Fiber Fingerprints of Hidden Learning-State Dynamics

Qinyou Wang

Source-linked AI summary

Fiber Fingerprints of Hidden Learning-State Dynamics

Qinyou Wang

arXiv:2608.15976v1Aug 17, 2026cs.LG

TL;DR

The paper asks whether execution states with identical present behavior must learn identically, given that parameters and training-state variables can affect future trajectories. It formalizes controlled future-learning responses into a predictive quotient and finds that present behavior is not sufficient to determine declared future learning.

Problem
The paper asks whether execution states indistinguishable under present-behavior readouts must learn identically, despite differing training-state variables that can alter future trajectories.
Method
The paper uses controlled finite future-training probes to construct a predictive quotient, minimal recursively sufficient representation, and set-level predictive fiber without assuming smoothness or fixed dimension.
Results
Present behavior is not a sufficient statistic for declared future learning, while Transformer studies support structured local responses, longer-horizon non-closure, and reuse alongside a low-rank irreducible sector.
Takeaways & Limitations
The supported conclusion is that future-learning behavior requires a support-, scale-, metric-, and context-resolved state description beyond present behavior.
Takeaways & Limitations
The re-anchored transport study rejects one specific membership but leaves global path independence and stable ambient linear transport unresolved above the measurement floor.

Abstract

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A learning system can occupy execution states that are indistinguishable under every declared present-behavior readout yet respond differently to future training. We formalize this through fiber fingerprints: controlled future-learning response laws restricted to present-behavior equivalence classes. Prefix-compatible finite probes induce a predictive quotient functor, a Nerode-type minimal recursively sufficient representation, and a canonical set-level predictive fiber without assuming smoothness, reversibility, finite rank, or a manifold. Under an explicit finite-dimensional Hilbert realization, response decomposes into visible, visible-mode-reuse, and irreducible-new sectors; a history-reachability bridge retains only distinctions generated by natural training histories. Conditional mechanism results then identify a graph-Hodge chronology decomposition, a regular switching class with root-mean-square scale $\sqrt{p}η^{3/2}$ and finite-scale corrections, and an exact Adam moment section whose immediate adaptive field is constant while common future gradients can reveal hidden moment differences. Frozen Transformer--LoRA--AdamW studies with Qwen2.5-7B and Mistral-7B-v0.3 support a local action backbone, longer-horizon first-return non-closure, and fresh visible-relative completion with output-range reuse and a low-rank irreducible sector. Stronger claims remain bounded by preregistered negative or mixed results: re-anchored transport is unresolved above its measurement floor; the strict finite-grid Hodge--$3/2$ conjunction is unmet despite prospective contraction; Qwen accessibility is not established in the frozen raw moment chart; and Mistral revelation is future-context dependent rather than bank invariant. Within these support-, scale-, metric-, and context-resolved boundaries, present behavior is not a sufficient statistic for declared future learning.

1 Introduction

The paper argues that present behavior need not determine future learning, and formalizes the remaining distinctions through finite, set-level fiber fingerprints. It separates unconditional predictive structure from conditional Hilbert, chronology, optimizer, and experimental results.

Motivation: Execution states with identical present readouts can differ in parameters, optimizer memory, schedules, data position, and other variables that alter future training trajectories.The paper shifts focus from present-function equality to whether execution states respond differently under future training.
Motivation: Prior work shows that function-preserving rescalings, hidden gauges, loss-invisible recurrent overlaps, optimizer memory, and task-order geometry can encode differences revealed through learning.These results motivate treating present behavior as insufficient to characterize learning state.
Predictive state: Fiber fingerprints retain future-response structure within present-behavior fibers using a finite-scale, set-level construction that does not require smoothness, reversibility, finite rank, or a global manifold.Metric, Hilbert, differential, switching, optimizer, and smooth-global structures are introduced only as explicit enrichments.
Contributions: The framework defines predictive state via operational fiber fingerprints, quotient descent, Nerode-type minimality, finite-horizon typing, a canonical global fiber, and a Transformer–LoRA–AdamW instantiation.In a finite-dimensional Hilbert realization, response separates into visible, visible-mode-reuse, and irreducible-new sectors, with history-weighted obstruction determining optimal finite-rank completion.
Conditional mechanisms: Conditional mechanisms include graph-coboundary plus interaction chronology, cycle response with root-mean-square scale √pη^3/2, and Adam moment revelation under common future gradients.The graph result requires a separately declared crossing regime, while the Adam result preserves the immediate adaptive field.
Scope and boundaries: The finite predictive quotient is unconditional relative to a declared probe doctrine, whereas completion, Hodge, switching, Adam, smooth-global claims, and experiments require separate assumptions.Negative studies define informative boundaries rather than refuting the set-level theory; bank-dependent revelation remains compatible with positive future observability.

