel: it asks whether anxiety-by-questionnaire correlates more with depression-by-questionnaire (same method, different trait) than with anxiety-by-clinician (same trait, different method).<!-- FACT-D61-158 -->[^campbell-fiske-1959] When the same-method correlations dominate, the tight cross-construct pattern is `λ_i·λ_j·var(c)` — *method variance*, not substance. The decisive structural fact the prime names is visible here: from the self-report data *alone* the inflation is indistinguishable from real covariance, and collecting more questionnaires cannot help because the contamination is structural, not stochastic. Only the orthogonal second method (or an explicit method factor in a confirmatory model) separates `λ_i·λ_j·var(c)` from `cov(t_i,t_j)`.<!-- FACT-D61-159 -->[^campbell-fiske-1959] **Mapped back:** the three symptom scales are the output dimensions, the questionnaire is the shared channel, the same-method correlation block is the inflated cross-covariance, and the clinician rating is the orthogonal crossing that performs the partition — exactly the prime's "cross the channel, then partition" resolution.

applied_industry: Two industry instances run the identical structure. First, genomics batch effects: a lab profiles gene expression for hundreds of *output dimensions* (genes) across samples processed in several assay *batches*.<!-- FACT-D61-160 -->[^leek-etal-2010] The shared channel is the batch — reagent lot, technician, machine-day — which loads onto every gene at once. Apparent co-expression across many genes can be `λ_i·λ_j·var(batch)` rather than coordinated biology, and the giveaway is that samples cluster by batch rather than by condition. More samples *within the same batch* do not fix it; the remedy is to randomise condition across batches (decouple by design) or fit an explicit batch covariate (model the shared factor), then test which co-expression survives.<!-- FACT-D61-161 -->[^johnson-etal-2007] Second, machine-learning feature-importance auditing: a model is trained on many features, and a confounding feature correlated with the target silently inflates the apparent importance of every feature that co-varies with it, so an importance report reads channel-driven covariance as evidence about the underlying drivers. The corrective is experimental decoupling — permutation or interventional importance that breaks the confound — not a larger training set drawn through the same correlated feature distribution.<!-- FACT-D61-162 -->[^strobl-etal-2007] In both cases the prime's counter-instinct is decisive: the practitioner's reflex to "collect more data" is wrong because the inflation does not average out, and the only remedies are an orthogonal channel or an explicit shared-factor model. **Mapped back:** genes and features are output dimensions; assay batch and the confounding feature are shared channels; batch-driven co-expression and confound-driven importance are the inflated covariances; and batch-randomisation/covariate-modelling and interventional importance are the channel-crossing and explicit-modelling moves the prime prescribes.


Cross-Impact Analysis

one_liner: Interacting trends.

core_idea: (1) **Cross-impact analysis is a structured method for examining how multiple future events, trends, or factors influence each other — assessing, for each pair of factors, how the occurrence or strengthening of one factor raises, lowers, or leaves unchanged the probability or intensity of another — thereby revealing interaction effects that single-factor analysis misses.** (2) The distinctive focus is on pairwise interaction assessment across a systematically-bounded factor set, typically represented as a cross-impact matrix where each cell captures the impact of the row-factor on the column-factor, supported in more-formal variants by mathematical aggregation that computes adjusted probabilities or trajectories accounting for all pairwise interactions — distinct from single-factor trend analysis (which treats factors independently), from scenario narratives (which build integrated stories without explicit pairwise matrices), and from full systems-dynamics simulation (which models continuous-time dynamics rather than discrete pairwise impacts). (3) The method typically involves: identifying a bounded factor set (usually 10-30 factors selected for strategic relevance from STEEP/PESTLE-style scanning or Delphi inputs); eliciting pairwise impact assessments (often through expert workshops or structured questionnaires, with magnitudes and directions specified); constructing the cross-impact matrix; running the mathematical aggregation where applicable (Gordon's EIR method, Godet's MICMAC method, probabilistic variants); and interpreting the results for strategic implications. (4) The deeper abstraction is that **in systems of moderately-interconnected factors, the emergent behavior of the system cannot be inferred from independent analysis of the factors — factors that look unimportant in isolation may become critical when their interactions are considered, and factors that look important in isolation may be offset by opposing interactions. Cross-impact analysis is a pragmatic method for surfacing these interaction effects at a tractable level of analytical rigor between the simplicity of single-factor analysis and the complexity of full dynamic simulation.**

structural_signature:
The operation presumes (a) a bounded factor set sufficient to capture the strategic question but small enough for pairwise analysis to be tractable, (b) expert judgment or data capable of supporting pairwise-impact assessment, and (c) an analytical intent that values interaction-effect surfacing rather than only single-factor trajectory analysis. A cross-impact analysis has five structural components. The component decomposition separates factor selection (a gating step that constrains everything downstream) from pairwise elicitation from matrix construction, aggregation, and interpretation:

