Researcher Degrees of Freedom

one_liner: The unpinned analytic choices between a question and a reported result, where a silently explored decision tree collapses into a single declared comparison, inflating false confidence without any individual choice being made in bad faith.

core_idea:
Researcher degrees of freedom name the *unpinned analytic choices* that
sit between a research question and a reported result — which subjects
to exclude, which transformations to apply, which covariates to include,
which test to run, when to stop collecting data, which subgroup to
report, which outcome to feature. Each choice is locally defensible; the
structural problem is that the *garden of forking paths* explored
silently in private becomes a *single declared comparison* in public.
This silent multiplicity inflates the false-positive rate by orders of
magnitude even when no individual decision was made in bad faith.

The pattern is not bias, fraud, or motivated reasoning in any
single-choice sense. It is the *gap between a flexible decision tree and
the singular report*, where the flexibility itself is the source of
inferential failure. The structure has a definite shape: a research
question or estimation target; an analytic decision tree with a branch
at every unfixed choice; a silent comparison budget, equal to the size
of the tree actually explored; a visible single report, one leaf
summarised as the result; an inferential warrant gap between the
declared and the exercised multiplicity; and a pre-commitment lever —
registration, holdout, multiverse — that can collapse or reveal the
budget.

What makes the pattern distinctive is that the multiplicity is
*invisible*. Declared multiple testing has standard corrections; here
the comparisons are made silently, as analytic choices rather than
explicit tests, so the corrections do not apply because no one can see
the budget to correct for it. The inferential warrant depends not on the
comparison reported but on the size of the tree from which it was
selected — a counterfactual ("which fraction of the tree would have been
reported had it come out positive?") that no reader can audit.

structural_signature:
*the question or estimation target* — *the analytic decision tree branching at every unfixed choice* — *the silent comparison budget equal to the tree actually explored* — *the visible single report, one leaf declared as the result* — *the warrant gap between declared and exercised multiplicity* — *the pre-commitment lever that can collapse or reveal the budget*

A process exhibits this pattern when each of the following holds:

- **A question or estimation target.** A research, evaluation, or inference goal whose answer will be reported.
- **An analytic decision tree.** A set of unpinned choices — exclusions, transformations, covariates, tests, stopping rules, subgroups, outcomes — each branching the path from question to result; every branch is individually defensible.
- **A silent comparison budget.** The de-facto multiplicity is the size of the tree actually explored, exercised privately as analytic choices rather than as declared tests, so standard multiple-comparison corrections do not see it.
- **A visible single report.** One leaf of the tree is summarised publicly as *the* result, as though it were a single pre-planned comparison.
- **A warrant gap.** The inferential warrant depends not on the comparison reported but on the size of the tree from which it was selected — a counterfactual no reader can audit.
- **A pre-commitment lever.** Registration, holdout separation, or multiverse reporting can collapse the silent multiplicity into something visible or fix the tree before the data are seen.

These compose so that the pathology requires no bad faith in any single choice: invisible multiplicity inflates false confidence, and every remedy is the same move — make the comparison budget visible or pre-committed.

what_it_is_not:
- **Not regret.** `regret` is a backward-looking *valuation* of a forgone alternative outcome; researcher degrees of freedom is a *forward inferential pathology* of silent multiplicity inflating false confidence. One is about counterfactual loss felt; the other about an un-auditable comparison budget.
- **Not selection bias.** `selection_bias` distorts a sample at *data collection*; researcher degrees of freedom distorts inference at *analysis*, through choices made after the data are in hand. Sampling vs. analytic flexibility.
- **Not multiple comparisons.** `multiple_comparisons_correction` handles *declared* tests with known corrections; the whole pathology here is that the comparisons are *silent* — analytic choices no one can see, so corrections cannot be applied. (Same statistical root, opposite visibility.)
- **Not overfitting.** `overfitting` is a *model* fitting noise in training data; researcher degrees of freedom is a *reporting* pathology where one leaf of an analytic tree is declared as if pre-planned. Backtest overfitting is one instance, not the prime.
- **Not confounding.** `confounding` is a *causal-structure* error — a lurking common cause; researcher degrees of freedom is an *inferential-warrant* error from selecting a result out of a large tree, even with no causal confound.
- **Common misclassification.** Hunting for the one biased choice and auditing each decision (finding all defensible) while the warrant is already gone. Catch it by shifting from "was any choice biased?" to "how many de-facto comparisons did this report collapse into one?"

broad_use:
The pattern recurs wherever flexible analysis culminates in a singular
declared result. In **statistics and empirical science** — the canonical
home — ordinary, plausible analytic flexibility can raise the
false-positive rate of a nominal five-percent test above sixty percent,<!-- FACT-D70-626 -->[^simmons-etal-2011]
and the "garden of forking paths" extends the point even to
single-comparison analyses that are data-dependent.<!-- FACT-D70-627 -->[^gelman-loken-2013] In **machine-learning
evaluation**, tuning on the test set, model selection across many
architectures, choice of benchmark suite, and prompt selection each
reproduce the structure: many silent comparisons summarised as one.<!-- FACT-D70-628 -->[^recht-etal-2019] In
**financial backtesting**, strategy researchers explore hundreds of
variants on the same historical data and report the best, the pattern
known there as backtest overfitting.<!-- FACT-D70-629 -->[^bailey-etal-2014] In **policy and program
evaluation**, the choice of outcome window, comparison group, control
variables, and treatment definition each introduces flexibility that
survives into the published estimate. In **audit and accounting**, the
choice of inventory method, depreciation schedule, accrual timing, and
segment definition gives the same forking structure for one underlying
business.<!-- FACT-D70-630 -->[^healy-wahlen-1999] In **investigative journalism and intelligence analysis**, the
choice of framing, which sources to weight, and which timeframes to
compare reproduces the identical structure under a different label.<!-- FACT-D70-631 -->[^heuer-1999]

clarity:
The label clarifies a phenomenon that single-study failure modes cannot
explain: the *systematic over-statement of confidence across an entire
field*, even when each study looks careful. Once one sees the
flexibility as a multiplicative comparison budget rather than as care,
the inferential pathology snaps into focus — the field is not unlucky or
sloppy study by study; it is selecting from a large tree and reporting
the selection as though it were the whole.

The frame also forces a separation between two questions that are
routinely fused: whether each individual analytic choice was defensible
(usually yes), and whether the *set* of choices, taken as a silent
comparison budget, warrants the reported confidence (usually no). By
making the budget the object of attention rather than any single
decision, the frame defuses the unproductive search for the one bad
choice and replaces it with a structural question about the size of the
tree. The clarifying move is to stop asking "was this analysis biased?"
and start asking "how many de-facto comparisons did this report quietly
collapse into one?"

manages_complexity:
The pattern compresses a sprawling list of micro-choices — exclusions,
transformations, covariates, tests, stopping rules, subgroups, outcomes
— into a single structural quantity: how many de-facto comparisons did
the report quietly collapse? An analyst can communicate the entire
diagnosis in one phrase, and the remedy menu follows directly from it,
because every remedy is a way of either pre-committing the tree or
revealing it. A confusing audit of dozens of individual decisions
becomes one estimate of the comparison budget.

The compression matters because it reframes the analysis itself as a
*decision tree of branches with implicit selection*, where the visible
report is one leaf and the inferential warrant depends on the size of
the tree. This lets the analyst reason about inferential confidence as a
function of the comparison budget exercised rather than the comparison
reported — a single lever — and it makes the remedies commensurable,
since pre-registration, holdout separation, and multiverse reporting are
all the same structural move (collapse the silent multiplicity into
something visible or pre-committed) expressed in different vocabularies.

abstract_reasoning:
The frame licenses a specific inference: an analysis should be modelled
as a tree whose branches are the unfixed choices, with the reported
result one leaf, and the warrant of that result discounted by the size
of the tree that could have been explored and selectively reported. From
this follows the central deduction — that confidence stated as though
the report were a single pre-planned comparison is unwarranted whenever
the underlying tree was large and data-dependent, regardless of the good
faith of any branch.

The reasoning carries a heavy institutional and normative load that the
frame does not hide. The very category "researcher" presupposes a
scientific or evaluative reporting institution; the framing of
false-positive inflation as an *inferential failure* presupposes norms
about what a reported result is supposed to warrant. The pattern is
therefore strongly framed rather than structural: its vocabulary travels
only with translation, it carries an explicit evaluative charge, and it
is bound to human practices of analysis and reporting. The structural
core that *could* be extracted — silent multiplicity collapsed into a
singular declaration — is portable, but as the prime is written it
imports the reporting-norm context wholesale, which is what makes the
inference about warrant meaningful rather than merely descriptive.

knowledge_transfer:
The remedies travel together with the diagnosis because the roles map
across domains: the *decision tree* maps to analytic-choice trees,
hyperparameter and architecture sweeps, backtest variant spaces, or
specification spaces; the *silent comparison budget* maps to the size of
any of these; the *visible single report* maps to the published effect,
the headline benchmark number, the reported strategy return, or the
published estimate; and the *pre-commitment lever* maps to
pre-registration, held-out test sets, or multiverse and specification-curve
reporting. Because the roles correspond, each remedy is the *same
structural move* — collapse silent multiplicity into something visible
or pre-committed — even though every domain invented its own name for it.