2 Finite controlled experiments and predictive quotients

Finite controlled-learning probes define present-behavior fibers and operational fingerprints, yielding a Nerode-type predictive quotient that is recursively sufficient relative to the declared probe doctrine. The framework instantiates for frozen Transformer–LoRA–AdamW execution without smoothness or low-rank assumptions, while keeping operational dimensions distinct from physical state dimension.

Operational fibers: Prefix-compatible future probes define operational fingerprints on present-behavior fibers, without requiring latent coordinates, physical dimensions, or a manifold.Completeness is relative to the declared probe doctrine, and the fibers are exact set-level objects.
Predictive quotient: Predictive equivalence is a congruence, so finite controlled protocols descend to a functorial predictive quotient.This quotient supports recursive reasoning over controlled transitions.
Predictive quotient: The complete predictive quotient is the coarsest recursively sufficient representation through which every declared response and controlled protocol factors uniquely.This is the controlled-learning analogue of Nerode minimality.
Global fiber: A canonical global finite-scale fiber exists as a discrete opfibration even when quotient cardinalities or local ranks jump, contexts are singular, protocols are irreversible, or no global chart exists.The construction remains set-level and does not depend on smoothness or constant rank.
Concrete instantiation: Finite Transformer–LoRA–AdamW training satisfies the controlled finite-scale axioms when primitive execution is single-valued from the complete execution state and control.Its predictive quotients, history-natural endpoints, directed quotient transport, and global set-level predictive fiber require no smoothness or low rank.
Limits: Operational quotient, bridge, and completion ranks do not identify physical neural-state dimension, which can increase arbitrarily under response-ignored auxiliary systems.Approximate matching is a separate measurement and stability layer because tolerance relations may be nontransitive and transition-unstable.

3 Visible-relative predictive completion

Under a conditional finite-dimensional Hilbert realization, future-response distinctions split canonically into visible, visible-mode-reuse, and irreducible-new sectors relative to declared metrics and ranges. History weighting retains only naturally reachable distinctions, while completion rank measures required response modes rather than physical state dimension.

Conditional realization: The finite-dimensional Hilbert realization quantifies which future distinctions are explained by a declared visible action backbone and which require additional predictive modes.It supports pseudoinverses, Hilbert–Schmidt norms, traces, and spectral tails under fixed metrics and stable ranges.
Canonical relative decomposition: The canonical decomposition separates visible-input response, input-invisible response reusing the visible output range, and irreducible response in an orthogonal new output direction.These three components are pairwise Hilbert–Schmidt orthogonal and uniquely determined by the declared visible input and output ranges.
Factorization obstruction: The shorted residual vanishes exactly when every input-invisible response lies in the visible response range.Thus the relative factorization obstruction is characterized by Ran(𝐾𝑄) ⊆ Ran(𝐾𝑃).
Minimal irreducible completion: The rank of the residual is the finite-horizon irreducible completion dimension relative to the declared realization, not the physical state dimension.Optimal rank-m completion errors are determined by the residual spectrum through the Eckart–Young theorem.
History-reachable completion: History weighting retains only naturally occupied irreducible response directions, yielding a minimal reachable predictive completion on the covariance-supported quotient.A geometric residual may exist without being generated by natural histories, and low completion rank identifies response modes rather than neural-state dimension.
Horizon filtration and predictive sequence: Irreducible distinctions cannot decrease with cumulative horizon, and the reachable predictive tangent separates visible-mode reuse from the irreducible bridge quotient.All operator-level claims remain relative to declared metrics and stable ranges; the finite response law is primary when those conditions fail.

4 History generation, chronology, and switching

This section separates reachable-history generation from future observability and decomposes chronology effects into graph-coboundary and cycle interactions. Under explicit regularity and concentration conditions, it derives a conditional 3/2 switching law with finite-scale corrections while limiting its universality.