1. **Factor-set selection** — *scope-setting only*: choosing typically 10-30 factors for analysis. Smaller sets lose coverage; larger sets produce unmanageable N² pairwise-assessment loads and become uninterpretable. Factor selection typically draws from STEEP/PESTLE-style scanning, Delphi priority lists, or domain-expert judgment, and is itself a methodological commitment: the analysis cannot surface interactions among factors that are not in the set. No impact assessment is done at this step; the output is a committed bounded factor set.
2. **Pairwise-impact elicitation** — assessing, for each ordered factor pair, what effect the row-factor has on the column-factor in magnitude and direction. Elicitation is typically through expert workshops or structured questionnaires; the assessments may be qualitative labels, ordinal ratings, or conditional probabilities depending on the variant chosen.
3. **Matrix construction** — organizing the pairwise assessments into the N×N cross-impact matrix (with the diagonal typically left blank as factors' impact on themselves is trivially defined). The matrix is the analytical artifact that supports aggregation and inspection.
4. **Aggregation analysis** — running the mathematical aggregation appropriate to the variant: simple matrix visualization, MICMAC with eigenvalue-style influence-and-dependence ranking, Gordon's EIR with conditional-probability chains, or probabilistic variants with Monte Carlo simulation. Different variants produce different primary outputs (driver-dependent quadrants, adjusted probabilities, influence networks).
5. **Interpretation** — drawing strategic implications from the matrix and aggregation outputs: identifying high-driver factors suitable for policy leverage, high-dependent factors that reflect system state rather than intervention points, strongly-interacting clusters that warrant coordinated treatment, and asymmetric influence patterns that shape priority-setting. Integration with downstream methods (scenario planning, policy analysis) typically happens in or alongside this step.

Structural distinctions include: the form of the factors (events with discrete probabilities; trends with continuous intensity; conditions with binary or categorical states); the mode of impact assessment (qualitative labels, ordinal ratings, conditional probabilities); the aggregation mathematics (simple matrix visualization, MICMAC with eigenvalue analysis, EIR with conditional-probability chains, probabilistic variants with Monte Carlo simulation); and the integration with other methods (standalone vs input to scenario planning vs complement to Delphi). The distinguishing structural commitment is systematic pairwise analysis across a bounded factor set: methods that informally assess some interactions without systematic coverage are not cross-impact analysis in the technical sense.