The documented transfers are concrete. Pre-registration fixes the
analytic plan before the data are seen so flexibility cannot be
exercised silently; multiverse analysis reports results across many
plausible branches and lets the reader see the distribution; held-out
test sets physically separate exploration data from evaluation data so
exploration multiplicity cannot leak into the evaluation; reporting
standards make the comparison budget visible by requiring declaration of
the branches considered; specification curves visualise the distribution
of estimates across all defensible specifications; and adversarial
collaboration lets opposing teams set the analytic plan together,
eliminating one-sided flexibility. The same diagnosis — a silent
decision tree exceeding the declared comparisons — and the same
intervention menu — pre-commitment, holdout separation, multiverse
reporting — work in finance backtests, machine-learning benchmarks,
policy evaluations, and audits, which is the cross-domain signature: the
pattern travels with its mechanism and its remedy set, not merely its
vocabulary. The transfer remains framed rather than purely structural,
because in every destination domain it carries the same normative claim
that a singular declared result must warrant the confidence placed in
it, and that claim presupposes a reporting institution whose standards
the silent multiplicity violates.

formal_abstract:
Consider a psychology experiment testing whether a priming manipulation affects a behavioural outcome, the canonical home of the prime. The question is fixed, but the path from data to result branches at every unpinned choice. There are two candidate outcome measures (reaction time, accuracy); three defensible exclusion rules (drop responses faster than 200 ms, slower than 3 s, or beyond 2.5 SD); a choice of whether to log-transform skewed reaction times; the option to control for age and sex or not; and two plausible subgroups (the effect "in women," "in the high-anxiety subset"). These choices multiply: even this modest tree has roughly $2 \times 3 \times 2 \times 2 \times 3 = 72$ analytic paths.<!-- FACT-D70-632 -->[^simmons-etal-2011] If each path is an independent-ish test at a nominal $\alpha = 0.05$, the probability that *at least one* yields $p < 0.05$ under a true null is $1 - 0.95^{72} \approx 0.97$ — near-certain.<!-- FACT-D70-633 -->[^simmons-etal-2011] This is the silent comparison budget: the researcher explores the tree privately, finds the one leaf where "the priming effect is significant in women after excluding fast responders and controlling for age," and writes it up as a single declared comparison. No individual choice was made in bad faith; each is defensible. But the warrant gap is total — the reader sees one $p$-value and cannot audit the 72-path tree it was selected from, so the nominal 5% false-positive rate is a fiction. The pre-commitment lever collapses the budget: a pre-registered analysis plan fixes outcome, exclusions, transform, and covariates *before* the data are seen, so the tree shrinks to one path and the reported $p$ means what it claims; a multiverse analysis instead reports the effect across all 72 specifications, letting the reader see the distribution rather than the cherry.

**Mapped back:** the priming hypothesis is the question, the outcome/exclusion/transform/covariate/subgroup choices are the analytic decision tree, the 72 paths are the silent comparison budget, the single written-up significant result is the visible report, the un-auditable gap between nominal and effective $\alpha$ is the warrant gap, and pre-registration or multiverse reporting is the pre-commitment lever.

applied_industry:
Quantitative financial backtesting reproduces the identical structure under the name "backtest overfitting," and the substrate is the same fixed historical price series. A research team wants a profitable trading strategy. The decision tree branches over lookback window (20, 50, 200 days), entry threshold, which technical indicators to combine, the universe of assets, the rebalancing frequency, and the in-sample date range — easily thousands of variant strategies, all run against the *same* market history.<!-- FACT-D70-634 -->[^bailey-etal-2014] The silent comparison budget is the full set of variants tested in private; the visible single report is the one strategy with the best Sharpe ratio, presented to the investment committee as "our momentum strategy returns 18% annually with a Sharpe of 2.1."<!-- FACT-D70-635 -->[^bailey-etal-2014] The warrant gap is exactly the prime's: a Sharpe of 2.1 selected as the maximum over 2,000 variants is statistically unremarkable — you expect a high-Sharpe outlier by chance alone — but the committee sees one number and cannot discount it for the size of the tree it won. The remedies are the same structural move as pre-registration, in finance vocabulary: hold out a test period the researchers never touch during exploration (physically separating exploration data from evaluation data so exploration multiplicity cannot leak in); report the deflated Sharpe ratio that corrects for the number of trials; and run the strategy forward on genuinely new data before committing capital.<!-- FACT-D70-636 -->[^bailey-etal-2014] The same diagnosis and remedy menu govern machine-learning benchmark gaming (tuning architectures and prompts on the test set, then reporting the best as a single headline number) and policy-evaluation specification search.

**Mapped back:** the profitable-strategy goal is the question, the lookback/threshold/indicator/universe choices are the decision tree, the thousands of tested variants are the silent comparison budget, the best-Sharpe strategy is the visible report, the un-discounted selection-from-the-max is the warrant gap, and holdout periods plus deflated-Sharpe correction are the pre-commitment levers — the same framed structure operating across empirical science, quantitative finance, and ML evaluation.


Reserve

type: prime

slug: reserve

one_liner: Deliberately maintained surplus held beyond expected need so the system can absorb variation, uncertainty, or shock without failing.

status: draft

review_flags: ACCEPTED as a prime from project-06 (Kurt, 2026-05-27). Name "reserve" chosen over "buffer" because `buffering` already exists as the PROCESS prime (the act of maintaining a reserve), so "reserve" names the held surplus without collision.

review_flags: HUB: re-parenting of `margin_of_safety`, `system_slack`, and `buffering` to `reserve` is PROPOSED for round-7 model review (not yet committed). `margin_of_safety` remains provisional -> `system_slack` until that confirms.

review_flags: substrate_independence scores are PROPOSER estimates, pending triangulation.

review_flags: 2026-05-28 schema reformat: original project-06 v1 used the 5-section template (Core Idea / Broad Use / Structural Signature / Distinction from Neighbors / Notes); reformatted to the canonical 8-section runbook v1 schema. Structural Signature content folded into Manages Complexity + Abstract Reasoning; project-06 load-bearing rationale preserved in Notes.

core_idea:
A reserve is a **deliberately maintained surplus of capacity, resource, or time held beyond expected need**, kept so the system can absorb variation, uncertainty, or shock without failing or degrading, a pattern Cyert and March (1963) named "organizational slack" in their behavioral theory of the firm and Bourgeois (1981) later operationalized for empirical work.<!-- FACT-D56-046 -->[^cyert-march-1963][^bourgeois-1981] The surplus is unused in the nominal case *on purpose* — its value is precisely that it is available when demand, load, or disturbance exceeds the expected. The pattern recurs unchanged across engineering safety factors (Petroski, 1985), inventory buffers, capital reserves, cardiac reserve and other physiological capacities (Cannon, 1932), seed banks, spinning reserve on power grids, and memory headroom in computing systems, which together establish reserve as one of the most substrate-neutral structural primes in the catalog.<!-- FACT-D56-047 -->[^petroski-1985][^cannon-1932]

Five roles decompose any reserve: a *resource or capacity* held; an *expected or nominal level of demand* on it; a *maintained surplus* above that level; a *contingency* (the variation, shock, or uncertainty the surplus is held against); and a *draw-down rule* (when and how the surplus is consumed and replenished). Once those five roles are named, an opaque "this system feels fragile" or "this system feels over-built" judgment becomes a structured question about sizing, replenishment, and trigger design. The defining structural commitment travels with the pattern: the surplus is held on purpose and unused in the nominal case, which is what makes it a reserve rather than waste, headroom rather than over-capacity, and prudence rather than hoarding.

structural_signature:
Reserve encodes a structural pattern: **resource + nominal demand + maintained surplus + contingency + draw-down rule**. The surplus persists by policy, not by accident; the contingency is named explicitly; the draw-down is conditional on a triggering deviation from the nominal, the same architecture Hopp and Spearman (2008) develop for inventory and capacity buffers in production systems.<!-- FACT-D56-048 -->[^hopp-spearman-2008] It separates two regimes (nominal-load and contingency-load) and names the held quantity that lets the system cross between them without rupture.

