[amaybaum]

Reviewed: independent ACCEPT at 2649bd0dff6b49d521edc91d733729c135895c44; CI green there (run 42416235712).

• Paper only, draft. Guiding PR for OI-QM-EXT-1: establish conditional equivalence with explicit added conditions, then minimize and source them #1169 step 3, Q-A (owner approval and scope; Q-B target).
• Builds on Apparatus-1: embedded reciprocal registration and the one-observer test (#1169 steps 1–2) #1183. One new file: verification/programmes/oi-qm/reconstruction/quarter-phase-native-20261107/DESIGN.md.

Result (as reviewed): a stop

1. Native class N.
   • For non-adaptive processes, N excludes the quarter phase S, for any encoding and any hidden sector. Lemma G1 shows native nearest-neighbour updates keep two Lagrangian sectors unmixed. Lemma G2 shows no encoding gives S together with native X reads.
   • Adaptive native S (record feedback) is open.
2. Lemma Q. At q = 2 the native step conserves Q = Σ xᵢ(t)xᵢ(t−1). Under terminal registration and half-known ready cells, any absolute parity with Q* = 1 is never determinable, under any protocol, feedback included. Relative parities are not protected. This inaccessibility is derived, not stipulated.
3. Minimal departure beyond Apparatus-1: embedded reciprocal registration and the one-observer test (#1169 steps 1–2) #1183's posits. NNB alone, an armable center-free same-sublattice coupling. A record cell set to 1 is an instance of the existing ready-cell premise P2 via H-PREP.
4. Under NNB:
   • (A1) and (A2) pass by paper proof: a protected parity, a Y read as a conjugated minimal read, and S as an affine bijection matching the comparator.
   • (A3), transformation contextuality, passes relative to the encoded subtheory, which is the operational equivalence of Lillystone–Wallman–Emerson. In the full theory, the parity cell's slots distinguish T₁ from T₂.
5. Lemma R and C-CP. In every linear encoding, S's linear part and its translation are each separately available encoded reflections.
   • C-CP already fails within N for any translatable-parity encoding, through the constant translation; NNB adds the linear-part reflection.
   • Excluding both needs posit I: a conditional premise, not adopted; as stated, target-defined and easy to vary.
6. Kernel position. The physical theory's operations lie in permClass, so it is a subtheory of permTheory. permTheory_not_control and permTheory_not_qm therefore apply by a paper monotonicity step, within the finite cells of a protocol's cone or under H-FIN. The construction claims neither composite unitary control nor exact finite QM.
   • rot stays unreachable, and two-system correlations miss the comparator (⟨YY⟩ = 0 vs −1).

Three items remain open: adaptive native S, a native derivation of posit I, and masking without randomization. No V3 round is proposed. The adaptive case is a protocol question, listed as open.

Reviews

• First review at cfe5200d: REVISE, Q1–Q9.
• Delta at b9c61b95: ACCEPT WITH CHANGES, D1–D3.
• Final checks at 2d666ab4 (F1–F2) and a0429851 (one example).
• ACCEPT at 2649bd0d, recorded in the PR comments.

Author and reviewer exact checks ran locally. They are not committed and not cited as evidence.

Not authorized: premise adoption, simulation or enumeration, Lean, dispatch, freeze, manuscript change, claim promotion or merge. Marking ready and merging are the owner's actions.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

[amaybaum]

Transcribed from a separate independent reviewer, an agent of this Claude Code session that is separate from the author. It reviewed read-only at exact head cfe5200d4aa78647ba7d290d59664c590cdf5a14. CI at this head: run 42413175166, 25 successful jobs and one conditional skip.

Independent review: Q-A quarter-phase DESIGN.md (#1169 step 3)

Object: verification/programmes/oi-qm/reconstruction/quarter-phase-native-20261107/DESIGN.md on branch research/oi-qm-qa-quarter-phase-20261107, at exact head cfe5200d4aa78647ba7d290d59664c590cdf5a14, whose base is main b1d782f954f02cec578a10e071b73e48f86eb3dd. I read the worktree only. Nothing was edited, committed, pushed or posted. Line numbers refer to the file at that head.