History generation: History laws induce reachable state distributions, with local covariance transport governed by a primary set-level commuting square and differentiable chart relations only under stated assumptions.The construction uses endpoint pushforwards of rooted histories and distinguishes set-level naturality from its local differential form.
Chronology decomposition: Cycle projection removes common-affine single-task potential memory and retains the state-dependent interaction obstruction in the common-operator specialization.For task-dependent operators, an additional contraction/commutator obstruction must be retained, so the exact decomposition does not automatically extend to heterogeneous operators.
Regular switching class: Under Assumption 4.2, the graph-projected switching response follows a conditional 3/2 law tied to regular crossing counts, centered marks, finite second moments, and weak aggregate dependence.The 3/2 exponent is one conditional universality class, not a universal consequence of a named architecture.
Finite-scale corrections: Under Assumption 4.4, the second-order effective exponent supplies finite-scale corrections, while the generic joint-limit fluctuation scales as (pη)^−1/2 rather than unconditionally p^−1/2.The concentration statement is imposed explicitly; bounded dependency graphs with suitable fourth-moment control are one sufficient route.
Generation and observability: Chronology generation and future observability factor separately: reachable directions may have positive generation covariance yet lie in Ker W_c,H, while revealing directions may be rarely generated.Storage and revelation efficiency therefore remain distinct, so weak visibility alone does not identify rapid dissipation.

5 Adam execution fibers, accessibility, and future revelation

Adam admits exact matched moment sections whose states share current parameters, present behavior, and immediate adaptive fields, yet can become distinguishable under common future gradients. The section separates optimizer-level and neural accessibility from context-conditioned revelation and cross-bank coherence.

Matched-section cancellation: Different Adam moment states can share the same current parameter, present behavior, and immediate adaptive field through exact matched-section cancellation.The cancellation follows because the exponential factors in the numerator and denominator match.
Accessibility: For K≥2, reachable terminal injections fill an epigraph, while K=1 requires equality; the result is optimizer-level and need not reflect coupled neural gradients.A first-moment-null component preserves M_K while continuously increasing V_K.
Accessibility: Surjective local neural accessibility yields nearby dynamically reachable matched-section points, but accessibility has distinct algebraic, local, metric-stable, and finite-panel levels.Metric transport preserves generalized singular values, unlike a raw Euclidean condition number.
Future-gradient revelation: Common future gradients can first-order resolve matched states at horizon n when the revelation expression is nonzero, whereas n=0 is identically unresolved.Unequal decay rates alone do not reveal differences when all future gradients vanish and ε=0.
Revelation and coherence: Revelation is future-gradient and context conditioned: positive revelation by every bank does not imply positive cross-bank directional coherence.The general theory therefore uses a context-indexed observability field rather than one universal resolving vector.

6 Global transport and resolution-supported geometry

Global transport is canonically defined at the set-level through the predictive quotient functor, while endpoint-independent trivialization requires equivalent identity-holonomy conditions. Empirical transport is resolution-supported and locally stable only under retained-rank and spectral-gap conditions, so unresolved directions cannot establish identity action or path independence.

Global transport: Endpoint-only transport, identity loop holonomy, and path-independent trivialization are equivalent on connected context groupoids with isomorphic quotient transports.The equivalence is Theorem 6.1.
Resolution-supported geometry: Resolution-supported transport acts on the declared resolved source support, vanishes orthogonally, and is locally Lipschitz under preserved retained dimension and spectral gap.Its stability constant depends on the resolved singular scale, spectral gap, and a local target bound.
Resolution-supported geometry: A composed empirical path yields only a partial monodromy operator on the common admissible domain; undefined unresolved directions do not prove identity action there.This distinction prevents non-definition from being interpreted as trivial holonomy or path independence.
Global geometry: The unconditional global object is the category of elements of the predictive quotient functor, not necessarily a smooth bundle, differential connection, fixed action propagator, or nontrivial holonomy.These structures require additional hypotheses or empirical factorization.

7 Transformer studies and empirical membership

The Transformer studies support a local response backbone, but longer-horizon learning remains history-conditioned and includes visible-output reuse plus a small irreducible completion. Stronger transport, switching, accessibility, and revelation claims are mixed or bounded by preregistered negative results.