what_it_is_not:
- Not independent-factor trend analysis — the entire point of the method is to capture interactions that independent analysis misses.
- Not scenario planning — scenarios build integrated narratives; cross-impact analysis surfaces interactions that can feed into scenarios but does not itself produce coherent scenario stories.
- Not systems-dynamics simulation — systems dynamics uses continuous-time modeling with stocks, flows, and feedback loops; cross-impact analysis uses discrete pairwise impacts at a snapshot or conditional level.
- Not Bayesian network analysis — Bayesian networks formalize conditional probabilities with full probability distributions and inference algorithms; cross-impact analysis is typically less mathematically-formal, though probabilistic variants overlap with Bayesian methods.
- Not factor analysis in the statistical sense — statistical factor analysis identifies latent factors from correlated observed variables; cross-impact analysis works with pre-specified factors and their mutual influences.
- Not factorial design in the experimental sense — factorial design (see factorial_design #443) manipulates factors to test their interaction effects empirically in controlled settings; cross-impact analysis elicits interaction judgments from experts about factors that cannot be experimentally manipulated. The two form a reciprocal tight pair: factorial design is the experimental analog that directly observes interaction effects when manipulation is possible; cross-impact analysis is the judgment-based analog for domains where manipulation is not possible. The underlying principle — that interaction effects cannot be inferred from independent single-factor analysis — is shared. "Reciprocal" here denotes a symmetric, mutually-illuminating pairing rather than a hierarchical one: neither method is prior to or derivative of the other; each articulates the shared interaction-effect principle in the domain appropriate to its epistemic conditions (manipulability vs non-manipulability), and the two together articulate the principle more completely than either does alone.
- Not a future wheel — future-wheel analysis (see future_wheel #460) traces forward-branching consequences from a single trigger; cross-impact analysis examines pairwise interactions among a bounded set of pre-specified factors. The methods are complementary: future wheels often surface consequences that become inputs to cross-impact matrices, and cross-impact matrices may identify pairs whose interaction warrants dedicated future-wheel treatment.
- Not prediction — the method identifies interaction patterns but does not predict specific outcomes; outputs typically include adjusted-probability ranges, factor-influence rankings, and interaction patterns.
- Not a complete foresight method — typically used in combination with other methods in a staged workflow. STEEP/PESTLE scanning (see steep_pestle_analysis #463) is commonly the upstream step that produces the candidate factor pool from which the cross-impact factor set is selected; the STEEP/PESTLE dimensional structure (social, technological, economic, environmental, political, and the extended-variant dimensions) ensures the factor pool is not prematurely narrowed to the analyst's familiar domain. Delphi method (see delphi_method #457) is often the elicitation mechanism for the pairwise-impact assessments when expert panels are geographically dispersed or when anonymity is analytically valuable; the iterative-feedback structure of Delphi can be applied to cross-impact matrices to refine impact assessments across rounds rather than committing to single-round elicitation. Scenario planning typically consumes cross-impact analysis downstream: the driver-dependent structure and the high-interaction clusters identified by the matrix analysis inform the selection of scenario-axes and the narrative content of scenario stories. The workflow ordering is not rigid — cross-impact analysis can also be run as a standalone exercise, or iteratively with scenario development — but the characteristic pattern is STEEP/PESTLE upstream, Delphi as elicitation mechanism, scenario planning downstream.
- Not scalable to very large factor sets — pairwise analysis is N² in factors; sets beyond 30-50 factors become impractical for expert elicitation and interpretation.
- Not immune to elicitation bias — the impact assessments reflect the judgment of experts who may share blind spots, cultural assumptions, or analytical frames; the method is only as good as its inputs.
- Not static — the interaction patterns identified are themselves subject to change as the environment evolves; periodic refresh is typically needed.

broad_use: Cross-impact analysis was developed in the late 1960s and early 1970s at RAND Corporation and the Institute for the Future, with Theodore Gordon and Olaf Helmer[^helmer-contributions] as principal developers. The technique was developed partly in response to recognized limitations of single-factor Delphi analysis: experts could provide meaningful trajectory estimates for individual factors but often struggled to systematically incorporate interactions. Gordon's Enhanced Impact Report (EIR) method[^gordon-eir] and subsequent variants provided mathematical frameworks for aggregating pairwise assessments into adjusted factor probabilities. Michel Godet's MICMAC method[^godet-micmac] (developed in France in the 1970s-80s) provides an alternative matrix-analytical approach emphasizing structural influence and dependence patterns across factors, widely used in French and European foresight practice. In contemporary practice, cross-impact analysis is a recognized methodology in academic futures-studies (featured in standard references including Glenn and Gordon's *Futures Research Methodology*[^glenn-gordon-frm-cross] and various Masini-Porter and related textbooks). It is used in governmental foresight (UK Foresight, EU JRC[^eu-jrc-cross-impact], various national foresight programs), in corporate strategy (particularly for long-range planning in industries with strong factor-interaction dynamics like energy and pharmaceuticals), in technology-assessment work (where technology interactions shape adoption pathways), and in environmental and sustainability analysis (where social, economic, environmental, and policy factors interact in complex ways). In risk and emerging-threats analysis, cross-impact methods support scenario development by identifying which factor combinations produce outsized joint risk. In climate-policy analysis, cross-impact methods have been used to examine interactions between technology developments, policy commitments, behavioral shifts, and economic conditions. In business-strategy consulting, cross-impact work is sometimes used in long-range scenario-development engagements, though less often in routine strategy work where simpler methods prevail.

