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:

```bash
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.