**Recurring features:**

- Deliberately maintained surplus held beyond expected need
- Resource kept unused on purpose against named contingency
- Capacity held in reserve, drawn down under disturbance
- Asymmetric value profile: invisible nominally, decisive under shock
- Held quantity, not the process that maintains it
- Five-role decomposition: resource, demand, surplus, contingency, draw-down
- Defended slack, structurally opposite to eliminable waste

The structural insight is robust across substrates that share no domain vocabulary: a cardiologist's *cardiac reserve* (heart capacity beyond resting output, drawn on under exertion, in the homeostatic vocabulary of Cannon, 1932), an ecologist's *seed bank* (dormant seeds in soil drawn on after disturbance, in the life-history vocabulary of Lack, 1954), a grid operator's *spinning reserve* (generation capacity synchronized and ready), a CFO's *liquidity buffer* (cash held against redemption shocks), and an engineer's *safety factor* (load capacity above maximum expected stress, in the structural-engineering vocabulary of Petroski, 1985) all instantiate the same five-role pattern.<!-- FACT-D56-049 -->[^cannon-1932][^lack-1954][^petroski-1985]

what_it_is_not:
Reserve is **not** waste, though in the nominal case the two are visually indistinguishable. Waste is capacity that is unused because no one needs it; reserve is capacity that is unused *on purpose* because someone is holding it against a named contingency. Both look identical when nothing is happening — neither is doing visible work — but they are structurally opposite. Waste should be eliminated; reserve should be defended. The diagnostic that separates them is the contingency-removal counterfactual: take a candidate held surplus and ask what would happen if the disturbance distribution were known to be zero. If the surplus still looks valuable, it was waste being justified by appeal to contingency; if the surplus stops looking valuable, it was a genuine reserve, a category distinction that aligns with Perrow's (1984) analysis of how coupling and slack determine which surpluses are decorative and which are load-bearing in high-risk systems.<!-- FACT-D56-050 -->[^perrow-1984]

Reserve is **not** the same as the *process* of maintaining or replenishing a surplus. That process is `buffering`. Reserve names the *held quantity*; buffering names the *activity* that keeps the quantity at its target level. A bank's cash reserve is a stock; the treasury operations that move cash in and out to hold the stock at target are buffering. Confusing the two collapses a useful distinction: you can have a reserve with poor buffering (the surplus exists but degrades because no one replenishes it) or strong buffering of an inadequate reserve (the activity is disciplined but the target is set too low). The state-versus-process distinction is the reason the prime was named "reserve" rather than "buffer," which would have collided with the existing process prime.

Reserve is also **not** simply over-provisioning or excess capacity in general. Excess capacity is whatever capacity exceeds current draw; reserve is excess capacity that is held *against a specified contingency*, with a draw-down rule attached. A factory that happens to be running below its theoretical maximum has excess capacity; a factory that explicitly keeps a third shift staffed and trained against the contingency of a demand spike has a reserve. The contingency and the rule are what make capacity a reserve rather than mere headroom.

Reserve says **nothing about optimality of the holding decision**. A system can maintain a reserve that is too small for the actual disturbance distribution (under-reserved, prone to depletion), too large (over-reserved, paying carrying costs without commensurate protection), or correctly sized but badly governed (reserve exists but the draw-down rule is wrong, so the surplus is consumed too early or held past the point of usefulness). The prime describes the structural pattern, not the policy parameters; recognizing that something is a reserve is the start of the sizing conversation, not its conclusion.

broad_use:
**Engineering**: Safety factor and design margin — structural capacity reserved above the maximum expected load, with the surplus expressed as a ratio (a bridge designed to a safety factor of 3 holds three times the worst expected load before yielding), the quantified reserve form Petroski (1985) traces through the cyclic history of structural failure and redesign.<!-- FACT-D56-051 -->[^petroski-1985] Reserve appears in tolerance stacks, derating of electrical components, ballast in ships, and thermal headroom in electronic systems.

**Operations & Supply Chain**: Buffer stock, safety stock, and inventory reserves absorbing demand and supply variability; scheduling slack absorbing timing variability. Just-in-time systems famously minimize reserves to expose waste, accepting greater contingency risk in exchange for lower carrying cost — a deliberate trade-off whose downsides become visible only when the contingency arrives.

**Finance**: Capital reserves and liquidity buffers absorbing losses and redemption shocks; regulatory capital requirements (Basel III) institutionalize reserves as protection against tail-risk losses, as the Basel Committee on Banking Supervision (2011) sets out in the post-crisis "global regulatory framework for more resilient banks."<!-- FACT-D56-052 -->[^bcbs-2011] Central banks hold foreign exchange reserves against currency-market shocks; insurance companies hold loss reserves against claim experience worse than expected.

**Physiology**: Metabolic reserve (substrate stores drawn on under prolonged effort), cardiac reserve (the heart's capacity above resting output, drawn on under exertion), respiratory reserve, and hepatic reserve (the proportion of liver function that can be lost before clinical decompensation). The five-role decomposition is unusually clean in physiology because the contingency (stress, exertion, illness) and the draw-down rule (autonomic regulation) are mechanically observable.

**Ecology**: Seed banks (dormant seeds persisting in soil, drawn on after fire, drought, or canopy disturbance), fat stores in hibernating mammals, energy reserves in migrating birds, and lipid reserves in invertebrates wintering through resource scarcity, instances Lack (1954) integrated into his framework for the natural regulation of animal numbers.<!-- FACT-D56-053 -->[^lack-1954] The ecological case is substrate-furthest from human institutions: no manager is setting the policy; the reserve and its draw-down rule are encoded in the organism's life history.

**Neuroscience**: Cognitive reserve — the brain's capacity to tolerate neurodegenerative pathology without proportionate clinical decline — operationalized as education level, occupational complexity, and engagement, all of which raise the threshold at which underlying damage produces visible deficits. The contingency is age-related neuropathology; the draw-down is the gradual consumption of compensatory capacity.

**Power systems**: Spinning reserve (generators synchronized to grid frequency, producing below rated output, ready to ramp within seconds), non-spinning reserve (fast-start capacity ready within minutes), and replacement reserve (slower-deploying capacity), each sized against a different contingency distribution.

**Computing**: Memory buffers, free-list headroom, swap space, and CPU headroom — all surpluses held against bursty demand, GC pauses, or peak-load spikes, with Hennessy and Patterson (2019) treating the memory hierarchy itself as a stack of reserves sized against access-time and bandwidth contingencies.<!-- FACT-D56-054 -->[^hennessy-patterson-2019] Cluster capacity-planning explicitly sizes reserves against failure-domain contingencies (lose a rack, lose a zone, lose a region).

**Chemistry**: Excess reagent in stoichiometric reactions — a deliberate quantity above the stoichiometric requirement, held against incomplete mixing, side reactions, or analytical uncertainty in the limiting reagent. The excess is consumed only insofar as the contingency manifests; the remainder is recovered or discarded.

clarity:
The prime sharpens a distinction that ordinary language blurs: there is a category difference between *waste* (capacity that is unused because it is not needed) and *reserve* (capacity that is unused on purpose because it is being held against contingency). Both look identical in the nominal case, but they are structurally opposite. Naming the pattern lets the analyst separate "slack we can cut" from "slack the system depends on" — and avoid the chronic error of optimizing reserves away during calm periods, only to find them missing when the disturbance arrives, the very dynamic Bourgeois (1981) identifies in his measurement-focused critique of organizational-slack erosion.<!-- FACT-D56-055 -->[^bourgeois-1981]

It also clarifies why short-horizon optimizers chronically under-fund reserves: the value of a reserve is asymmetric — invisible during nominal operation, decisive during disturbance — and asymmetric value is systematically mis-priced by any objective function that doesn't explicitly model the contingency distribution. The prime gives the analyst a vocabulary for arguing against an optimizer who can't see the contingency: "this is not slack to be cut; it is the system's tolerance for the thing you are not modeling." Without that vocabulary the argument has to be made each time on substrate-specific grounds (the engineer talks about safety factors, the CFO talks about Basel, the grid operator talks about N-1 contingency), and the substrate-specific framings don't transfer when the same person moves between roles.

manages_complexity:
Reserve decomposes a system's relationship to uncertainty into five concrete, separately-tunable roles. A vague intuition that "this system feels under-resourced" becomes: *Which resource is short? Against which contingency? At what surplus level? With what draw-down rule? With what replenishment policy?* Each question is locally tractable; together they specify a reserve policy. The decomposition turns reserve-design from artistry into engineering — sizing, replenishment, and trigger design fall out once the roles are named.

The decomposition also supplies a diagnostic for whether something is a real reserve at all: remove the named contingency from the analysis. If the surplus still looks valuable, the candidate was waste being post-hoc rationalized as a reserve (a common failure mode in organizations that keep capacity around out of habit and only later attach a contingency story). If the surplus stops looking valuable, it was a genuine reserve and the carrying cost is the price of the protection. This contingency-removal test is the same across substrates, which is why the prime carries diagnostic weight without needing domain-specific calibration.

In operations and engineering practice, the five-role decomposition organizes a class of policy decisions that otherwise blur together: how big to make the buffer, how to trigger consumption, how fast to replenish, how to detect chronic under- or over-reserving, when to retire a reserve whose contingency has materially changed. Each decision maps to one or two roles, and conflating the roles is the source of common failures — replenishment policy implicitly setting the surplus level, draw-down triggers being tuned to nominal variation rather than contingency, and so on.

abstract_reasoning:
Reserve supports a class of counterfactuals about robustness: *if the disturbance were larger, more frequent, or of a different shape, would the surplus still absorb it?* That question, applied across substrates, generates the same set of operations — compute the worst-case draw, compute the recovery time, compute the failure mode when the reserve is exhausted, compute the carrying cost of holding it. The defining structural commitment — surplus held on purpose, unused in the nominal case — is what makes the reasoning portable, and is what lets Perrow's (1984) analysis of tight-coupling failures in nuclear, chemical, and aerospace systems be read as a single argument about how unbuffered reserves cascade.<!-- FACT-D56-056 -->[^perrow-1984]

The pattern also enables reasoning about *reserve-of-reserves* structures and recursive contingency layering. A grid has spinning reserve for second-scale contingencies, non-spinning reserve for minute-scale, and replacement reserve for hour-scale; each is sized against a different contingency distribution and each can in principle be exhausted, at which point the next layer engages. A bank has Tier 1 capital, Tier 2 capital, and contingent convertible bonds in similar layering. The structural reasoning that organizes these stacks is the same: each layer is a reserve against the next-faster contingency, and the layering itself becomes a design object once the prime is named.