Verdict at cfe5200: REVISE

What checks out. I re-derived the load-bearing algebra exactly. All of the following hold:

• Lemma G1: the grading itself, sector isotropy, and why phase shears and Fourier maps are not generated.
• Lemma Q: conservation, transport of Q*, and the selection rule under P1/P2. The controls break the selection rule as they should.
• The U′ construction:
  • there are 4 symplectic affine S, all of which preserve Q;
  • 2 of the 4 lie in the 36-element graded+NNB group;
  • the graded group has 6 elements, and graded plus centre terms gives all 720;
  • p(τ) = 1 in every case.
• The comparator match: 2,380 cases with 0 failures.
• C-B2: 138 of 588 cases fail.
• Lemma R, including its general proof.
• The 256-offset check.
• The composite ⟨YY⟩ and the Mermin–Peres signs.
• LWE Theorem 1 and eqs. (5)–(7), read first-hand.

Why REVISE. The file is not acceptable as written:

• The headline native-class negative drops its stated scope. Lemma G2 is proved only for non-adaptive processes. §0, §4 and §4.3 state it without that scope. That conflicts with the accepted apparatus-1 Lemma 5, which counted adaptive record-conditioned corrections as SA-1 processes.
• (A3) is passed on a property the realizations do not have. T_1 and T_2 do not differ "exactly" on the inaccessible parity. They also differ on the parity cell's individual slots, which the file itself says are readable.
• Two classification errors. R-ONE is counted as a departure although it falls under P2 and G2's own allowance. C-CP is said to hold "vacuously" in N, which is false.
• Pass verdicts rest on uncommitted self-checks that §0 and §7 say are not evidence.

The fixes are local, but they change §0 items 1, 3, 4 and 5 and the §4 tables. The core construction needs no recomputation.

Required corrections

Q1. The non-adaptive scope of G1's "no mixing" and of G2 is missing from every summary. The narrowing of the SA-1 class conflicts with apparatus-1.

• Where. L25–32 (§0 item 1: "no armed protocol mixes"; "no encoding … admits"), L81 ("the native class is settled by proof"), L140, L340–341, L647, L694, L701–704, L728, L739–741. The qudit claim at L240–247 has the same gap.
• The defect.
  • G2's proof (L319–326) needs f_X^{final}(R1) = f_X^{final}(R0) + λc. That identity is false once armings or translations depend on records.
  • Feedback from an E-sector record into an O slot is exactly what replaces the λc term. Take an internal read of g with ω(f_X^{mid}, g) ≠ 0 and ω(g, F) = 0, followed by a translation of F by the record. The record then carries the middle-read kick w into the final X outcome. G2's contradiction no longer follows.
  • L140 says that non-adaptivity "is SA-1's P3 as stated". But apparatus-1 Lemma 5 (apparatus-1 L55 and L732–736) explicitly includes "adaptive record-conditioned corrections" among SA-1 processes.
• A bounded probe of my own. Two same-colour carrier cells, no ancilla. Generators: graded maps, constant translations, and "measure a single-sector functional, kick along its Hamiltonian vector, translate by the record". The semigroup closes at 4,053 distinct channels, and none has the encoded action of S.
  • Countercontrol: adding the NNB generators gives 9,925 channels, 2 of them with the action of S.
  • So no small counterexample exists. The adaptive case is still not proved.
• Minimal fix.
  • Add "non-adaptive (no record feedback)" at each listed site.
  • Replace "That is SA-1's P3 as stated" with a statement that reconciles the class with apparatus-1 Lemma 5.
  • Either prove G2 for adaptive processes, or list "adaptive native S" as an open item in §4.1, §4.3 and §4.5.

Q2. The (A3) pass condition is not met as stated. The realizations leave accessible traces on the parity cell.