Local action and non-closure: A low-dimensional local response backbone exists, but longer-horizon response contains history-conditioned first returns not exhausted by the declared current action core.The full 9 × 9 first-return system has local r90 and r95 near four over horizons H3–H5, while fixed context-independent propagation is unsupported.
Visible-relative completion: 13.64%: the one-sided 95% lower bound on the irreducible-new fraction at source horizon H5; at shifted H6, the lower bound is 10.87%.The completion picture retains a declared three-dimensional visible action core, structured visible-output reuse, one or two dominant irreducible modes, and a weaker residual tail.
Transport: 3.57 × 10−6: mean cross-bank energy after exact AA+C re-anchoring, but its one-sided 95% lower bound is −3.00 × 10−6 and only one of twelve reconstructions passes the principal criterion.The synchronized sign p-value is 0.171875 and the median signal-to-noise ratio is 0.001651, leaving nontrivial re-anchored transport unresolved.
Switching and Hodge mechanism: The switching results provide strong prospective support for the controlled hard-ReLU Hodge–3/2 mechanism, but the complete preregistered conjunction is not met because four finite-grid boundaries are exceeded by 2.8 × 10−4 to 3.6 × 10−4.The initial-grid cycle response scales approximately as p^0.5113η^1.5163, while future-bridge η exponents are approximately 1.5061.
Optimizer-state accessibility: Mistral passes the frozen accessibility screen for all six tested candidate seeds, whereas Qwen satisfies none under the declared raw (m, v) Euclidean conditioning criterion.Natural alignment is high in both contexts, but Qwen accessibility is not established in the frozen raw moment chart.
Future-gradient revelation: 1.99895: median full/half norm ratio in Mistral revelation, with median direction cosine 0.99999894; future-gradient-conditioned revelation is supported, but bank-invariant direction is not.All twelve full-amplitude future-bank responses are nonzero, every full-amplitude zero-gradient control is exactly zero, and four of six cross-bank inner products are positive with a negative one-sided lower bound.

8 Related work and novelty boundary

The paper’s novelty lies in coupling present-behavior equivalence with controlled future-learning probes, rather than inventing its mathematical ingredients. Its contributions include predictive quotienting, history-generated fibers, visible/reuse/irreducible completion, chronology decomposition, and optimizer-state cancellation and revelation.

Observability and predictive state: The framework specializes observability and predictive-state ideas to complete training states, quotienting present behavior and using future training protocols as distinguishing experiments.This operationalizes state distinctions that ordinary present input–output behavior cannot expose.
Hidden learning state: Prior work shows that functionally equivalent or same-function parameterizations can have different training dynamics, while this framework makes those hidden distinctions optimizer- and architecture-agnostic.Related results include loss-invisible overlaps, path-conditioned rescaling, and hidden-gauge effects on specialization time.
Predictive completion: The paper combines established balancing, range, inversion, and approximation tools with a frozen visible learning-action backbone to separate visible-output reuse from irreducible-new response.The novelty concerns their coupling to present-behavior equivalence and controlled future learning, not those ingredients in isolation.
Chronology: The chronology contribution is narrower and mechanistic: graph-cycle projection removes task-potential memory, isolates state-dependent interaction, and yields a graph-projected 3/2 rare-event law under a separately declared crossing regime.Neither graph Hodge decomposition nor smooth Lie brackets is claimed as new.
Optimizer state: The optimizer contribution is an exact Adam moment-space section preserving the immediate adaptive field while characterizing reachability and future-gradient de-cancellation.This extends the coupled execution-state architecture into optimizer cancellation and revelation.

9 Limitations, non-implications, and open boundaries

The theory’s predictive quotients and fingerprints are conditional on declared probes, response semantics, horizons, metrics, and regularity assumptions. Experiments establish bounded, context-specific findings rather than global transport, native-model membership, coordinate-free accessibility, or broad replication claims.