A second class of counterfactuals concerns *whether something currently treated as nominal demand is actually contingency*. A reserve sized against last decade's disturbance distribution may be massively under-scaled if the distribution has shifted (climate-driven flood reserves, post-pandemic supply-chain reserves, fat-tailed financial-market reserves). The prime gives the analyst the language to ask: what contingency was this reserve sized against, and is that still the right contingency? Without the five-role decomposition, the question is unfocused; with it, the audit is mechanical.

knowledge_transfer:
The five-role pattern is recognizable across substrates that share no domain vocabulary. A cardiologist's cardiac reserve, an ecologist's seed bank, a grid operator's spinning reserve, a CFO's liquidity buffer, and an engineer's safety factor are instances of one pattern. The physiological and ecological cases are particularly clean because no human institution is in the loop — Cannon's (1932) homeostatic reserves and Lack's (1954) life-history energy and seed-bank reserves rule out the suspicion that "reserve" is a managerial specialty rather than a substrate-neutral pattern.<!-- FACT-D56-057 -->[^cannon-1932][^lack-1954]

The cross-domain test for a real instance is the contingency-removal counterfactual: take a candidate reserve and ask what would happen if the disturbance distribution were known to be zero. A genuine reserve becomes obsolete; merely-unused-capacity does not change in value. That test runs in any substrate where the five roles can be named, which is why the prime supports transfer of design intuitions across domains without metaphor. An engineer accustomed to safety-factor reasoning can ask the right questions about a hospital's surge-bed reserve; a treasury operator can ask the right questions about an ecosystem's seed bank. The questions are the same; only the substrate-specific units change.

formal_abstract:
**Chemistry — excess reagent in stoichiometric synthesis.** A reaction nominally consumes reagents in a fixed stoichiometric ratio (say, 1:1 between A and B to produce C). In practice the chemist supplies A in excess — perhaps 1.2 equivalents per equivalent of B — so that incomplete mixing, side reactions, and any analytical uncertainty in the actual concentration of B do not leave B unreacted at the end. The roles are visible: the resource is moles of A; the nominal demand is one equivalent per equivalent of B; the maintained surplus is the extra 0.2 equivalents; the contingency is the set of departures from idealized stoichiometry (mixing inhomogeneity, side reactions, concentration uncertainty); the draw-down rule is "consume as the reaction progresses to drive B fully to product." Remove the contingency (perfectly mixed, no side reactions, exactly known concentration of B) and the excess collapses to waste. Keep the contingency and the excess is what guarantees complete consumption of the limiting reagent. **Mapped back:** The contingency-removal counterfactual cleanly classifies excess reagent as a genuine reserve rather than waste, and the five-role decomposition recovers the chemist's intuitive practice as an instance of one substrate-neutral pattern. Chemistry is one of the substrate-furthest cases because no human institutional layer mediates the reserve — the practice is justified by the molecular-scale contingency distribution alone.

**Ecology — lipid reserves in hibernating mammals.** A ground squirrel accumulates fat during summer foraging and enters hibernation with lipid stores well above the resting metabolic requirement of the dormant phase. The roles are visible: the resource is stored lipid; the nominal demand is the basal metabolism of active-season life; the maintained surplus is the pre-winter accumulation above active-season needs; the contingency is the extended period of food unavailability across winter (which may vary in length and severity); the draw-down rule is the suppressed basal metabolism of torpor, with periodic arousal episodes drawing on the stores more aggressively. Remove the contingency (food available year-round) and the lipid reserve becomes pure metabolic cost (carrying weight reduces foraging efficiency and increases predation risk). Keep the contingency and the reserve is the difference between surviving winter and not. **Mapped back:** No human institution sets the policy; the contingency distribution and the draw-down rule are encoded in the organism's life-history strategy and selected for over evolutionary time. The ecological case is the cleanest demonstration that reserve is a substrate-neutral pattern rather than a managerial specialty, and that the five-role decomposition recovers a structural logic that natural selection arrives at independently of human reasoning about it.

applied_industry:
**Power grid — spinning reserve.** A regional system operator maintains generators synchronized to grid frequency, producing below their rated output, ready to ramp within seconds. The roles: resource is generation capacity; nominal demand is the forecast load curve; maintained surplus is the headroom above current dispatched output; contingency is the sudden loss of a large generator or transmission line (the N-1 criterion); draw-down rule is automatic, triggered by frequency drop, all of which Kirschen and Strbac (2019) catalogue as the operating-reserve services that hold modern power markets together.<!-- FACT-D56-058 -->[^kirschen-strbac-2019] Remove the contingency — assume no generator will ever trip — and the spinning reserve becomes pure inefficiency: those generators could be off, or producing at full rated output and selling more energy. Keep the contingency and the reserve is what prevents a frequency excursion from cascading into a blackout. Spinning reserve sits within a stack — non-spinning, replacement, regulating reserve — each sized against a different contingency timescale, illustrating the recursive-layering pattern that emerges when the prime is taken seriously as a design object. **Mapped back:** The same five roles organize a bank's liquidity buffer (resource = cash; nominal demand = expected withdrawals; surplus = held above expected; contingency = redemption shock; draw-down = honor withdrawals first, replenish later), and the same recursive-layering pattern shows up as the Tier 1 / Tier 2 / contingent-capital stack in bank capital regulation. The substrates differ; the structural design choices do not.

**Hospital — ICU surge capacity.** A regional hospital system maintains a target ICU occupancy below 100% — perhaps 75-80% in nominal operations — so that the unused beds, ventilators, and staff are available when a contingency arrives (mass-casualty event, seasonal respiratory surge, pandemic wave). The roles: resource is staffed ICU capacity; nominal demand is the routine critical-care census; maintained surplus is the gap between routine census and full staffed capacity; contingency is the surge event; draw-down rule is admission policy that holds the surplus for genuine surge cases rather than backfilling with elective admissions, the five-role discipline Christian et al. (2014) prescribe in the CHEST consensus statement on mass-critical-care surge capacity.<!-- FACT-D56-059 -->[^christian-etal-2014] Hospitals routinely fail this reserve discipline by treating the gap as waste (the bean-counter sees empty beds and presses for higher occupancy targets), with the result that surge capacity is exhausted on the first day of a contingency. The COVID-19 pandemic made this visible at population scale, and several health systems formalized post-pandemic reserve policies with explicit contingency targets and draw-down rules — a direct application of the five-role decomposition to a domain that had been operating largely on intuition, as Aziz et al. (2020) document in their rapid guidelines for managing ICU surge during the COVID-19 crisis.<!-- FACT-D56-060 -->[^aziz-etal-2020] **Mapped back:** The hospital case shows what happens when the contingency-removal counterfactual is misapplied: the planner asks "would I keep these empty beds if no surge were possible?" and answers "no, so cut them," collapsing a reserve into waste. The correct counterfactual holds the contingency distribution fixed and asks whether the surplus is correctly sized against it — a question the five-role decomposition makes mechanical.

title: Reserves and waste are visually indistinguishable in the nominal case

body: Both are unused capacity; neither is doing visible work when the system is operating normally. This makes reserves chronically vulnerable to short-horizon optimization: the bean-counter sees empty beds, idle generators, untouched inventory, or unspent cash, and presses for higher utilization without distinguishing surplus held against contingency from surplus that is genuinely wasteful. The contingency-removal counterfactual separates them analytically, but it requires the contingency to be explicit and the analyst to take it seriously — neither of which is guaranteed when reserves are evaluated by people whose performance metrics don't include the tail events the reserve is sized against.

title: The value of a reserve is asymmetric — invisible during nominal operation, decisive during disturbance — and asymmetric value is systematically mis-priced

body: Any objective function that doesn't explicitly model the contingency distribution will undervalue the reserve, because the reserve's protective benefit is realized only in a small tail of states that the optimizer either prices at zero or fails to enumerate. This produces a chronic dynamic in which reserves are eroded during calm periods (when the contingency hasn't materialized recently and is psychologically distant) and rebuilt only after a crisis exposes the under-provisioning. The cyclicality is structural, not a failure of individual judgment.

title: Reserves can be over-sized as easily as under-sized, and the over-sized case is harder to detect

body: Under-reserved systems advertise themselves by failing during contingencies; over-reserved systems pay carrying costs (capital, opportunity cost, storage, maintenance) silently, and the carrying cost may be normalized into the baseline of "how things are done." A factory that holds two months of buffer stock against a supply contingency that could be handled with two weeks is over-reserved, but no event will make this visible unless someone runs the counterfactual. The five-role decomposition gives a check (is the surplus correctly sized against the contingency distribution?), but the check requires the contingency distribution to be characterized, which is harder than the operational habit usually admits.

