Case packet

Neutral case identifier: case-47d9b2d46aa6b4

The possible directed relationship from Artifact A to Artifact B is under review.

Artifact A

Methodology with incomplete coverage and its live theory fallback form a two-layer execution system

Consider an operating domain with open-ended inputs, or an action-shaped methodology without demonstrated total coverage. Assume that out-of-coverage inputs must still be handled. This note proposes treating a general theory and its methodology as one execution system rather than as artifacts that supersede one another. The derived layer is the subset of methodology worked out from the theory; methodology-native structure may shape the same fast-path execution but is neither generated by the theory nor governed by derived-content maintenance.

The proposed model has three parts:

  • The derived layer — the theory-derived subset of methodology — is the fast path. It is shaped for action: cheaper to execute and narrower in scope than the theory. It covers a region of cases directly, without reasoning from first principles each time.
  • The generator layer — the theory — remains available while live fallback is required. A corner case — an input outside the methodology's covered region — is handled by dropping back to the theory and reasoning it out afresh. Within this scope, fallback is an expected operation, not a failure of the methodology.
  • Recurrence is the learning signal. When the same fallback reasoning happens repeatedly, its result is promoted into the methodology, which grows at its boundary, driven by use.

The arrangement only works if the theory is accessible in the effective execution context and the executor can reliably use the theory to derive handling for an out-of-coverage input. The theory is not merely an appendix kept for provenance; it is the live capability the fast path falls back onto.

When the theory remains a live execution layer

A closed declared domain with demonstrated total coverage is the boundary. There the derived layer may stand alone at execution time. Retaining the theory can still serve explanation, provenance, or future maintenance, but it is no longer a live fallback. In the scoped open or incomplete case, observed out-of-coverage traffic shows that the theory remains operationally necessary. Even without observed traffic, fallback remains load-bearing when exhaustive coverage cannot be established and missed cases must still be handled. The theory must therefore remain accessible, interpretable, and validated for execution.

That requirement includes coverage recognition. A declared cutoff is operational only if a coverage test can determine whether an input belongs in the fast path. A definite miss routes to the theory. Uncertain membership routes to the theory when the theory can handle the input safely; otherwise the system abstains or escalates. If the coverage test wrongly admits an input and the fast path gives a wrong answer, that is a missed-boundary error, not a detected fallback. The system must observe both fallback traffic and missed-boundary errors because fallback rate alone cannot reveal false admissions.

Fallback handling becomes a promotion candidate when it recurs and can be executed from the methodology alone. Promotion adds the handling and updates the coverage test so the recurrent case can be recognized. The maintenance regime below determines whether the promoted handling receives deterministic validation or semantic review. Until that verification passes, the case continues to use fallback. Promotion thereby amortizes a recurring derivation by trading one verified commitment against future fallbacks.

Two maintenance regimes govern the theory-derived subset

The theory-derived subset carries content worked out from the theory under a declared consumer goal. That dependency does not by itself make the content a recomputable copy in the technical sense: that label requires a deterministic derivation and comparison. Two maintenance regimes follow, separated by the available verification method:

  • Mechanical fragments are checked or absent. Where a machine can re-derive the same fragment and a deterministic validator can compare it, [a derived copy of recomputable truth must be checked or absent]. A theory revision invalidates the fragment until it is regenerated and the check passes.
  • Judgment-dependent natural-language uses managed staleness. A natural-language method whose relation to the theory must be judged is a lineage-tracked dependent artifact, not a mechanically recomputable copy. A theory revision makes semantic re-derivation or review due, following the general rule that [artifacts without consumer-facing source links need lineage signals when sources change]; it does not turn a loose comparison into a deterministic check.
  • Explicitness sharpens review without changing regimes. A crisp theory can make semantic comparison tighter, while a tacit or judgment-heavy one permits only a looser review. Only when both derivation and comparison are deterministic does content cross the boundary into checked-copy enforcement.