clarity: Cross-impact analysis clarifies interaction effects that single-factor analysis renders invisible. In the absence of explicit interaction assessment, strategic analysis frequently treats factors as independent trajectories — "population will age by X%, technology will mature by Y, policy will shift by Z" — without systematic attention to how these factors shape each other. Cross-impact analysis makes the interactions explicit: population aging shifts technology-adoption patterns; technology maturation enables policy options that were previously infeasible; policy shifts redirect technology investment, which in turn affects maturation rates. The explicit matrix makes these interactions visible and inspectable, including the asymmetries (factor A strongly affects factor B while B only weakly affects A) that are often strategically-consequential. The clarity also extends to identification of leverage factors: factors with strong influence on many other factors (high "driver" influence) are high-leverage targets for strategic action; factors influenced by many others (high "dependent" status) are reflection of the system rather than effective intervention points. The MICMAC method specifically structures output around this driver-vs-dependent quadrant analysis. Finally, the method clarifies risks of oversimplification: if a seemingly simple strategic question involves substantial factor-interaction effects, the cross-impact analysis surfaces this complexity and signals when additional analytical depth is required.

manages_complexity: Cross-impact analysis manages complexity by converting factor-interaction analysis into a systematic pairwise discipline that is tractable for expert panels and interpretable by decision-makers. The pairwise-matrix structure is cognitively accessible: experts asked to assess N-factor systems can do so much more reliably by working through each pair than by trying to hold the full system in mind. The matrix visualization supports interpretation: patterns of influence, clusters of mutually-reinforcing factors, and driver-dependent structures emerge visually from a well-constructed matrix. The mathematical aggregation (where applied) provides a principled way to combine pairwise assessments into system-level measures, though the mathematical output should always be interpreted with awareness of the judgment inputs it rests on. The complexity-management cost is the N² scaling: for factor sets of 20, there are 380 directed pairs (excluding diagonal); for 30 factors, 870 pairs; for 50, 2,450. At larger sizes, the elicitation becomes prohibitively costly and the interpretation unmanageable. Mature practice responds by tight factor-set selection (using STEEP/PESTLE scanning and Delphi prioritization to select the 15-25 most strategically-relevant factors), by hierarchical cross-impact analysis (breaking the factor set into clusters with separate within-cluster analysis plus across-cluster analysis), and by selective elicitation (using expert judgment to identify which pairs are likely to have substantial impact and focusing elicitation on those).

abstract_reasoning: Cross-impact analysis embodies a deep principle about emergent behavior in interconnected systems: *the behavior of a system of interconnected factors is not the sum of the behaviors of the individual factors; interactions produce emergent patterns (amplification, cancellation, thresholds, cascades) that cannot be inferred from single-factor analysis*. This connects to several analytical traditions. In statistics, interaction terms in regression and factorial-design models capture the same principle (see the reciprocal-tight-pair with factorial_design #443). In complex-systems theory, the concept of emergence describes how system-level behavior differs qualitatively from component-level behavior. In ecology, the community-level dynamics of ecosystems cannot be inferred from species-level population biology alone. In economics, general-equilibrium analysis captures how markets interact with each other in ways that partial-equilibrium analysis misses. In engineering, system-of-systems analysis addresses how the interactions of subsystems produce overall behavior. The abstract-reasoning depth of cross-impact analysis lies in its pragmatic middle-ground position: it is more systematic than informal interaction-awareness but more tractable than full dynamic simulation; it captures genuine interaction structure without requiring the data or computational resources of more-formal methods. This pragmatism makes it valuable in strategic-analysis contexts where the information to support more-formal methods is unavailable but where interaction-ignorance is strategically costly.

knowledge_transfer:
**Governmental foresight (national)** → factor-set size: 20-30 → impact-assessment mode: qualitative scale + rationale → primary output: factor-interaction map, scenario inputs
**Corporate long-range planning** → factor-set size: 15-25 → impact-assessment mode: qualitative + sometimes probabilistic → primary output: driver-dependent analysis
**Technology-assessment studies** → factor-set size: 10-20 → impact-assessment mode: qualitative → primary output: technology-adoption pathway analysis
**Energy / climate planning** → factor-set size: 20-40 → impact-assessment mode: mixed → primary output: scenario inputs, policy-leverage analysis
**Pharma / biotech long-range** → factor-set size: 15-25 → impact-assessment mode: qualitative + probabilistic → primary output: technology-market convergence analysis
**Defense / security analysis** → factor-set size: 15-30 → impact-assessment mode: qualitative → primary output: threat-environment analysis
**Risk-management / enterprise** → factor-set size: 20-30 → impact-assessment mode: ordinal rating → primary output: risk-interaction patterns
**Urban / infrastructure planning** → factor-set size: 15-25 → impact-assessment mode: qualitative → primary output: development-dynamics analysis
**Policy analysis (specific domain)** → factor-set size: 10-20 → impact-assessment mode: qualitative + sometimes probabilistic → primary output: policy-leverage identification
**Academic futures research** → factor-set size: 15-30 → impact-assessment mode: various → primary output: methodological contribution / specific-domain insight

