Datasets:
Expert review brief
Question for specialists
Does the stated finite pair-guard architecture have exactly the parity record threshold in Theorem 4.1, and does an independent product-parity context force dual directed records as in Theorem 8.2? If correct, is this a new restricted result, a known theorem in another representation, or an elementary consequence already established in adjacent literature?
The manuscript is an AI-assisted draft. Its definitions, proofs, and tests are available. This support kit is an invitation and a review structure, not an endorsement.
Main claims and priority of review
| Priority | Claim | Location | Critical obligation |
|---|---|---|---|
| 1 | C04: sharp threshold | Theorem 4.1; thm:threshold |
An adjacent swap changes only the pair's surviving records; the independent parity context preserves the inclusion direction |
| 1 | C10: context-forced duality | Theorem 8.2; thm:compositionmin |
The second block reverses product parity without changing the first pair's inclusion orientation |
| 2 | C06: delayed parity | Theorem 5.1; thm:delayed |
Every proper protocol leaves an unresolved pair and no empty pair; all comparisons resolve at completion |
| 2 | C07: commuting obstruction | Theorem 6.1; thm:commuting |
Prefix-set parity pairing works for every cumulative extinction count, including boundary prefix sizes |
| 2 | C08/C11: exact certificates | Theorems 7.2/8.3 | A live accepting positive term determines unique local linear extensions and needs all adjacent chain comparisons |
| 3 | C01-C03/C05/C09/C12 | Claim ledger and manuscript | Verify algebra, subsequence semantics, universality, interleaving stability, and explicit resource accounting |
The original complete proof/check mapping is in results/proof_test_map.csv. Computational searches are finite support for the proofs and must be assessed separately.
Proof checklist
- Check whether the definitions permit arbitrary monotone observers, and ensure the lower bound does not secretly restrict the observer to the supplied circuit.
- Confirm that optional record allocation, mandatory markers, simultaneous input guards, and distinct labels are handled exactly as stated.
- Test no-direction, one-direction, and two-direction allocations for an adjacent pair. Confirm all other comparisons remain unchanged.
- In Theorem 4.1, check the use of two labels outside the chosen pair when $n\geq4$; verify the exceptional $n=2,3$ constructions.
- In Theorem 8.2, check $n=2,m=2$ as well as two triads. Inspect necessity independently of sufficiency.
- Check whether a valid partial state contains an accepted complete-order certificate whenever the claimed observer stays one.
- Confirm that the commuting obstruction does not imply individual extinction order independence. The $n=2$ exception must remain.
- Audit the unique-linear-extension argument for positive terms and the exact term width. Distinguish dead terms from live ones.
- Inspect the explicit off-protocol DNF/circuit counterexample. Preserve the difference between a restricted-domain representation result and a total Boolean-function lower bound.
- Verify that logs, observers, resets, and recursive resource growth are not omitted from any proposed application.
Equivalence and prior-art review
Begin with audit/novelty_audit.md and paper/references.bib; their access-depth limits are part of the record. The following conventional formulations are especially relevant:
| Neighbor | Question to resolve |
|---|---|
| Unate Boolean functions on pairwise permutation comparisons | Is the 1/3/full-direction threshold known as a monotone or unate representation theorem? |
| Weak order, total-order comparison vectors, and order polytopes | Is the projected-state monotone-separation argument already a standard corollary? |
| Reliability signatures and failure-order statistics | Which parts reduce to established extinction-position calculations? |
| Dynamic fault trees and order-sensitive failure | Is the compiler a known finite-state realization, and are equivalent resource bounds already established? |
| Write-once/one-directional memory | Do known coding constructions give an equivalent restricted compiler or explain its bounds? |
| Dual-rail and hazard-free circuits | Which circuit ingredients are standard, and is the stated restricted-domain certificate comparison correctly framed? |
| Permutation-stream algorithms | Keep unrestricted streaming space separate from this cell-allocation model |
An equivalence assessment should include the primary source, theorem/page, mapping of states and operators, translated assumptions, and matching conclusion. Report equivalent_prior_art_identified only when that translation is supplied. Otherwise identify unresolved comparisons. No finite audit can establish absence from all literature.
Reproduction and report
python tools/check_manifest.py
python tools/reproduce.py --full --output runs/expert-reproduction
Use the review template to record your selected claims, actual review scope, proof gaps, counterexamples, source equivalences, and recommendations. Anonymous review is supported by leaving the name blank while specifying reviewer kind. Independent status must reflect the reviewer's actual relationship to the work; it is never inferred from a passing command.
Provide an exact replacement theorem when recommending a correction. If rejecting a novelty claim, include a translation to the antecedent. If finding an error, include a minimal example or the precise missing inference. Mark unfinished claims not_reviewed.