Formal scope: Predictive quotients are relative to declared probe families, response gauges, horizons, and measurement semantics; finite banks need not be complete, and approximate equality need not be transitive.Population, finite-readout, and floating-point responses remain distinct objects.
Formal scope: The unconditional global object is the predictive quotient functor’s category of elements, not necessarily a manifold, smooth bundle, connection, or stable-rank geometric construction.Tangent spaces, Gramians, pseudoinverses, spectra, and shorted operators require declared regularity, rank, range, and metric conditions.
Transport limits: Re-anchored transport rejects one empirical membership claim but does not prove global path independence or stable ambient linear transport.When source directions approach the measurement floor, resolution-supported partial transport is the appropriate finite estimand.
Conditional mechanism claims: The 3/2 exponent is conditional, and the preregistered finite-grid conjunction was not met; hard-ReLU controls do not establish native Qwen or Mistral SiLU membership.The second-order proposition explains possible asymptotic slope convergence but does not change the empirical verdict.
Accessibility and revelation: Algebraic matched sections need not be visited by natural training, raw-coordinate accessibility is metric dependent, and Mistral revelation is future-gradient conditioned rather than bank invariant.The closed derivative formula covers the first resolving event under exogenous common gradients; longer endogenous dynamics require the coupled tangent recursion.
Empirical boundaries: Evidence is limited to declared model revisions, LoRA, AdamW, domains, horizons, and numerical contracts; cross-context and cross-family claims require independent replication.Open questions include complete finite-probe criteria, all-horizon rank stabilization, native switching membership, supported transport, and broader replication.

10 Conclusion

Present behavior is not a sufficient statistic for declared future learning: behaviorally equivalent states can carry distinct future-response laws. Fiber fingerprints provide a canonical operational representation of this missing predictive structure, while explicit realizations and Transformer studies clarify its structure and empirical boundaries.

Core theory: Finite controlled probes induce a canonical predictive quotient, minimal recursively sufficient representation, and global set-level fiber without smoothness or fixed dimension.These constructions represent structured future-response laws within present-behavior equivalence classes.
Explicit realizations: Visible-relative completion separates declared action response, visible-output reuse, and irreducible-new modes, restricted by history-reachability to training-generated directions.Graph-Hodge chronology further distinguishes task-potential memory from state-dependent interaction, with a conditional graph-projected 3/2 scale.
Empirical boundaries: Transformer studies support structured local action response, longer-horizon non-closure, fresh completion with reuse and a low-rank irreducible sector, and future-gradient revelation that is not bank-invariant.The re-anchored transport panel remains unresolved, while the controlled switching mechanism approaches but does not satisfy its full finite-grid conjunction.
Conclusion: Present behavior is not a sufficient statistic for declared future learning.This is the paper’s principal conclusion.
Implication: Fiber fingerprints operationalize the predictive structure missing from present behavior, while deciding what to acquire for production decisions remains a downstream decision-theoretic problem.The state theory does not require resolving that downstream choice.

A Proof details for the finite predictive core … C.2 Second-order switching law

The appendix proves the finite predictive core and its mechanism refinements using sets, finite protocols, and prefix-compatible responses, while deriving Hilbert, chronology, switching, and Adam results with explicit resolution and feedback boundaries. It also establishes minimality, history-restricted completion, implementation-dimension non-identifiability, and finite-grid limitations without topology, rank, smoothness, or reversibility assumptions.

A Proof details for the finite predictive core; A.1 Proof of predictive descent and functoriality; A.2 Grothendieck construction; A.3 Nerode minimality; A.4 Finite-horizon loss of depth; A.5 Probe enrichment; A.6 Depth filtration: Finite protocols induce a functorial predictive quotient that is Nerode-minimal among response-sufficient representations, with horizon loss and monotone refinement under probe enrichment.The construction uses only sets, functions, finite protocols, and prefix-compatible response semantics; no topology or rank assumption is involved.
A.6 Depth filtration; A.7 Regular tangent specialization; A.8 Finite operator data are not a complete ontology: Regular tangent arguments require locally constant rank, whereas singular points provide only tangent cones, so centered finite probes need an admissible two-branch realization.First-order Hilbert data likewise cannot reconstruct unrestricted finite-scale geometry without a complete response profile or an explicit closure condition.
A.9 Non-identifiability of implementation dimension: An arbitrary auxiliary controlled system can be appended without changing the predictive quotient, proving operational responses cannot identify full implementation dimension.Projection remains response sufficient even when auxiliary dimension and complexity are arbitrary.
B.1 Visible-relative decomposition; B.2 History bridge; B.3 Monotone cumulative shorting: Visible-relative Hilbert–Schmidt orthogonality yields the shorted identity and Eckart–Young optimal completion, while the history bridge retains only distinctions generated by reachable training histories.The cumulative shorting operators are monotone in PSD order as the retained history horizon increases.
B.4 Common-affine chronology; B.5 Graph-projected rare-event law: Graph-Hodge cycle projection removes common-affine chronology, and under the rare-event assumption the diagonal contribution reduces to q b_1(G) while off-diagonal and remainder terms are o(pη^3).The common-affine half-difference splits into a graph coboundary and a residual term; the coboundary is annihilated by cycle projection.
B.6 Exact Adam moment epigraph: For K≥2, perturbations orthogonal to the fixed first moment preserve M_K while continuously increasing V_K, reaching every point above the exact Adam epigraph boundary.This establishes an exact moment section in which distinct hidden moment states can share the relevant immediate constraint.
B.7 Matched-section cancellation and future derivative; B.8 Endogenous feedback boundary: Matched common future gradients reveal hidden Adam moment differences through the logarithmic derivative μ_n−ν_n, but endogenous feedback begins once paired parameter paths diverge.The conditional study freezes the first future-gradient comparison to test exogenous revelation before full tangent recursion is required.
C Resolution refinements and separation results; C.1 Resolution-supported transport; C.2 Second-order switching law: Resolution-supported transport has inverse dependence on the retained singular scale, while finite secant regressions can lie above or below exponent 3/2 yet converge to the same asymptotic class.The family X_t = diag(1, t) establishes the ambient no-go as t↓0; the switching-law conclusion follows under the stated graph-cycle assumptions.

