docs/EXPERT_REVIEW.md

FNE–AXIOMESH: expert review guide

This guide makes the exact research artifact auditable. It supplies entry points, assumption checks, and falsification targets. Independent human peer review has not been performed; no endorsement is implied.

The narrow claim worth examining

Counterfactual Quotient Weaving couples a supplied capability extension to its future observation closure, missing ancestral information, recoverability checks, and executable consolidation. The reference code demonstrates that contract in finite linear systems. Whether joint selection gives an advantage over separately optimized learning and repair is the central unresolved question.

The important boundary is between validity, distinctness, and advantage. A correct quotient compiler is not evidence that the coupled architecture is new. A novel contract is not evidence that it improves intelligence. The strong finite learner ties the principal predictive benchmark.

Fast review path

Read README.md, docs/CLAIMS.json, and docs/IMPLEMENTATION.md; inspect the manuscript's problem statement and exact theorems; then run:

python -m pip install -r requirements.txt
python validate_release.py
python -m pytest -q
python examples/minimal_cycle.py
python agent_interface.py --request examples/agent_recover.json
python run_experiments.py --seed 20261007 --output local_runs/expert-check

The example outputs are [9] after one acquisition and reunification, and [47] for the independently restored saved quotient. local_runs prevents exploratory output from replacing the archived evidence. For structural/schema checks, install requirements-validation.txt and run python validate_release.py --schemas.

Proof-to-code map

The named labels are searchable in manuscript/FNE_AXIOMESH_Manuscript.tex. The manuscript PDF is bundled for normal reading. Theorems are human-readable derivations; there are no Lean/Coq proof certificates.

Question / claim	Manuscript location	Implementation	Relevant tests
Least query space stable under declared actions	thm:quotient, thm:compile	close_operators, Closure.compile	test_closure_exact_and_frozen, test_random_closure
New actions reveal a previously forgotten distinction	“Why present recall is not future recall”	hole_certificate, Memory.recall	test_static_recovery_is_not_future_recovery; adapter capability-growth test
Exact behavior identification from memory	thm:recall	Memory.recall, solve_affine	test_inconsistent_memory_rejected, test_partial_execution
Minimum missing unrestricted scalar information	thm:debt	Memory.supplement, Memory.acquire, weave	test_acquisition_lower_bound_and_transaction
Minimal complement beyond combined child views	thm:tether	split_with_tether, FractalSplit.reunify	test_minimal_fractal_tether, test_split_rejects_missing_cover_or_unidentified_parent
Recursive reconstruction without internal parent seeds	thm:recursive	fractalize, regenerate_tree	test_recursive_fracture
Known-erasure coding and bounded-radius correction	“Fractal checkpoints and lower bounds”	Capsule.recover, Capsule.correct	test_all_erasures_within_radius, test_one_corruption_bounded_distance
Mixed-action complementarity	“Why individual branch novelty can fail”	emergence_rank; scheduler experiment	test_emergence_requires_mixed_words
Unrestricted future actions defeat universal compression	thm:full	Interpretation limit, not an all-worlds solver	Inspect the theorem assumptions directly

Assumptions requiring explicit review

1. State is a finite-dimensional column vector over a prime field. Queries and action matrices are supplied; their semantics are not autonomously discovered.
2. Every execution word uses the admitted operations; witnesses are chronological.
3. Measurement values are trusted and consistent. Identifiability is relative to this declared family, rather than a certificate that the family fits reality.
4. The tether rank subtraction assumes combined child information lies within the parent relevant row space. Without inclusion, use the appropriate rank deficit of the stacked spaces rather than blindly subtracting dimensions.
5. Minimum acquisition debt assumes unrestricted scalar linear observations. A physical sensor family, noise, cost weights, or unavailable observables changes the attainable minimum.
6. Recursive recovery requires the needed leaf information, tether values, and transformation metadata to survive or be recoverable. The construction does not retrieve independent information after all identifying traces are lost.
7. Coding guarantees concern known erasures or the explicitly declared small bounded-distance regime. Consistent corruption of unchecked shares or program metadata can invalidate the recovered semantics.
8. State symbols, serialized bytes, and total memory have different meanings. Charge operators, queries, maps, certificates, code, and search history.

Disciplinary review routes

Expertise	Focus	What would change the conclusion
Observability / abstract interpretation	Reduction to standard minimal sufficient state constructions	A direct established equivalence for the full coupled admission transaction
Coding / information theory	Conditional information, erasure assumptions, repair cost	An invalid minimality bound or uncounted state channel
Program synthesis / library learning	Whether representation growth is supplied or learned	Strong shared-language learning baselines that explain any gain
Continual learning / neural memory	Relation to representation-dependent forgetting	A useful implementation on trained models with controlled ablations
RSI / empirical evaluation	Next-discovery productivity under fixed resources	Repeated improvement in discovery efficiency, or persistent controlled null results

Highest-value falsification targets

• Construct a supplied-family case where Memory.recall reports exact but two consistent states give different declared future outputs.
• Find a parent/child split with an inclusion or overlap assumption missing from the stated tether bound; report the exact spaces and dimensions.
• Show that an alleged advantage disappears when both systems receive the same operators, compiler, coding tools, proposal language, oracle calls and total cost.
• Determine whether apparent neural regeneration uses hidden replay samples, a retained full state, privileged sensor information, or an uncharged teacher.
• Test whether next-generation search productivity stays flat after deployment gains; that would support retention or synthesis without recursive acceleration.

Use docs/EVALUATION_PROTOCOL.md for a proposed controlled experiment and docs/REVIEW_REPORT_TEMPLATE.md to report findings. The prior-art material in docs/PRIOR_ART.md is inherited from the original release and is not exhaustive.