title: Reserves can erode invisibly through misclassification of their role

body: A reserve that has been held against a specific contingency may, over time, be re-purposed to absorb nominal-load variability; from outside, the reserve still appears to exist (the surplus is still in place), but it is now being routinely drawn down and replenished against ordinary demand fluctuations rather than held against the original contingency. When the original contingency arrives, the reserve is partially or fully depleted because it has been functioning as buffer-stock-against-noise rather than as reserve-against-shock. Inventory reserves sized against supply disruption that get repurposed as demand-smoothing buffers are the canonical case; the structural similarity of noise-buffering and shock-buffering makes the misclassification easy.

title: Reserve and adaptive-capacity trade off against each other under fixed total resource

body: A system can spend a unit of resource on holding a larger reserve against a specified contingency or on investing in faster reconfiguration that lets it handle novel contingencies; under a fixed budget, more of one means less of the other. Held reserves are powerful against the contingency they are sized for and useless against contingencies they aren't (a liquidity reserve doesn't help with a solvency crisis; a spinning reserve doesn't help with a transmission failure). Adaptive capacity is the opposite — flexible across contingency types but weaker against any specific one. The strategic question of how to split a fixed protection budget between holding reserves and building adaptive capacity is a real one, and it is obscured when "reserve" and "adaptive capacity" are conflated.

title: Replenishment is structurally separate from the reserve itself, and getting one right does not guarantee the other

body: A reserve has both a target level (the held quantity) and a replenishment policy (the rate and conditions under which it is restored after draw-down). A correctly sized reserve with slow or unreliable replenishment is single-use: it absorbs the first shock and leaves the system exposed to any subsequent contingency before replenishment completes. A fast replenishment policy with too-small a held quantity may be unable to keep up during a sustained disturbance. The five-role decomposition keeps these two parameters analytically separate, but operational policy frequently bundles them — the bundled parameter is then the wrong unit of optimization and produces failure modes that look mysterious if the decomposition isn't named.

prose:
1. **Five-role specification:** Before designing or evaluating a reserve, write down explicitly the resource, the nominal demand, the maintained surplus, the contingency the surplus is held against, and the draw-down rule. This forces the contingency to be named (which exposes reserves that have lost their justification), the draw-down rule to be specified (which prevents the reserve from being silently consumed against nominal-load variation), and the surplus level to be tied to the contingency distribution rather than to habit.

2. **Contingency-removal counterfactual:** For any candidate reserve, ask what would happen if the contingency distribution were known to be zero. If the surplus still looks valuable, the candidate was waste being justified by post-hoc appeal to contingency; cut it. If the surplus stops looking valuable, the candidate was a genuine reserve and the carrying cost is the price of the protection; defend it. This is the substrate-neutral diagnostic that separates reserves from waste.

3. **Recursive layering by contingency timescale:** When a system faces contingencies at multiple timescales, stack reserves accordingly — fast-deploy reserves against second-scale contingencies, slower reserves against minute-scale, slower still against hour-scale and beyond. Spinning / non-spinning / replacement reserve on power grids and Tier 1 / Tier 2 / contingent-capital stacks in bank regulation are canonical examples. The layering itself becomes a design object once reserve is named as a prime.

4. **Periodic contingency-distribution audit:** Reserves are sized against assumed contingency distributions, which drift over time (climate change shifts flood distributions; supply-chain restructuring shifts disruption distributions; financial-system evolution shifts redemption-shock distributions). Periodically re-derive the contingency distribution from current data and re-size the reserve, rather than letting the sizing crystallize into operational habit.

5. **Replenishment-policy separation:** Treat the held quantity and the replenishment policy as analytically separate parameters. Specify the target level explicitly; specify the rate and conditions of replenishment explicitly; resist bundling them into a single operational rule. This prevents the failure mode in which a correctly-sized reserve is paired with replenishment so slow that the reserve is effectively single-use against any sustained disturbance.

6. **Reserve-vs-adaptive-capacity split:** When allocating a fixed protection budget, explicitly split it between holding reserves (powerful against known contingencies, useless against unknown ones) and building adaptive capacity (flexible across contingency types but weaker against any specific one). Avoid the default of spending the whole budget on whichever mechanism is more legible in the local discipline.

notes:
Promoted from a project-06 candidate once the family it organizes made the case clear: `margin_of_safety`, `system_slack`, and `buffering` all look like kinds or uses of one underlying pattern, which is the signature of a genuine prime rather than a connector. The re-parenting of those three to `reserve` is proposed for round-7 model review before commit.

The naming choice "reserve" over "buffer" is load-bearing. `buffering` already exists as the *process* prime — the activity of maintaining a reserve at its target level. Naming this prime "buffer" would have collided with the process prime and erased the state-versus-process distinction. "Reserve" names the held surplus without ambiguity and leaves `buffering` to name the activity that maintains it.

The substrate-furthest cases — ecological reserves (lipid stores, seed banks) and chemical reserves (excess reagent in stoichiometry) — are diagnostically important because they have no human institutional layer. The contingency distribution and draw-down rule are encoded in life-history strategy or synthetic protocol. That these cases instantiate the same five-role pattern as engineered and financial reserves is the strongest evidence that reserve is a substrate-neutral structural prime, not a managerial specialty pattern projected onto natural systems.

The asymmetric-value structure of reserves — invisible nominally, decisive under disturbance — is what makes them chronically under-funded by short-horizon optimization. The prime's contribution is to give the analyst a substrate-neutral vocabulary for arguing against optimizers who can't see the contingency, rather than re-deriving the argument in each domain's local language.


Reservoir-Flux Network

one_liner: Named stocks linked by conserved flows.

core_idea:
A reservoir-flux network is the structural arrangement in which a
system is decomposed into a finite set of *named reservoirs* — stocks,
compartments, pools, accounts, levels — connected by *fluxes* — flows,
transfer rates, directed channels — under a *conservation closure* that
holds the total content of the system invariant except across an
explicitly declared boundary. Three commitments are jointly
load-bearing, and dropping any one collapses the family of reasoning
the pattern licenses. Reservoirs individuate the things whose
accumulated levels matter. Fluxes specify the directed pathways along
which content moves between reservoirs. Conservation asserts that
whatever leaves one reservoir arrives somewhere else inside the bounded
system, or else crosses a named boundary to the outside, so that the
summed contents — corrected for boundary exchanges — do not change
under the internal dynamics.

The conservation closure is the discriminating feature. It is what
separates the pattern from a bare graph of connected nodes (which
carries no conservation) and from a single isolated flow (which carries
no graph structure and no stocks). The closure is also what makes the
characteristic reasoning catalogue available: mass-balance accounting
(inflow equals outflow plus accumulation), steady-state analysis
(finding the reservoir levels at which all fluxes balance),
residence-time calculation (reservoir size divided by through-flux)<!-- FACT-D70-651 -->[^bolin-rodhe-1973],
time-constant estimation (how long a perturbation takes to relax around
the graph), and shock propagation (how a disturbance to one reservoir
redistributes through the connected topology). Without conservation the
bookkeeping that makes intervention calculable simply disappears.

A fourth structural feature is naming: reservoirs are individuated and
labelled rather than treated as anonymous nodes. The decision of where
to draw reservoir boundaries — lumping a heterogeneous pool into one
reservoir versus splitting it into sub-pools with their own internal
flux structure — is itself the major modelling choice, and it
determines where every later intervention can be located on the graph.
Once the reservoirs are named and the fluxes drawn, the question "where
should we act?" becomes a question about a specific edge or node, and
the question "is our account complete?" becomes an auditable arithmetic
identity.

structural_signature:
*the set of named reservoirs* — *the directed fluxes connecting them* —
*the rate laws governing the fluxes* — *the conservation closure over
the bounded total* — *the declared boundary across which content is
non-conserved* — *the reservoir-individuation (naming) choice*

A system is a reservoir-flux network when each of the following holds:

- **Named reservoirs.** The system is decomposed into a finite set of
  individuated, labelled stocks — compartments, pools, accounts, levels
  — whose accumulated contents are the quantities that matter. Naming,
  not anonymous nodehood, is part of the structure: where reservoir
  boundaries are drawn is the major modelling choice.
- **Directed fluxes.** The reservoirs are connected by flows — transfer
  rates, channels — specifying the directed pathways along which
  content moves from one reservoir to another.
- **Rate laws on the fluxes.** Each flux is governed by a law (often
  first-order in a reservoir's content, possibly nonlinear) that fixes
  how fast content moves, making the dynamics calculable rather than
  merely topological.
- **A conservation closure.** Whatever leaves one reservoir arrives in
  another inside the bounded system, so the summed contents — corrected
  for boundary exchange — are invariant under the internal dynamics.
  This is the discriminating feature: it separates the pattern from a
  bare graph (no conservation) and from a single isolated flow (no
  stocks, no graph).
- **A declared boundary.** An explicit interface separates inside
  (conserved) from outside; content may cross it as boundary fluxes that
  are non-conserved with respect to the inside. Misplacing this boundary
  is the most common and most diagnostic error, since a failed
  conservation check points straight at it.