Physics already operates this architecture, and the parallel is an illustration from another discipline, not evidence for the maintenance model. An effective theory — thermodynamics over statistical mechanics, ray optics over wave optics — is worked out from a deeper theory, dramatically cheaper to apply, and strictly less general, with a known breakdown boundary at which one drops back to the fundamental layer; physics retains both layers permanently because the domain of application is open-ended. Theoretical physicist Riccardo Penco's [introductory lectures] describe matching between a fuller and an effective theory and the energy scales that bound an effective description's validity. Borrowing those ideas, promotion resembles matching because it makes the fast path agree with the theory on a newly covered case, while the declared coverage region acts as a cutoff. This note calls the reverse maintenance relation a correspondence check: a revised theory should still account for established fast-path behavior on its home turf. “Correspondence check” is this note's label, not a claimed effective-field-theory term.

Cognitive architectures offer a second, narrower illustration rather than evidence for the model. The reference manual for [the cognitive architecture ACT-R] defines a production as a condition–action rule and describes production compilation as composing two sequentially fired productions into a new one. The manual for [the cognitive architecture Soar] describes chunking as turning substate problem solving into a learned production that can supply the result in one step. Both learn a faster production during use, though their mechanisms and learning conditions differ from this note's promotion policy.

The coverage bet is not the correctness bet

The fast path carries separate correctness and coverage risks. A correctness shortfall yields wrong answers. A coverage shortfall leaves a correct fast path underused. For a frequency-optimized fast path, detected fallback rate helps test whether expected use and per-use savings justify construction, routing, maintenance, and staleness costs. A numerical comparison would require common units and a time horizon. Missed-boundary errors must be tracked separately, and frequency alone cannot settle safety, contractual, normative, or latency value.

Choosing a region to capture common cases adds a falsifiable hypothesis that future cases will concentrate there. Recurrence supplies evidence for promoting an individual case under that frequency lens. Safety, contractual, or normative requirements can instead justify immediate inclusion, so recurrence is a default learning signal rather than a universal admission rule.

Caveat: not all of a methodology is worked out from the theory

A methodology can be mixed, as the opening definition allows. In [Emergence, Singularities, and Symmetry Breaking], philosopher of physics Robert W. Batterman argues that a finite microscopic theory cannot explain some coarse-scale phenomena without an idealized limit, such as treating system size as infinite. Such a limit exposes behavior that no finite model displays. This is an illustration, not evidence for the maintenance model: methodology-native organizing concepts can be real and load-bearing at the coarse methodology level without being outputs of theory-to-method derivation.

A second illustration shows the mix at discipline scale: the physics–chemistry pair. Chemistry is in principle grounded in quantum mechanics, and computational quantum chemistry serves as a live fallback for cases chemical rules do not cover, with recurrent results promoted into chemical practice. Yet chemistry's organizing vocabulary — bonds, electronegativity, aromaticity — is native to its own level of description and resists smooth derivation from the deeper theory; revising the physics does not invalidate it. A chemist's working theory is a mixed artifact: partly re-derivable from the deeper theory, partly level-native structure maintained on its own terms.

The theory-derived subset sits beside that native structure within the methodology layer, and both can shape execution. Mechanical derived fragments receive checked-copy enforcement; judgment-dependent derived natural-language receives managed-staleness review. Native structure is reviewed on its own terms, and revising the theory does not automatically invalidate it. The worked-out / native split decides whether a theory revision creates a dependency obligation; within the worked-out side, the mechanical / judgment-dependent split decides whether the response is deterministic validation or semantic review.

Open Questions

  • How to detect the mixed boundary in practice: given one methodology artifact, what signal separates its recomputable part from its level-of-description-native part before a theory revision forces the question? A candidate signal comes from [fixed artifacts splitting into exact specs and proxy theories]. The recomputable part should behave like an exact spec: fast-path cases added from recurring fallback handling should never need removal. Level-native content should behave like a proxy theory: under distribution shift, errors or brittle behavior would signal that its narrowed fast path should be broadened or retired. Behavior under shift would then reveal the boundary. This correspondence remains a hypothesis, not an identity. An added fast-path case can nevertheless erode because the theory it was worked out from was itself imprecise.
  • Whether the fallback rate is cheap enough to instrument to actually serve as the coverage bet's live adjudicator, or whether it stays a conceptual metric.
  • Promotion grows the methodology from the corner cases the system happened to encounter, so the fast path's quality depends on how that corner-case distribution was sampled. Does this argue for deliberately seeking corner cases rather than waiting for recurrence — and is the fallback traffic itself the right place to look for them?