• Where. L56–59, L164–166, L515–527, L695–697.
• The defect. LWE's Theorem 1 needs the H realization's translation to flip p (Lemma R). That translation flips z_2 or x_2 individually, and every H realization in the graded+NNB group also swaps z_2 ↔ x_2.
• Exact check. Prepare encoded Z+ with the parity cell ready, z_2 = 0 known.
  • After T_1: P(z_2 = 0) = 1.
  • After T_2: P(z_2 = 0) = 1/2 and P(x_2 = 0) ∈ {0, 1}, depending on the solution.
  • So T_1 and T_2 differ on z_2 and x_2, not "exactly" on p. Those slots are readable: L492 says "Reciprocal access reads z_2 or x_2".
  • The encoded S also leaves a trace. On Z+ with x_2 (or z_2) known, S flips that slot deterministically, so S is distinguishable from I on Z± by a parity-cell read.
• Minimal fix.
  • State (A3) relative to the encoded subtheory's preparations and reads. That is LWE's notion of operational equivalence.
  • Say that in the full NNB theory the parity cell's slots are readable, so T_1 and T_2 (and S versus I on Z±) are distinguishable there.
  • Alternatively, compose both maps with the parity-cell twirl over {(0,0), (1,1)}. After the twirl they differ only on p within one system, though they become distinguishable again with a correlated parity ancilla (node 10).
  • Correct "differ exactly" accordingly.

Q3. R-ONE is classified inconsistently.

• Where. L45–47, L74–75, L305, L509, L630, L645–647.
• The defect.
  • G2's class N already allows "supplied constant translations" (L305).
  • Apparatus-1 SA-1(c)/P2 supplies a ready cell with "exactly one known linear functional", and does not restrict its value to 0.
  • Yet R-ONE is listed as a supplied resource beyond P1–P3, "needed for every translation", and the minimal departure is given as "NNB plus R-ONE".
• Minimal fix. Either show where P2 restricts the known value to 0, or classify R-ONE as an instance of P2 (with H-PREP). In the second case the minimal departure beyond apparatus-1 is NNB alone, and L74–78 and the §4.1 table change accordingly.

Q4. C-CP does not "hold vacuously" in N. The reflection is not caused by NNB.

• Where. L649, and the attribution in L60–66, L580 and L660–662.
• The defect. L580 itself shows that the translation z_2 += 1 acts as Y ↦ −Y. That is an orientation-reversing encoded map, and it needs only a constant translation, which is in N (L305) or comes from R-ONE. No NNB is involved. So for the U′ encoding C-CP already fails without NNB. NNB adds only the second reflection, the linear part L.
• Minimal fix.
  • Replace "Holds vacuously" with the actual status per encoding: CP under R1, and failing for any linear encoding with a translatable parity.
  • Attribute the translation reflection to the constant-translation resource and the linear-part reflection to NNB.

Q5. Pass verdicts rest on self-checks that the file says are not evidence. One of them is a finite test of a universal claim.

• Where. L11–14 and L776–778 versus L502–512 (A2), L505–507 (group membership), L539–540 (C-B2), L584–588 and L686 (c8), and L576–580 ("available on its own", c5 and c6).
• Minimal fix. Supply the short paper arguments, which exist:
  • A2. Uniform laws on encoded level sets {f_a = b} are closed under the native Z/X reads (record, then kick) and under affine S. So the one-step facts give every sequence by induction. The 2,380-case check then becomes a control.
  • L as a coupling word. Write L explicitly as a word in armable couplings.
  • Separate availability in every linear encoding. Any P3/P2 process is affine in the supplied known constants. Setting them to 0 gives L alone (P2 supplies known-0 cells), and τ = S ∘ L^{−1}.
  • The rest. Otherwise state the computational facts with a recipe under §A.42.

Q6. The Y read is called a "native minimal read".

• Where. L484–486, against the definition at L134–136 and the pass condition (A1)(a) at L149–152.
• The defect. S† · X · S (or conjugation by L, which needs no R-ONE) is a minimal read conjugated by NNB couplings. It is not one armed coupling to one ready meter.
• Minimal fix. Name it as such, and restate the (A1)(a) pass at L490 ("registrable by a minimal read conjugated by available couplings").

Q7. Position the file relative to readWriteSourced_not_qm / monomialSource_not_qm (the coordinator's item).