Together these license the characteristic reasoning catalogue —
mass-balance accounting, steady-state analysis, residence-time
calculation, time-constant estimation, and shock propagation — and make
"is our account complete?" an auditable arithmetic identity. Drop the
conservation closure and the entire calculable bookkeeping disappears.

what_it_is_not:
- **Not a bare `network`.** A network is a graph topology — nodes and ties — that carries no conservation. The reservoir-flux network is the conjunction of graph plus stocks plus a *conservation closure*, the minimum required for mass-balance reasoning to work.
- **Not a single isolated flow.** A lone directed channel describes one movement but carries no graph structure and no stocks. This prime requires multiple named reservoirs whose summed contents are conserved.
- **Not `turnover`.** Turnover is the *rate* at which a stock's contents are replaced; this prime is the whole reservoir-and-flux structure under conservation, from which turnover (and residence time) is one derived quantity.
- **Not `buffering`.** Buffering is the capacity of one reservoir to absorb fluctuation; the reservoir-flux network is the multi-reservoir conserved system in which buffering is a property of a particular stock.
- **Not `equilibrium`.** Equilibrium is a *state* (flux balance, no net change) that a reservoir-flux network may or may not reach; the prime is the structural arrangement whose dynamics produce equilibrium, oscillation, or runaway depending on topology and rate laws.
- **Common misclassification.** Calling a connected diagram of pools a reservoir-flux network when no total is conserved. Without the closure, the mass-balance bookkeeping that makes intervention calculable simply disappears — it is then a bare graph, not this prime.

broad_use:
- **Biogeochemistry.** The canonical case: the carbon cycle as
  reservoirs (atmosphere, ocean surface, deep ocean, biosphere, soils,
  fossil reserves) linked by photosynthesis, respiration, dissolution,
  and combustion fluxes, with total carbon conserved.<!-- FACT-D70-652 -->[^ipcc-2021-carbon] The nitrogen,
  phosphorus, water, and sulfur cycles share the shape.<!-- FACT-D70-653 -->[^schlesinger-bernhardt-2013]
- **Pharmacokinetics.** Compartmental PK/PD models represent the body
  as one to three reservoirs with first-order rate constants between
  them and to elimination; drug mass is conserved minus elimination.<!-- FACT-D70-654 -->[^gibaldi-perrier-1982]
- **Epidemiology.** SIR/SEIR models partition a population into
  Susceptible, Infected, and Recovered reservoirs with infection,
  recovery, and death fluxes; total population is conserved, and
  interventions read as perturbations on the flux constants.<!-- FACT-D70-655 -->[^kermack-mckendrick-1927]
- **Macroeconomics.** Flow-of-funds and sectoral-balance accounting
  treat households, firms, government, and rest-of-world as reservoirs
  whose monetary flows conserve by double-entry bookkeeping.<!-- FACT-D70-656 -->[^godley-lavoie-2007]
- **System dynamics.** The entire Forrester stock-and-flow discipline
  is built around stocks, rates, and the equations connecting them.<!-- FACT-D70-657 -->[^forrester-1961]
- **Ecology and hydrology.** Trophic energy budgets and watershed water
  balances are reservoir-level analyses with thermodynamic or
  hydrological conservation as the closure.<!-- FACT-D70-658 -->[^odum-1983]

clarity:
Naming the reservoir-flux network as its own object separates three
things that surface vocabulary persistently conflates. A flow is a
single directed channel — useful for describing one movement, useless
for accounting. A network is a graph topology — useful for describing
connectivity, silent on conservation. A reservoir-flux network is the
conjunction with closure: graph plus stocks plus conservation, the
minimum required for mass-balance reasoning to work. When someone says
"the carbon cycle is just a network," they have dropped the
conservation closure that licenses the policy arithmetic; when someone
says "pharmacokinetics is just a flow," they have dropped the
compartment structure that organises the dose calculation.

The pattern also makes the closure boundary an explicit modelling
choice. Every reservoir-flux model must declare what counts as inside
(conserved) and what crosses to outside (boundary fluxes,
non-conserved with respect to the inside). Misplacing that boundary —
treating the atmosphere as closed when emissions cross in, treating the
body as closed when elimination crosses out — is at once the most
common reservoir-flux error and the most diagnostic, because a failed
conservation check points straight at the misplaced boundary.

manages_complexity:
The pattern compresses an arbitrarily complicated multi-substance,
multi-place, multi-rate system into a short specification: how many
reservoirs, what fluxes connect them, what rate laws govern the fluxes,
and what total is conserved. Once those are fixed, a wide family of
derived quantities becomes computable from the same pipeline regardless
of substrate — steady-state levels, residence times, equilibration time
constants, sensitivity coefficients, and shock-propagation patterns.
The same machinery runs whether the conserved content is carbon,
dollars, viral particles, or vehicles.

The structural commitment also disciplines the modelling. Conservation
is auditable: if the contents do not add up, then a reservoir is
mis-sized, a flux is mis-specified, or a boundary exchange has been
overlooked. This is precisely the diagnostic value that double-entry
bookkeeping discovered for finance, generalised — an arithmetic
identity that can be checked against measurement, with every
discrepancy forcing the model back into contact with reality. The
discipline turns "the model seems wrong" into a short, finite list of
possible structural faults.

abstract_reasoning:
The dynamics on a reservoir-flux network admit clean mathematical
treatment: a system of coupled rate equations, one per reservoir, in
which each reservoir's change equals the sum of its inflows minus the
sum of its outflows, with conservation enforced when boundary fluxes
vanish. Steady-state levels are the solution of a linear system in the
flux coefficients; residence times read off directly; the response to a
perturbation is governed by the eigenstructure of the system's
Jacobian.<!-- FACT-D70-659 -->[^jacquez-1985] The graph's topology constrains the qualitative behaviour:
pure feed-forward networks relax monotonically to equilibrium, while
networks containing loops can oscillate or settle into multiple stable
states depending on flux nonlinearities.

The pattern also licenses a clean abstraction ladder. At one extreme,
lumped models with a few reservoirs are analytically tractable and
yield order-of-magnitude reasoning; at the other, spatially distributed
models written as continuous fields over reservoir position handle
fine-grained structure. The choice of granularity is itself a
structural trade: adding reservoirs adds parameter burden and data
demand, while lumping risks hiding dynamics behind an aggregate stock.
A trained reasoner uses the same questions at every rung — what is
conserved, what flows, on what timescale, across what boundary — and so
can move up and down the ladder without changing vocabulary.

knowledge_transfer:
The reservoir-flux pattern transfers with unusual cleanness because its
core identities are substrate-blind, and the role mappings are exact.
The *reservoir* maps to a compartment in pharmacokinetics, a population
class in epidemiology, a sector in flow-of-funds, a trophic level in
ecology, a warehouse in inventory management. The *flux* maps to a
rate constant, an infection rate, a monetary flow, a feeding rate, a
shipment. *Conservation* maps to mass balance, population
conservation, double-entry bookkeeping, the first law of
thermodynamics, physical inventory continuity.<!-- FACT-D70-660 -->[^godley-lavoie-2007] *Residence time* maps
identically across all of them: a reservoir's contents divided by the
flux running through it, whether the contents are drug molecules,
infected individuals, dollars, or cars.

Because the mappings are exact rather than analogical, closed-form
results travel intact. The one- and two-compartment solutions that
pharmacology uses for dosing carry over without modification to
SIR-family epidemic models, since both are linear reservoir-flux
networks.<!-- FACT-D70-661 -->[^jacquez-1985] The sectoral-balance identity from macroeconomics ("one
sector's surplus is another's deficit") is the same closure that yields
trophic energy budgets in ecology. The system-dynamics insight that a
stock keeps rising even as its inflow flux levels off — the "bathtub"
result — transfers directly to climate reasoning about atmospheric
carbon and to inventory reasoning about backorders. Most powerfully,
the conservation-failure diagnostic transfers as a single reusable
move: across auditing, climate modelling, epidemiology, and
supply-chain control, "the contents are not adding up, therefore a
reservoir is missing, a flux is unmeasured, or the boundary is drawn
wrong" is the same inference with the same three resolution paths. A
practitioner who has internalised the pattern in one substrate arrives
in another already knowing which questions are answerable, which
quantities are computable, and which discrepancies are diagnostic —
the transfer cost is close to zero because nothing about the reasoning
was ever tied to the original medium.

formal_abstract:
The two-compartment pharmacokinetic model is the pattern with every role instantiated and the conservation closure doing visible arithmetic. The *named reservoirs* are two: a central compartment (blood and well-perfused tissue) and a peripheral compartment (slowly-perfused tissue). The *directed fluxes* connect them — a rate constant $k_{12}$ moving drug from central to peripheral, $k_{21}$ returning it, and an elimination flux $k_{10}$ carrying drug out of the central compartment across the declared boundary (metabolism and excretion). The *rate laws* are first-order: each flux equals a rate constant times the source compartment's current content, so the dynamics are the coupled linear system $\dot{C}_1 = -(k_{12}+k_{10})C_1 + k_{21}C_2$ and $\dot{C}_2 = k_{12}C_1 - k_{21}C_2$. The *conservation closure* is exact: total drug mass equals what is in both compartments plus what has been eliminated across the boundary, and that sum equals the dose — an auditable identity. The *declared boundary* is elimination; treating the body as closed (forgetting $k_{10}$) is the diagnostic error, and a conservation check that fails to balance points straight at the missing elimination flux. From this specification the entire derived catalogue follows mechanically: steady-state levels under continuous infusion solve a linear system in the rate constants; the central-compartment residence time is its volume divided by clearance; the biexponential plasma decay (fast distribution phase, slow elimination phase) is read off the eigenstructure of the system's Jacobian; and a dosing perturbation propagates through the two-compartment topology on time constants set by those same eigenvalues. None of this reasoning references chemistry — it is pure reservoir-flux bookkeeping.<!-- FACT-D70-662 -->[^gibaldi-perrier-1982]

