# Editorial scope of other-v5

This revision changes checkpoint boundaries, not just prose length. The earlier collections, original decompositions, and historical evaluations are preserved. Berenstein is identical to other-v4; unit distance is unchanged. The six other families have 27 revised endpoints, out of their 32 checkpoints.

Each transition still supplies only its named starting statement and target. Definitions required to identify an object repeat locally; earlier conclusions, certificate data, proof instructions, and unused objects do not. These notes are outside solver inputs. None of the statements is certified by formatting or synchronization, and no model evaluation is launched.

## Knot polynomials

- H1 now asks only for the odd-linking Laurent polynomial's modulo-four norm factor. The general norm-class description and closure properties are omitted; a solver can establish them if useful.
- H2 is the Conway-square theorem for an orientation-reversing involution preserving the knot orientation. It does not state finite cyclic-action classification or a quotient tower. This is a narrower checkpoint than v4's complete finite-symmetry construction.
- H3 is only the branched-double-cover factorization, with the component and Laurent-unit conventions required to state it. The Conway/Torres specialization and nonvanishing at minus one are omitted.
- H4 is only integral two-variable normalization for the specified rotary-reflection links. The exact specialization at plus two and congruence at minus two are omitted. The odd linking hypothesis remains.
- H5 and H6 retain the original finite-symmetry and general amphicheiral splitting conclusions verbatim.

## Periodic BBM

- H1 states propagation of the observed zero values of z, w, and w_x. Analytic flow, uniqueness, conservation, and the evolution identity are no longer separate conclusions of that checkpoint.
- H2 is the weighted evolution identity, and H3 is finite total flux. Unused norm definitions are removed. The underlying PDE, observation hypothesis, and flux definition remain local.
- H4 is unchanged: global rigidity for every real observed constant.

## Scalar Crouzeix

- H1 and H2 retain their completion endpoints; notation is limited to what those statements use.
- H3 states positivity and unitality of the boundary map for a smooth convex domain parametrized by arclength. It no longer asks for the more general Lipschitz radial parametrization or repeats a supporting-normal inequality. This is a deliberate restriction of the checkpoint's boundary regularity, not an assertion of equivalence between the two formulations.
- H4 is the numerical-range inequality directly for a simple-spectrum matrix. The convex outer-domain formulation is removed. Establishing the numerical-range version, including any necessary approximation, is the solver's obligation.
- H5 retains the original general holomorphic inequality and sharp constant. Unused algebra/positivity notation and the redundant rational-function remark are removed.

## Groups with isomorphic factors

- H1 asks only for the two semidirect-product realizations. The equivariance, diagonal quotient, and cocycle identities are no longer separately stated conclusions.
- H2 asks for the factor isomorphism; H3 retains the invariant-measure bound; H4 asks for property (T).
- H5 is now abstract nonisomorphism of the two explicit groups. ICC, characteristic-kernel detection, and quotient-normal-subgroup conclusions are removed from that target; they may be supporting facts in a proof. This changes the endpoint, rather than just shortening the previous kernel lemma.
- H6 retains the original existential ICC/property-(T) counterexample statement verbatim. ICC has not been silently assumed for the constructed groups in any intermediate target.
- The group presentations, not an asserted action or kernel embedding, define the objects in H2/H4/H5. The shared construction is shorter but must still be repeated to make each target self-contained.

## Jamming exponent identity

- H1 is the classical profile equation across zero. It omits auxiliary B identities and tail conclusions. The original Gaussian hypotheses imply the stated endpoint limits; they are written as one two-sided estimate.
- H2 is the integrated exponent-defect identity in one integral. It does not expose a list of named K,N,D quantities and an adjoint proof plan.
- H3 is the integrated marginality relation. The p differential equation and unused exponent a are removed because the relation only needs a positive continuous polynomial-growth weight. J's raw ODE and interface hypotheses remain, so no classical-gluing conclusion is granted.
- H4 states range preservation only; the additional attained-profile corollary is omitted.
- H5 asks only for a+b=1. The equivalent a value and derived alpha/theta/kappa identities are omitted. Raw ODE, tail, integrated marginality, parabolic-flow, and attained-profile assumptions remain: deleting them would change this conditional theorem. The maximum-principle conclusion, marginality conclusion, and defect identity are not granted as hypotheses.
- This retains v4's precise generic parabolic comparison setting. It still does not prove the omitted physical derivation from a fullRSB model or an unconditional theorem about sphere packings.

## Quartic SYK

**Review flag, 2026-10-11: needs mathematical review.** The proof basis and H1–H6 checkpoint chain require an independent mathematical audit before SP-1 is treated as a validated benchmark. The flag is stored in `review-flags.json` and displayed in the local reader; it is excluded from solver and judge inputs.

The completed experiment produced 80 failing proof verdicts, one operationally unknown review, and three missing solver answers for SP-1. Representative submitted arguments use a false differential identity for a Dyson pair, assert a pressure limit from two-point convergence without justifying the required connection, or infer an annealed expectation bound from an event for one realization. These are defects in those submissions. The checkpoint statements have not been independently certified or disproved by this experiment.

Evidence: [final grades](../../runs/2026-10-11-other-v5-sol-grading-465-192122/final-report.md) and [recorded verifier reasons](../../runs/2026-10-11-other-v5-sol-grading-465-192122/failure-reasons.md). Keep the existing statements and historical verdicts while this review is pending.

- H1 asks only for the unique positive thermal fixed point. The transform theorem for arbitrary sources and the second-moment conclusion are omitted.
- H2 retains history-weighted locality; H3 retains a common directing law for the real pair words. Their random-matrix and bath definitions are compressed without changing coefficients, representations, trace normalization, word signs, or quantifiers. A malformed TeX fragment in H2's even-N limit is corrected.
- H4 asks for uniform convergence of the finite-bath thermal kernels to a family characterized by the mixed Dyson equation. It no longer claims uniqueness of all mixed-equation solutions as a separate conclusion. Existence of the limiting family is part of the convergence statement; no fixed point is assumed from H1.
- H5 asserts an unconditional finite pressure limit and its value for every self-consistent Dyson pair. It omits a repeated assertion that such pairs exist; existence and uniqueness belong to H1. The pressure-convergence obligation is not made conditional or vacuous.
- H6 asserts the almost-sure edge with its original integral constant and an existing measure satisfying the zero-temperature equation and normalization. It omits uniqueness of the zero-temperature measure as a separate claim. The deterministic edge and existence of a representing measure must still be proved; neither is assumed. This narrows the original bundled obligation while preserving the spectral-edge conclusion and constant formula.

The revisions are based on the supplied decompositions and previously reviewed sources. Live source-page retrieval was unavailable during this pass. Structural checks verify prompt isolation, exact generated copies, mathematical rendering, and version preservation; they are not reference proofs or judge calibration.