C.3 Metric-aware accessibility … E.3 Status of the mathematical package

The paper separates metric-aware accessibility, revelation, coherence, transport, and observability, then documents reproducible frozen-model studies with explicit quantitative boundaries. Its mathematical package distinguishes theorem-level results, assumption-dependent extensions, and empirical memberships limited to declared execution contexts.

C.3 Metric-aware accessibility: Metric-aware accessibility is coordinate-invariant only after metric transport, while raw (m, v) conditioning is a declared metric membership rather than a coordinate-free theorem.Whitened operators preserve singular values under unitary factors; raw-chart condition numbers can change under v′ = λv.
C.3 Metric-aware accessibility: If r≤τ/(2L), the fixed-point contraction proves local surjectivity near F(0), with ∥R0∥≤τ^-1 and contraction factor at most 1/2.The metric Moore–Penrose right inverse satisfies J0R0 = IM, and the contraction maps the radius-r ball into itself.
C.4 Revelation–coherence separation: Collective visibility and pairwise coherence are distinct: W is positive semidefinite, whereas O* b O b′ may have opposite response directions despite complete bank visibility.The rotation example establishes that revelation does not determine response-direction agreement.
C.5 Four-resolution separation: The four-resolution theorem rejects unqualified implications among set-level predictive transport, ambient linear transport, metric accessibility, and coherence.The refined coupling is history-generated reachable geometry × support-, scale-, metric-, and context-resolved observability.
D Reproducibility contracts and study registry; D.1 General contract: Reproducibility requires complete serialized or reconstructed execution state, frozen candidate selection before protected outcomes, and separated analysis.The contract covers model, LoRA, Adam, schedules, random streams, data cursor, precision, and mutable runtime state.
D.2 Models, adapters, and domains; D.3 Formal study registry; D.4 Detailed empirical ledger: Frozen Qwen2.5-7B and Mistral-7B-v0.3 experiments use frozen base weights, trainable LoRA modules, AdamW moments and step counters, and disjoint token windows across domains A, B, and C.Exact model, tokenizer, data, source, and analysis hashes are included in released experiment packages.
D.5 Selected numerical details: 13.64% and 10.87% are one-sided 95% lower bounds on irreducible-new fractions, while the refined switching study leaves four conjunction criteria unmet.The switching study covers sixteen frozen seeds, five widths, and six η levels; its listed endpoints narrowly exceed preregistered thresholds.
D.5 Selected numerical details; D.6 Artifact integrity; E.1 Licensed and unlicensed interpretations; E.2 Minimal assumption map; E.3 Status of the mathematical package: The conditional revelation study finds minimum tangent alignment 0.919397, median 0.981713, and response norms from 5.74 × 10^-9 to 1.41 × 10^-7, with one reconstruction comparison narrowly missing 1%.Lower-bound and coherence criteria remain unmet independently of that comparison cell; released packages include executable notebooks, logs, archives, frozen analysis, and claim ledgers.