**Mapped back:** Central and peripheral compartments are the named reservoirs, $k_{12}/k_{21}/k_{10}$ are the directed fluxes under first-order rate laws, dose conservation across the elimination boundary is the conservation closure, and clearance-over-volume is residence time — a reservoir-flux network with the mass-balance identity made numerically explicit.

applied_industry:
The SIR epidemic model and macroeconomic flow-of-funds accounting run the identical structure in unrelated substrates, and the closed-form results transfer between them because both are linear (or near-linear) reservoir-flux networks. In SIR, the *named reservoirs* are three population classes — Susceptible, Infected, Recovered — and the *directed fluxes* are infection (S to I, governed by a rate law nonlinear in the product $S \cdot I$) and recovery (I to R, first-order in $I$). The *conservation closure* is population conservation: $S + I + R$ is invariant (with births and deaths as declared boundary fluxes if included), so the model's total always balances, and a public-health planner reads interventions directly as perturbations on the flux constants — vaccination drains S, isolation cuts the infection rate, treatment raises the recovery rate.<!-- FACT-D70-663 -->[^kermack-mckendrick-1927] The same pattern governs flow-of-funds: the *reservoirs* are economic sectors (households, firms, government, rest-of-world), the *fluxes* are monetary flows between them, and the *conservation closure* is double-entry bookkeeping, which guarantees the sectoral-balance identity "one sector's surplus is exactly another's deficit"<!-- FACT-D70-664 -->[^godley-lavoie-2007] — the same closure that yields trophic energy budgets in ecology. The conservation-failure diagnostic transfers as one reusable move across both: when the contents do not add up — an epidemic count that does not reconcile, a national account that does not balance — a reservoir is mis-sized, a flux is unmeasured, or the boundary is drawn wrong, with the same three resolution paths. An epidemiologist sizing an outbreak and a national-accounts statistician auditing a balance are running one bookkeeping discipline.<!-- FACT-D70-665 -->[^godley-lavoie-2007]

**Mapped back:** S/I/R classes and economic sectors are named reservoirs; infection-and-recovery and inter-sector monetary flows are directed fluxes; population conservation and double-entry bookkeeping are the conservation closures; the "it doesn't add up, so a reservoir/flux/boundary is wrong" check is the shared diagnostic — the same prime in epidemiology and macroeconomics.


Residual Analysis

one_liner: Subtract the best explanation and study the leftover as the next site of structure, not as noise.

core_idea:
Residual analysis is the structural move of subtracting the best available
explanation from observed data and then studying *what is left over* — the
residuals — as a source of further structure rather than as inert noise. The
model captures what it captures; the residual is everything the model failed
to absorb; the inferential payoff comes from asking whether the residual has
pattern. If the leftovers are patternless — independent, mean-zero,
constant-variance — the model has captured the captureable signal. If the
leftovers carry structure — a trend, autocorrelation, heteroscedasticity, a
cluster of like-signed errors — the residual *is* a signal, a fingerprint of
what the model is missing and a pointer toward the next refinement.

The structural commitment is an inversion: residuals are not the *failure*
of explanation but its next *site*. This overturns the naive workflow in
which one fits the best model, declares the rest "error," and stops. The
residual-analysis stance treats every error series as a candidate dataset
for further modelling, and accepts the current explanation as adequate only
when the residuals are demonstrably patternless. A subtle but load-bearing
feature is that the move presupposes a *specification* of what patternless
means. Without a prior model of "noise," any departure of residuals from
theoretical noise properties can be over-interpreted as discovery (data
dredging) or under-interpreted as overfitting and dismissed. The
substrate-independent discipline is therefore to commit to a model of noise
*before* inspecting the residuals — noise is earned by demonstration, not
assumed by default.

structural_signature:
*the observed data* — *the best-available explanatory model* — *the subtraction operation* — *the residual (observed minus predicted)* — *the prior noise specification* — *the pattern test on the residual* — *the next-layer (iterate-or-stop) rule*

A procedure is residual analysis when each of the following holds:

- **Observed data.** There is a body of observations a system has produced — measurements, a signal, symptoms, transactions.
- **An explanatory model.** A best-available account is fitted to capture as much of the data as it can — a regression, an orbital model, a leading diagnosis, a baseline of expected behaviour.
- **A subtraction operation.** The model's prediction is subtracted from the observation, isolating what the model failed to absorb.
- **The residual.** The leftover, observed-minus-predicted, is the central object. The load-bearing inversion: the residual is treated not as inert error but as the next *site* of structure.
- **A prior noise specification.** Before inspecting the residual, the analyst commits to a model of what *patternless* looks like — the theoretical properties (independence, mean-zero, constant variance) a correctly-specified model's residuals should have. Noise is earned by demonstration, not assumed; this commitment-before-inspection guards against both data-dredging and dismissal-as-overfitting.
- **A pattern test.** The residual is examined against the noise specification: a trend, autocorrelation, heteroscedasticity, or clustered like-signed errors is a *signal* — a fingerprint of what the model is missing — while conformance to the noise model licenses acceptance.
- **A next-layer rule.** Patterned residuals become the dataset for a subsequent modelling step; the process iterates, and converges only when residuals stop carrying pattern.

Composed: subtracting the best explanation and studying the leftover against a pre-committed model of noise turns explanation into iterative layers — each well-specified model the platform from which the next, smaller structure becomes visible, with the rate of discovery set by how precisely the current model can be subtracted.

what_it_is_not:
- **Not `predictive_coding`.** Predictive coding (the nearest embedding neighbor) is a *processing architecture* in which a system continuously transmits only prediction errors upward; residual analysis is an *analytic discipline* of subtracting a fitted model and studying the leftover for structure. One is an ongoing perceptual mechanism, the other a deliberate modeling step.
- **Not `signal_extraction`.** Signal extraction *recovers the signal* and discards the rest; residual analysis treats the *leftover as the next signal*. The inversion is the point — the residual is not what you throw away but the next site of structure.
- **Not `correlation`.** Correlation measures *linear association between two variables*; residual analysis examines the *patternlessness of a model's leftovers* against a noise specification. Patterned residuals may reveal nonlinearity, omitted variables, or dependence that no single correlation captures.
- **Not `baseline_deviation`.** Baseline deviation (a candidate prime) flags *departures from an expected level*; residual analysis adds the *iterative next-layer discipline* and a *pre-committed noise model* that distinguishes signal-bearing structure from noise. Deviation detection is one use; the prime is the whole subtract-test-iterate engine.
- **Not `decomposition`.** Decomposition splits a whole into parts by a known structure; residual analysis *fits an explanation and studies what it failed to absorb*, where the leftover's structure is unknown in advance and must be tested. Decomposition partitions; residual analysis discovers.
- **Not `regression_to_the_mean`.** That is a statistical tendency of extremes to moderate; residual analysis is the discipline of studying model leftovers for unmodelled structure. They co-occur in statistics but answer different questions.
- **Common misclassification.** Declaring "the rest is error" and stopping, or chasing patternless residuals as discovery (data dredging). Catch it by checking whether a model of *patternless* was committed to *before* inspecting the residuals — noise must be earned by demonstration against a prior specification, not assumed or read in after the fact.

broad_use:
- **Statistics and regression** (origin): residual-vs-fitted plots, Q-Q
  plots, serial-correlation tests, and partial-residual plots distinguish
  well-specified from misspecified models and reveal omitted variables,
  nonlinearity, and dependence.
- **Time series and econometrics**: forecast residuals are tested for
  autocorrelation and recursively modelled, so residual structure motivates
  each successive model layer.
- **Physics and astronomy**: subtracting a known orbital model and examining
  the residuals inferred Neptune from Uranus's discrepancies and detects
  exoplanets in radial-velocity and transit data.<!-- FACT-D70-676 -->[^anglada-escude-2016]
- **Quality control**: variation left after accounting for known inputs is
  mined for assignable causes, distinguishing common-cause from
  special-cause variation by reading residual patterns.<!-- FACT-D70-677 -->[^shewhart-1931]
- **Medicine**: a clinician's leading hypothesis is the model, and the
  symptoms it *fails* to explain are the residual that drives
  differential-diagnosis refinement.
- **Machine learning**: gradient boosting fits successive weak learners to
  the residuals of prior learners; residual connections instantiate the
  move at the architecture level.<!-- FACT-D70-678 -->[^friedman-2001]
- **Auditing and forensics**: a baseline model of expected transactions is
  subtracted, and the deviations form the investigation set.
- **Engineering and instrumentation**: calibration removes the modelled
  response, and residuals are inspected for drift, gain errors, and
  unmodelled physics.

clarity:
Naming residual analysis makes three distinctions sharp. It separates *the
model's explanation* from *the data's behaviour*: the residual is the
difference, and the difference has its own structure to be studied. It
separates *noise as assumption* from *noise as conclusion*: assuming
residuals are noise is one move, and demonstrating they are noise via
diagnostic tests is a different and necessary one. And it separates *fitting
a model* from *believing a model*: a model with patterned residuals fits the
data in some sense yet is detectably misspecified, and the prime keeps those
two states from being confused.