The shared structure across contexts is systematic pairwise factor-interaction analysis with some form of aggregation or interpretation; the distinctions lie in the factor-set size, impact-assessment rigor, and primary output emphasis. Larger factor sets (energy/climate, risk-management at 20-40) reflect the breadth of genuinely interacting factors in those domains but impose substantial elicitation costs; smaller factor sets (technology-assessment, policy-specific at 10-20) reflect the tighter analytical focus and the tractability constraint of expert panels. The impact-assessment mode is also analytically consequential: qualitative scales (strong positive / weak positive / neutral / weak negative / strong negative) are cognitively accessible for large panels but lose nuance; probabilistic modes produce richer output but require substantially more elicitation effort and tolerate less expert disagreement. The primary-output column signals what the analysis is for: scenario-input work produces qualitatively different output than policy-leverage work, and selecting the output emphasis shapes the earlier steps of the analysis.

prose:
*(Pass B — pending; see `tracker/v2_upgrade.md`.)*

### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As related prime (2):** `interaction_effect_mapping`, `teleconnection_mapping`

notes:
Origin-domain: v1 had only futurism_strategic_foresight. V2 adds operations_research as alternate, reflecting the method's development with operations-research-flavored mathematical aggregation (Gordon's EIR[^gordon-eir], Godet's MICMAC[^godet-micmac]) and its substantial overlap with operations-research methods for analyzing interacting-factor systems. The primary origin remains futurism_strategic_foresight because the method's codification and primary use is in strategic-foresight practice; the operations-research alternate acknowledges the mathematical-methods overlap.

No review flags — the method is well-defined with multiple stable variants (Gordon EIR, Godet MICMAC, probabilistic variants) that are well-characterized in the literature. Its relationship to related methods (factorial interaction analysis in factorial_design #443 as reciprocal tight-pair, Bayesian networks, systems dynamics, future_wheel #460, steep_pestle_analysis #463) is clear.

The reciprocal tight-pair with factorial_design (#443) deserves a brief note: factorial design is the experimental analog that directly observes interaction effects when manipulation is possible; cross-impact analysis is the judgment-based analog for domains where manipulation is not possible. Both methods share the underlying principle that interaction effects cannot be inferred from independent single-factor analysis. Analytical practice that treats interaction effects as secondary afterthoughts — rather than as first-class analytical objects — routinely underestimates them in both experimental and judgment-based contexts; the two primes jointly articulate the principle across both contexts.

Pass B Solution Archetype authoring deferred.


Cross-Level Inference

one_liner: Carry a predicate, relationship, estimate, or explanation from one level of an organized system to another through a stated or assumed bridge whose preservation conditions determine whether the target claim is warranted.

core_idea:
Cross-level inference carries a predicate, relationship, estimate, or explanation from one level of an organized system or representation to another. It begins with a claim supported at a **source level**, advances a corresponding claim at a different **target level**, and relies on a stated or assumed **bridge** that is supposed to preserve the relevant content across the change of level.

Cross-level movement is not automatically erroneous. The mass of known components can determine the mass of their whole when the system boundary is fixed and addition is the appropriate bridge. Group-level observations may support individual-level conclusions when a model supplies and tests the necessary assumptions. Historical evidence about a person may support a wider descriptive claim when case selection, representativeness, and interpretation justify the reach. The operation becomes unwarranted when the bridge is absent, when its preservation conditions fail, or when the target claim is stronger than the bridge supports.

