[amaybaum]

Reviewed: independent ACCEPT at c88de8daa0f195cd8b06cb05ebfd72e138ad4f36; CI green there (run 42427342745).

• Scope: paper only, draft. Guiding PR for the OI-QM-EXT-1: establish conditional equivalence with explicit added conditions, then minimize and source them #1169 unit MECH-1 (authorization, research question, owner review guidance).
• Change: one new file, verification/programmes/oi-qm/reconstruction/mechanism-1-20261107/DESIGN.md, from main 313a93ef.

Result (as reviewed): a type (ii) stop

• O3, selection: passes natively at odd q. The symmetric second-order rule u′ = F(u) − v is affine symplectic, and in one fixed phase-space frame exactly those maps act completely positively (Theorem W; Proposition AS). That frame is singled out by a property of the quantum comparator. O3 fails at q = 2.
• O2, capability:
  • Without NNB: fails in bipartite N at odd q (Lemmas S and G). At q = 2, adaptive gradedness is open.
  • With NNB at odd q: passes at stabilizer scope (Lemmas N and M; composition battery). The mechanism's own noncontextual model reproduces it exactly, and there is no quarter phase and no infinite-order unitary.
• O4, continuation: passes under P1, P2 and H-PREP.
• O1, physical source: fails natively (Lemma A; Theorem T). With a static controller slot, T′ gives sufficiency for symplectic branches with an independent uniform v_c. Confinement is necessary whenever a non-eigenstate pure stabilizer controller law is admissible.
• Owner shortcut checks:
  • SC-1: no import in the dynamics. The frame is chosen by comparator covariance, the model has no interference, and the confinement premises are flagged as reconstructions.
  • SC-2: external control is present and disclosed (P3, P2, H-PREP and the CTRL-MON items).
  • SC-3: representation only. The physical dynamics are permutations, and the record statistics are those of a noncontextual model.
• Named missing premises:
  • M1: a controller-dependent coupling with diagonal-confined controllers, flagged as a reconstruction.
    • CTRL-MON relocates rather than removes it: meter supply and delivery, unregistered-meter terminality (also flagged), a static slot or a clock, and a gauge-violating coefficient.
    • Nothing smaller was found.
  • M2: NNB.
  • M3, open: a qubit quarter phase with C-CP.
• No V3 round proposed.
• Logged for a separate unit: Main L296's memory-term sign (+v) differs from Substratum and SM at odd q.

Reviews

• First review at d587446f: REVISE, R1–R11. Proposition AS was checked exhaustively at q = 3: 216 of 362,880 bijections act CP, exactly the affine symplectic ones.
• Delta at 104318af: ACCEPT WITH CHANGES, D1–D5.
• Final check at 39705074: F1.
• ACCEPT at c88de8da, recorded in the PR comments.

Author and reviewer self-checks were run locally. They are not committed and not cited as evidence.

Not authorized: premise adoption, simulation or enumeration, Lean, V3 execution, claim promotion or merge. Marking the PR ready and merging it are the owner's actions.

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https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

[amaybaum]

Independent review at exact head d587446f29b5f2eac9c306fa088bd55a486b8e67, condensed and transcribed from a separate reviewer agent of this Claude Code session; the reviewer is separate from the author and worked read-only. CI at this head: run 42424562552, 25 successful jobs and one conditional skip.

Verdict: REVISE

The core mathematics holds, but the verdicts and the stop's premise claim more than they support.

What holds.

• Theorem W, Proposition AS, Lemma A, Lemma N, Proposition C(a)–(c) and Observation E are correct within their hypotheses.
• Proposition AS was checked exhaustively at q = 3: of all 362,880 bijections of the 3×3 phase space, exactly 216 act completely positively, and those are exactly the affine symplectic ones.
• Theorem T is proved in general, given AS.
• Gross (quant-ph/0602001), read first-hand, matches the cited theorems. The author's purity step is correct, because the measure-and-prepare case is excluded by injectivity.
• The type (ii) stop is the right outcome.

Owner shortcut checks

• SC-1, imported quantum behaviour: no import in the dynamics, with qualifications. No unitary, interference mechanism or CP restriction is a premise. However:
  • the phase-space frame is chosen for its Clifford covariance, a property of the quantum comparator, so the O3 pass means "native rules are affine symplectic, and one fixed frame exists in which exactly those act CP";
  • the model has no interference;
  • CTRL-REC's confinement of controllers to records is motivated by keeping CP.
• SC-2, hidden external control: present, though disclosed.
  • P3 schedules every coupling and coefficient, including Lemma N's word, the mediator and the NNB edges.
  • An outside agent runs the adaptive feedback.
  • P2 and H-PREP supply the special inputs.
  • CTRL-REC depends on "registration", which is an observer act, not a dynamical property.
• SC-3, representation vs physical implementation: representation only. The physical dynamics are permutations. Non-monomiality exists only in the chosen frame and depends on the basis. The physical content is the record statistics of a noncontextual hidden-variable model.