It also clarifies why an apparently small effect can be highly informative.
The residual is precisely where small effects live once the big ones are
removed, so discoveries that came from residuals — Neptune, the anisotropies
of the cosmic microwave background, exoplanet detections — were exactly that:<!-- FACT-D70-679 -->[^smoot-etal-1992]
small structure invisible against unsubtracted data, made visible by
subtracting a good prior model first. The clarifying force is to direct
attention to the leftover as the place where the next finding will appear.

manages_complexity:
Residual analysis is the basic engine of iterative modelling. Instead of
attempting to build the full explanatory model in a single shot — intractable
for any non-trivial system — the analyst layers explanation: fit what is most
obvious, examine the residuals, fit the next layer, repeat. Each pass is
bounded in complexity because each works against a smaller signal, and the
complexity of the final model is *distributed* across explicit, inspectable
layers rather than concentrated in a single opaque specification. This is the
structural basis for boosting, for hierarchical regression, for ARIMA-family
decompositions, and for the standard trend-seasonal-residual decomposition of
time series.<!-- FACT-D70-680 -->[^box-jenkins-1970]

The compression also makes discovery cheap relative to the prior model. Once
the modelled signal is subtracted, the residual investigation becomes
tractable because it operates on a much smaller quantity: Neptune was found
cheaply *because* Newtonian mechanics already accounted for almost all of
Uranus's motion, and exoplanet detection became cheap *because* stellar
radial-velocity models became precise enough to make planetary tugs visible
against the residual.<!-- FACT-D70-681 -->[^anglada-escude-2016] The prime turns a hard search through raw data into an
easy search through a near-empty leftover.

abstract_reasoning:
Residual analysis supports a small set of substrate-independent inferences.
*Unmodelled structure is detectable from leftovers*: if a hidden variable
matters, removing the modelled variables exposes its footprint. *The noise
assumption is testable*: residuals have known properties under a correctly
specified model, and departures from those properties are themselves
evidence. *Successive modelling converges only when residuals stop having
pattern*: this is the stopping rule both in classical statistics and in
boosting.<!-- FACT-D70-682 -->[^friedman-2001] And *residual structure points to specification, not data
quality*: patterned residuals usually indicate a missing term or a
nonlinearity rather than bad data — though the analyst must still
distinguish them, because measurement error and outliers can mimic
specification failure.

A sharper inference concerns the economics of discovery. The cost of a
residual-driven discovery is roughly the cost of the prior model, because the
prior model is what renders the residual investigation tractable. This
reframes scientific and diagnostic progress as a sequence of subtractions:
each well-specified model is not an endpoint but the platform from which the
next, smaller structure becomes visible, and the rate of discovery is set by
how precisely the current model can be subtracted.

knowledge_transfer:
The roles map across substrates with no translation: the *current model* is
the regression fit, the orbital model, the leading diagnosis, the first
boosting stage, the expected-transaction baseline; the *residual* is the
observed-minus-predicted leftover, the unexplained symptom, the anomalous
transaction; the *noise specification* is the prior commitment to what
patternless looks like; and the *next-layer move* treats patterned residuals
as the dataset for a subsequent modelling step. Stripped of any field's
vocabulary, the prime reads: *subtract the best known model, examine the
leftovers for structure, and treat patterned leftovers as evidence of
something unmodelled.*

Documented transfers run in every direction. The residual-as-signal move
ports from statistics to the physical sciences without modification — the
Uranus-to-Neptune inference is the canonical case, and the same logic powers
gravitational-wave template subtraction and cosmic-microwave-background
foreground removal.<!-- FACT-D70-683 -->[^abbott-etal-2016] It ports from statistics to machine learning, where
residual fitting is the algorithm inside gradient boosting and residual
networks instantiate the same move in architecture. It ports to medicine,
where differential diagnosis is residual analysis on clinical presentations
— the leading hypothesis is the model, the unexplained symptoms are the
residual, the next-best hypothesis is fitted to those. And it ports to audit
and security, where subtracting a baseline behaviour model and inspecting the
residuals is the template for intrusion detection, fraud detection, and
distributional audits. What travels is a transferable inferential commitment
— *noise is earned, not assumed* — that supports intervention design in any
modelling domain: a regression of house prices with residuals systematically
high in one neighbourhood is missing a location effect, a radial-velocity
model with periodic residuals has an unmodelled orbiting body, and a patient
who fails to improve on a correct-seeming treatment has a residual symptom
pattern motivating a search for co-infection — the substrate changing from
real estate to celestial mechanics to medicine, the structural move staying
identical.

formal_abstract:
The discovery of Neptune is the prime's paradigm case, and it makes every role concrete in celestial mechanics. The *observed data* were the positions of Uranus, tracked across decades. The *best-available explanatory model* was Newtonian gravitation accounting for the Sun and the known planets — a model so good it absorbed the overwhelming majority of Uranus's motion. The *subtraction operation* compared observed positions to the model's predictions, isolating the *residual*: a small but systematic discrepancy of a few arcminutes that the gravitational model could not absorb.<!-- FACT-D70-684 -->[^grosser-1962] Here the prime's load-bearing inversion does the work — the residual was not dismissed as observational error but treated as *the next site of structure*. The *prior noise specification* was essential: astronomers knew the precision of their observations, so they could judge that the discrepancy *exceeded* what measurement noise should produce — the residual *failed the patternless test*, carrying a coherent, time-varying signature rather than scattering randomly. That patterned residual was read as the *fingerprint of something unmodelled*: a gravitational tug from an unseen body. Le Verrier and Adams then performed the *next-layer move*<!-- FACT-D70-685 -->[^grosser-1962] — they fit a new model to the residual itself, inferring the mass and orbit of a hypothesized eighth planet that would produce exactly that leftover pattern. Neptune was found within a degree of the predicted position.<!-- FACT-D70-686 -->[^grosser-1962] The prime's *economics of discovery* are exhibited cleanly: the find was *cheap* precisely because Newtonian mechanics already accounted for almost all of Uranus's motion, so the search operated on a near-empty leftover rather than on the raw, overwhelming signal. The intervention this licenses is the engine of much of physics: subtract the best model, test the residual against a pre-committed noise floor, and when the leftover carries pattern, fit the next layer to it — the same move that today detects exoplanets in radial-velocity residuals and finds structure in cosmic-microwave-background maps after foreground subtraction.<!-- FACT-D70-687 -->[^smoot-etal-1992]

**Mapped back:** The Uranus-to-Neptune inference instantiates the full signature — observed data, a near-complete Newtonian model, a subtracted residual that fails a pre-committed noise specification, and a next-layer model fit to the patterned leftover — making it the canonical demonstration that the residual is the next site of structure, not inert error.

applied_industry:
Gradient boosting in machine learning and differential diagnosis in medicine are the same subtract-and-study-the-leftover engine in software and at the bedside. Gradient boosting builds a predictor as an *explicit stack of residual layers*: the first weak learner (the *explanatory model*) fits the data and captures the coarse signal;<!-- FACT-D70-688 -->[^friedman-2001] its predictions are *subtracted* from the targets to form *residuals*; then a second weak learner is fit *to those residuals*, capturing structure the first missed; its contribution is subtracted, and the process *iterates*. This is the prime's next-layer rule made into an algorithm — each stage works against a smaller leftover, the model's complexity is *distributed across inspectable layers* rather than concentrated in one opaque fit, and training *converges only when the residuals stop carrying exploitable pattern* (further learners find nothing to fit), which is precisely the prime's stopping rule. Differential diagnosis runs the identical loop in clinical reasoning with no statistics at all: the clinician's leading hypothesis is the *explanatory model*, and the symptoms it *successfully* explains are "absorbed." The diagnostic engine is the *residual* — the symptoms the leading hypothesis *fails* to explain. A good clinician does not dismiss an unexplained symptom as noise; they treat it as the *fingerprint of something unmodelled* and fit the *next-best hypothesis to that residual* (a co-infection, a second condition, a drug interaction).<!-- FACT-D70-689 -->[^kassirer-1989] The *prior noise specification* appears as clinical judgment about which leftover findings are within normal variation versus genuinely anomalous, guarding against both over-reading (chasing every trivial symptom) and under-reading (dismissing a real residual as incidental). The shared intervention transfers verbatim: subtract the best current explanation, test the leftover against a pre-committed sense of what "unstructured" looks like, and when the leftover carries pattern, fit the next layer to *it* rather than declaring the case closed — a patient who fails to improve on a correct-seeming treatment has a residual symptom pattern that, exactly like a boosting residual or Uranus's wobble, points to an unmodelled cause.

**Mapped back:** Gradient boosting and differential diagnosis are the same prime as the Neptune inference — an explanatory model subtracted to expose a residual, the patterned leftover read as unmodelled structure and fit by a next layer, iterating until the residual goes patternless — so the iterative-subtraction discipline and its convergence rule transfer across the machine-learning, clinical, and astronomical substrates.<!-- FACT-D70-690 -->[^friedman-2001]