The prime therefore names neither a generic “level confusion” nor an error class. It names the neutral inferential operation whose valid and invalid instances can be distinguished. Direction matters—upward and downward transfers expose different confounds—but direction alone does not decide warrant.

structural_signature:
- **the organized levels** — at least two distinguishable levels in a system, population, representation, or explanation
- **the source level** — the level at which the predicate, relationship, estimate, or explanation is supported
- **the target level** — the different level at which a corresponding conclusion is proposed
- **the carried claim** — the content whose preservation is at issue
- **the level-changing bridge** — an aggregation rule, distribution rule, mechanism, sampling argument, interpretation, model, or other mapping between levels
- **the preservation conditions** — the assumptions under which the bridge retains the content relevant to the target claim
- **the direction and magnitude** — whether the inference moves upward, downward, or across nested levels, and how many inferential steps it spans
- **the warrant verdict** — the target is licensed, qualified, or rejected after the bridge and its assumptions are examined

what_it_is_not:
It is not a prohibition on reasoning across levels. Cross-level evidence is often indispensable, and explicit bridges can license it.

It is not a metaphysical claim that higher and lower levels must differ. Whether a property preserves, aggregates, emerges, or disappears is exactly what the bridge must establish.

It is not simply the choice of a level of analysis. One can choose a coarse or fine grain without carrying any claim between them.

It is not identical to statistical inference. Statistical inference can reason from a sample to a population at the same unit and level; cross-level inference can occur without sampling or probability.

It is not itself a fallacy. Fallacy of Composition and Fallacy of Division are defective directional species. The prime also includes warranted transfers and therefore cannot replace their independent Informal Fallacy ancestry.

broad_use:
- **Multilevel statistics and epidemiology** — using group-level measurements to estimate individual-level effects, or using individual observations to support group-level parameters, while controlling aggregation, composition, contextual effects, and model specification.
- **Historical description and case research** — using evidence about a person, event, archive, or locality to support claims about a group, institution, period, or population through an interpretation whose reach can be evaluated.
- **Organizational research** — moving between member reports and team- or organization-level constructs by specifying agreement, composition, emergence, and the unit to which the construct belongs.
- **Systems and engineering reasoning** — carrying component properties to configured systems, or system requirements to components, through explicit closure, interface, load, conservation, or allocation rules.
- **Biological and social explanation** — connecting processes or regularities at organism, population, institution, and collective levels without silently treating causation or selection at one level as a property of another.
- **Argument analysis** — diagnosing the upward and downward cases in which a whole–part predicate is transferred without a preservation rule.

clarity:
The abstraction replaces the vague warning “do not mix levels” with five inspectable questions:

1. At what level was the source claim actually established?
2. At what different level is the target claim asserted?
3. What content is meant to survive the move?
4. What bridge is supposed to preserve it?
5. Under what conditions does that bridge succeed or fail?

This decomposition matters because the same source fact can support targets of very different magnitude. A letter may support a claim about its author more readily than a claim about a regiment, a generation, or a society. Naming source, target, bridge, and magnitude prevents the scale of the conclusion from hiding inside an apparently ordinary generalization.

manages_complexity:
Cross-level problems appear heterogeneous because each domain names different failure modes: aggregation bias, ecological fallacy, atomistic fallacy, contextual effects, construct composition, reduction, emergence, or unrepresentative case extension. The prime compresses them without flattening them. Each case instantiates the same role structure while retaining a domain-specific preservation test.

It also separates the operation from its verdict. A catalogue organized only around fallacies makes valid transfers look exceptional and encourages the false rule that any change of level is illicit. A neutral parent instead permits the DAG to place defective upward and downward forms under a common mechanism while leaving additive, model-based, and well-supported interpretive transfers visible as legitimate instances.

abstract_reasoning:
Let \(L_s\) and \(L_t\) be distinguishable source and target levels. Let \(C_s\) be a claim supported at \(L_s\), and let \(B\) be a proposed bridge from claims at \(L_s\) to claims at \(L_t\):

\[
C_s \text{ at } L_s,\qquad B:L_s\rightarrow L_t,\qquad
\therefore C_t=B(C_s) \text{ at } L_t.
\]

The conclusion is warranted only when:

- \(B\) is appropriate for the kind of content being carried;
- the assumptions under which \(B\) preserves that content hold;
- no omitted composition, contextual, interaction, selection, or measurement process changes the target;
- and the specificity of \(C_t\) does not exceed what the bridge can support.