Required corrections

• R1. The native P is itself a classical statistical model, and it passes the composition battery; the measure-and-prepare imitation is the weakest imitation. Add the epistricted model as a countercontrol that passes the battery. Restate O2 at odd q as a pass at stabilizer scope that no test in the reachable fragment separates from classical imitation.
• R2. Monomiality depends on the basis. In the adopted per-cell frame, N's edge step is already a non-monomial CP unitary. Restate O2 relative to a named fixed product basis, and add the proof that every available unitary is graded.
• R3. The claim that controllers must be confined to setting-eigenstate laws rested on one uncommitted floating-point q = 3 check. Replace it with the exact all-odd-q argument: a stabilizer input maps to a uniform law on qⁿ points, which by Gross Thm 2 and Lemma 9 is PSD only on an affine Lagrangian support. State that sufficiency needs every S(s) to be affine symplectic.
• R4 (CTRL-REC).
  • Say "nothing smaller was found", not "smallest".
  • Its record confinement is adopted only to keep states quantum, which is Q-A's premise I in another form. The reconstruction countercontrol must flag it, and it does not meet §A.29's independent-prediction bar.
  • "Registered" has no dynamical meaning.
  • "Buys O1" is wrong; O1 would remain "supplied".
• R5. Engage the uncited record-control-20261107/DESIGN.md and native-setting-source-feasibility.md, both on main (§A.19).
• R6. Scope "no qubit" to uniform level-set qubit encodings, and correct the even-order statement to its precise form.
• R7 (§A.34). In "CP ⇔ affine symplectic ⇔ linear ∧ symmetric", the second equivalence holds only within the second-order form u′ = F(u) − v, with "affine" in place of "linear".
• R8. The +1 multiplier also needs the −x(t−1) memory term. With +v, as Main L296 displays the rule, a symmetric coupling gives an anti-symplectic step.
• R9. At q = 2 the operative fact is that the frame is not covariant under the q = 2 symplectic group (Zhu); "+1 = −1" only explains why the multiplier can't flag the reflections. In the adopted frame the free tick is the identity.
• R10. The P2 law maps to the eigenprojector Π itself, not Π/q.
• R11. Proposition C(a) is an odd-q statement and says nothing about qubit contextuality.

Owner item from the review (not this PR). Main's displayed wave rule (L296, +v) differs in sign from Substratum and SM at odd q. That should be logged for a separate unit.

The writer is revising. A delta review follows.

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[amaybaum]

Review record after the first review, condensed from the same separate independent reviewer, who worked read-only and is separate from the author.

Delta review at 104318af: ACCEPT WITH CHANGES.

• R1–R11 and the optional notes are resolved.
• The new material checks out:
  • Lemma G is correct at odd q, by a direct proof that U(E_C) ⊂ E_C.
  • Lemma M is correct and self-contained.
  • Lemma N's second word is exact at q = 3, 5 and 7.
  • Proposition T′(i) is correct.
  • CTRL-MON's composite, with the monitoring meters traced out, is CP on all inputs (Choi minimum −3.0 bare, 0 composite at q = 3).
• Required:
  • D1. Lemma G is odd-q only. At q = 2, adaptive gradedness is open.
  • D2. Each direction of T′ is stated separately. (ii) needs v_c uniform and independent of all other cells given u_c.
  • D3. A native controller cell rotates (z, −x, −z, x), so T′ and CTRL-MON need either a controller exempt from the native rule or a one-parity schedule. That is a further supplied element. Monitoring every tick would erase the setting.
  • D4. CTRL-MON relocates the premise rather than removing it. Still supplied: meter delivery and disarming, the P2 supply, terminality of unregistered meters (flagged as a reconstruction), a static slot or a clock, and the gauge-violating coefficient. It removes P3 from the setting value only.
  • D5. One-cell frame scope.

Final check at 39705074: ACCEPT WITH CHANGES.

• D1–D5, N1 and N2 are applied, and R1–R11 remain resolved. All 46 pinned links resolve.
• Required: F1, one missed propagation of the T′ narrowing in an assumption-watch marker.

At c88de8da: ACCEPT. F1 and the optional even-tick sign clause went in as written, and nothing else changed.

CI at c88de8da: run 42427342745, 25 successful jobs and one conditional skip.

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[amaybaum]

Merge record.

• Merge: 1287748, a normal merge. Parents are main 313a93e and the reviewed head c88de8d, and the tree a59897af equals the reviewed head's.
• Approval: owner, Claude Code chat (amaybaum, 2026-11-08), recorded on SHOULD-FIX-RT: Chapter 18 corrections and parked release-3.2 owner questions #1190 c.6716911862.
• Post-merge CI on main at 1287748: green, 25 successful jobs and one conditional skip (run 42444329656).

The scientific conclusion is preserved: the candidate does not supply the missing physical quantum mechanism. Its stabilizer-level behaviour has a classical reproduction, and the controller, coupling and quarter-phase requirements remain unresolved. The odd-q wave-rule sign discrepancy is tracked as #1193.

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