Relevant Notes:

In this vocabulary, [codification] is the crossing from natural-language into a symbolic artifact with formal semantics, while [constraining] narrows the range of valid interpretations an artifact admits.

Artifact B

First-principles reasoning selects for explanatory-reach over adaptive fit

Commonplace's first-principles methodology is valuable because it selects for explanations with explanatory-reach: claims that keep working outside the case that produced them because they capture why a pattern works, not just that it worked. This note adapts David Deutsch's adaptive-vs-explanatory distinction (his term is bare "reach") for KB design, treating adaptive fit and explanatory-reach as a polarity rather than a hard binary.

Adaptive information helps a system cope with the world. A genome, a neural network's weights, or a local rule of thumb can encode something useful without explaining why it works or where it stops working.

Explanatory knowledge gives a criticizable account of why the pattern works. It can be deliberately varied: change a load-bearing premise, and the explanation should constrain what changes in the conclusion. That variation is what gives an explanation its explanatory-reach.

Partial cases sit between the poles. A rule can transfer across a narrow family of cases because it captures shared structure, while still falling short of a full generative model. The point is not to demote every local observation; local fit is the evidence a later explanation must organize, predict, and improve.

Why this matters for the KB

When a note derives a design pattern from inherited constraints — finite context, no scoping mechanism, text-in/text-out interpretation — the derivation can be explanatory: it says why the pattern works and predicts where it will fail. Change the constraint, and the conclusion should change with it.

That "can be" matters. First-principles stories become post-hoc rationalization when broad premises can justify several rival practices equally well. A useful derivation should rule out at least one plausible alternative, name the constraint that does the ruling out, or predict a failure that later use can confirm.

The [computational-model] area is an explanatory-reach bet under audit. Programming-language concepts such as scoping, partial evaluation, and scheduling were developed for compilers, but they reach into KB design when the shared invariant is explicit: bounded processors compose text under constraints, and unscoped composition lets distant bindings interfere. [LLM context is composed without scoping] therefore works only if the dynamic-scoping comparison predicts real context failures and useful remedies, not merely because the analogy is elegant.

The negative test

This adapted distinction provides a quality check orthogonal to the KB's type system. A well-formed note can pass every structural check while still recording a pattern without explaining the mechanism. The test:

  1. Can you vary a load-bearing premise? If changing one premise lets you predict a constrained change in the conclusion, the note is exposing causal structure. If any premise can move while the conclusion stays rhetorically intact, the derivation may be decorative.
  2. Does it reach? Would the insight apply in a domain you have not considered, and can you say which invariant carries it there? If yes, the mechanism is deeper than the original case. If no, the note may be context-fitted.
  3. Can it be criticized? Is there a specific way the explanation could be wrong, not just incomplete? The [falsifier blocks] practice operationalizes this.
  4. Does observed fit discipline the explanation? Local success is not second-class residue; it is evidence. If the explanation cannot account for where the pattern actually works, fails, or costs too much to maintain, it has verbal explanatory-reach without operational grip.

The first three tests map to the three depths in [discovery]: shared feature (adaptive), shared structure (partially explanatory), generative model (fully explanatory, with explanatory-reach). The fourth is not a depth — it holds an explanation at any depth accountable to the observed fit it must organize.

Scope

Explanatory-reach is the quality goal for theoretical notes, not the only kind of KB value. Descriptions need economy, instructions need precision, and logs may preserve local observations before the mechanism is understood. The explanatory-reach filter says when an observation is ready to become a transferable claim; it does not replace the capture layer that supplies the observations.

Open Questions

  • Where in the KB are notes that are well-formed but merely adaptive? Those are candidates for deepening.
  • Which first-principles derivations currently rule out a rival practice, and which only explain an already-preferred practice after the fact?
  • Should this note keep a direct Deutsch source, or is the adapted distinction enough if the KB-specific test stands on its own?

Relevant Notes:

Derived into:

  • [review-explanatory-reach] — the four-part negative test restated as a recurring review procedure
  • [COLLECTION.md] — the four-part negative test condensed into the "Tests for explanatory-reach" authoring block

Under-review context phrase

explanatory-reach is what the theory layer contributes and the methodology gives up