For an upward transfer, an additive quantity may use summation, while a qualitative predicate may require closure under composition. For a downward transfer, a whole-level total generally cannot distribute, while membership predicates sometimes can. For an estimated relationship, equality between within-group and between-group effects is a substantive assumption rather than a consequence of observing an aggregate association.

knowledge_transfer:
The abstraction transfers as the same mechanism because its roles do not change. Statistics supplies group and individual units, an estimated association, and a model. History supplies evidence at one descriptive level, a broader population or period, and an interpretation. Organizational research supplies member-level observations, a collective construct, and a composition model. Engineering supplies component tests, system behavior, and an interface or closure rule.

The domain changes the bridge and the evidence used to validate it. It does not change the underlying act: a claim crosses from a source level to a target level under preservation conditions. That stable role set is what clears the prime bar. The human act of inferring keeps the node at the framed-formal boundary; its portability does not make it observer-free.

notes: _(New framed-formal prime; queued for Claude house-style harmonization, FACT anchoring, and independent citation review.)_


Crossover Interaction

one_liner: The same input moves an outcome in opposite directions across levels of a second condition, so neither factor has a context-free sign and a main-effect average can cancel the mechanism to zero.

core_idea:
A crossover interaction is the structural case in which the effect of one input
reverses direction across levels of a second condition. The same treatment, signal,
event, perturbation, or feature raises an outcome in one state and lowers it in another.
The effect therefore has no context-free sign: it is the joint input-by-condition term,
not either input's averaged main effect, that carries the mechanism.

In a two-factor representation, let `Y(x,z)` be the outcome under focal input `x` and
modifying condition `z`. A crossover is present when the conditional contrast
`Y(1,z)-Y(0,z)` is positive for at least one level of `z` and negative for another. The
lines in an interaction plot cross; in a regression the interaction term is large
enough to carry the conditional effect through zero; in a mechanistic description the
same incoming event is routed through state-dependent pathways with opposite net
directions.

The zero-crossing is the load-bearing feature. Ordinary effect modification includes
cases where an intervention helps strongly in one state and weakly in another. A
crossover interaction is narrower: the direction itself reverses. That makes marginal
summaries particularly dangerous. Averaging +3 and -3 can yield zero even though the
input is strongly active in every case, and changing the mixture of states can make the
reported main effect appear positive, null, or negative without changing either
conditional mechanism.

structural_signature:
*the focal input* — *the modifying condition* — *the conditional response function* —
*the positive-effect branch* — *the negative-effect branch* — *the zero-crossing* —
*the marginal-cancellation hazard* — *the state-qualified intervention rule*

The pattern is present when:

- **A focal input can be held fixed.** The same treatment, event, signal, or
  perturbation is compared across conditions.
- **A second condition changes the input's effect.** This may be an operating state,
  baseline level, co-present agent, environment, prior evaluation, or encoding context.
- **The conditional effect is signed.** Relative to an explicit reference, the input
  raises the outcome in at least one condition and lowers it in another.
- **The response crosses zero.** The difference is qualitative, not merely a change in
  strength.
- **The marginal effect is mixture-dependent.** An average over conditions can be
  small, zero, or directionally misleading because positive and negative branches
  cancel.
- **Action must be state-qualified.** “Apply X” is incomplete; the valid rule is
  “apply X when Z is in the branch where its conditional effect has the intended
  sign.”

what_it_is_not:
- **Not every `synergy_and_antagonism` case.** The parent covers any joint effect that
  departs from a declared no-interaction baseline. A combination can be mildly
  super-additive or sub-additive while the focal factor retains the same sign at every
  level. Crossover is the strict subset whose conditional effect reverses.
- **Not mere heterogeneity.** Different units can have effects of +2 and +5. That is
  heterogeneous magnitude but not a crossover; all effects point the same way.
- **Not `Simpson's paradox`.** Simpson reversal can arise because subgroup weights or
  base rates differ, even when every conditional association has the same direction.
  Crossover interaction is a property of the conditional effects themselves.
- **Not `contrast`.** Contrast makes a difference perceptible or measurable. Crossover
  specifies a two-factor response law in which that difference changes sign.
- **Not ordinary `bayesian_updating`.** With a fixed likelihood model, one observation's
  likelihood ratio has the same direction for all non-degenerate priors: it may move a
  posterior by different amounts, but it does not support a hypothesis under one prior
  and oppose it under another merely because the prior changed. A sign reversal requires
  the evidence model or response mechanism itself to be condition-dependent.
- **Not generic `nonlinearity`.** A saturation, threshold, or quadratic response is
  nonlinear without requiring two conditions or a sign reversal. Crossover is one
  specific interaction-shaped nonlinearity.

broad_use:
- **Factorial experiments and causal analysis:** a treatment helps one subgroup and
  harms another, making a pooled average an unsafe intervention rule.
- **Receptor pharmacology:** the same partial agonist raises response when acting alone
  or against low endogenous tone but lowers response when it displaces a stronger full
  agonist.
- **Psychology and social evaluation:** a minor blunder humanizes a person with a high
  competence prior but confirms a negative impression of a mediocre person.
- **Learning and memory:** a retrieval state helps when it matches the encoding state
  and hurts relative recall when it mismatches, producing the diagnostic matched-cell
  crossover.
- **Genetics and ecology:** a genotype or trait can raise fitness in one environment and
  lower it in another, so no environment-free fitness sign exists.
- **Engineering and operations:** a control action or design change can stabilize one
  operating regime and destabilize another, requiring regime-conditioned deployment.

clarity:
The prime replaces the sentence “the effect depends on context” with a testable claim:
name the focal input, name the modifying condition, estimate the conditional effect in
each branch, and check whether the sign crosses zero. This distinguishes a true
directional reversal from vague sensitivity, unequal effect sizes, or an aggregate
artifact.

It also prevents the most damaging interpretation of a near-zero main effect. When
positive and negative conditional effects cancel, “nothing happened” is precisely
wrong. The system reacted strongly in both branches; the analyst destroyed the
mechanism by averaging across the variable that sets its direction. The useful result
is the interaction table, not the pooled coefficient.

manages_complexity:
Without the abstraction, each state-conditioned reversal looks like a local exception:
one drug is paradoxically agonist and antagonist, one teaching condition helps and
hurts, one mistake raises and lowers trust. Crossover Interaction compresses these into
one two-factor object. Track a focal input, a modifying condition, two conditional
effects, and their zero-crossing. The apparent contradictions become ordinary branches
of one response function.

The compression also organizes interventions. If the modifying condition is observable,
route the input only into the beneficial branch. If it is controllable, move the system
across the crossover before applying the input. If it is hidden, a pooled policy is
unsafe and the immediate problem is state estimation. If the conditional effects are
large but the average is small, increasing sample size for the main effect will not
recover the mechanism; the design must preserve or manipulate the condition.

abstract_reasoning:
The prime licenses several moves:

- **Conditional-effect diagnosis:** compute the effect of X at each level of Z rather
  than reading a single main-effect coefficient. Opposite signs identify a crossover.
- **Backward inference from cancellation:** a small pooled effect combined with large
  within-state movements suggests an omitted modifier rather than an inert input.
- **State-qualified prediction:** the correct forecast is a branch rule — X raises Y
  under Z1 and lowers Y under Z2 — not a universal sign.
- **Intervention routing:** observe or control the modifier before deploying the focal
  input. A policy that ignores Z will help and harm different regimes by construction.
- **Mixture sensitivity:** changing the prevalence of Z can change the marginal effect's
  sign without changing the conditional response law, so transport to a new population
  requires its state mixture.
- **Mechanism search:** a crossover implies at least two routes, reference points, or
  competitive processes whose net dominance changes across Z; search for the
  zero-crossing mechanism rather than treating the branches as inconsistent evidence.

knowledge_transfer:
The role mapping is exact across substrates. In the Pratfall Effect, the focal input is a
minor blunder, the modifier is the observer's competence estimate, and liking rises in
the high-prior branch but falls in the mediocre branch. In Partial Agonism, the focal
input is the ligand, the modifier is competing agonist tone, and net receptor response
rises when the ligand supplies activation but falls when it displaces a stronger
driver. In State-Dependent Learning, the focal input is retrieval state, the modifier is
encoding state, and the same retrieval condition helps the matching trace while
hindering the mismatched one.

These are not analogies. Each has the same signed conditional-effect table and the same
failure mode: collapse over the modifier and the average conceals the response law. The
domain mechanisms differ, but a reasoner transfers the same diagnostic — hold X fixed,
stratify on Z, inspect the sign, and condition the intervention.

notes:
_(ChatGPT-authored to resolve the parked `prior_conditional_update_asymmetry` gate.
Claude should re-author in established house style, add primary-source citations and
FACT anchors, and preserve the formal identity, aliases, exact v1/v2 one-liner, and DAG
placement.)_