• Where. L76–78 and L649 ("For a quantum operation set (C-CP) … posit I"), and §6.1.
• The theorem (ReadWriteControl.lean L174, via SubstratumInterface.lean L192): a theory whose available composite conjugations are all permutations has no composite unitary control and is not exact finite operational QM.
• Consistency. The file implies no evasion:
  • every N and NNB+R-ONE process is a configuration bijection, so on the physical carrier the theory is read-write-sourced (apparatus-1 Lemma 2 / permClass);
  • S and H are encoded maps only;
  • rot remains unreachable (C-ROT);
  • composites fail (node 10).
• The ambiguity. "Quantum operation set (C-CP) … requires the posit I" can be read as "with I the operation set is quantum". The encoded theory with I contains the non-monomial H, yet it still lacks rot and composite control.
• Minimal fix.
  • Scope L76–78 and L649 to a "CP encoded single-qubit stabilizer operation set".
  • Add one sentence, citing the theorem, saying that the physical theory is read-write-sourced, so the theorem applies to it, and that the construction claims neither composite unitary control nor exact finite QM.

Q8. Posit I's standing is stated more strongly than §A.29 supports.

• Where. L76–79, L591–593, L632, L679–683.
• The defect. §A.29 bars adopting an easy-to-vary revision. It does not bar stating I as a conditional premise, and the file itself lists "What would derive it". Apparatus-1's precedent for MP-1 reads "not adoptable under §A.29 unless a specified native process selects the law".
• Minimal fix. Make the status "conditional premise, not adopted; as stated, target-defined and easy to vary". Add that I contradicts P3's arming of the individual couplings that compose L.

Q9. A finiteness hypothesis is replaced by a measure hypothesis without saying so.

• Where. L528 ("Green without a finiteness hypothesis") and L721 ("Neither result depends on the finiteness of the underlying sector").
• The defect. The dyadic C-ROT argument needs N2 and, for an infinite hidden sector, H-INF-μ. The ledger (L623, L635) lists H-INF-μ as a hypothesis.
• Minimal fix. Write "without H-FIN, under N2 (H-INF-μ for an infinite hidden sector)" at both sites.

Optional notes

• Lemma Q extends to record feedback. Within each branch the maps are symplectic and center-free, and translations do not change D, so (iii) holds with feedback as well. Saying so strengthens C-LEAK.
• The recombination paper's receiver. Its passive two-slice receiver registers both slots of a cell, so it determines Q* = 1 functionals. It is the P1-removed control (c5: 222 of 4,000), and the C-LEAK row could name it as such.
• Lemma R, step 1. For linear L, f_a ∘ L⁻¹ = f_{π(a)} exactly, so L acts as a pure axis permutation with no signs. The proof is correct as written, but "D P D" is more general than needed.
• Process-narration headings. "tested hardest" (L343), "found by pressure-testing the favourable branch" (L60) and "Maximum skepticism on the favourable branch" (L544) narrate process. A neutral register would state the content only.
• Qudit claim at L240–247. It holds for encodings whose Z and X functionals are single-sector, and for non-adaptive processes. Add that scope (see Q1).
• "No V3 round" (§4.3). This is sound under the owner's criterion, which concerns a search over native update rules. The adaptive question from Q1 is a protocol search, and it should be listed as an open item rather than silently closed.

What I verified, and how

All checks used exact arithmetic over F₂ (integer arithmetic, Fraction, and dyadic floats that are exact at these sizes). The scripts are local reviewer checks; they are not committed and not cited as evidence.

• r1_lemmaQ_G1.py: Lemma Q.

  • (i) Q = u·v is conserved for every symmetric zero-diagonal K on n ≤ 4 and every state: 0 violations in 16,932. With a centre term there are 966 violations in 2,000; with an asymmetric K, 534.
  • (ii) Q* is invariant under transport by M^{−T} for every functional, n ≤ 3: 0 violations.
  • (iii) Random center-free protocols with arbitrary (non-bipartite) graphs, P2 ready cells and terminal registration: a Q* = 1 active functional was determined in 0 of 3,000. With centre terms it was determined in 1,062 of 3,000; with P1 removed, in 2,883 of 3,000.
  • G1's induction was checked on paper, including simultaneous couplings and per-branch fixed coefficients. Grading survives within each branch; the breakdown with feedforward is in Q1.

• r2_Uprime.py: groups and S.

  • |Sp(4,2)| = 720.
  • Graded group 6; graded+NNB 36; graded plus centre terms 720.
  • Every element of the NNB group preserves Q.
  • Exactly 4 symplectic affine S exist (16 among all affine bijections). All 4 preserve Q, 2 lie in the 36-element group, and every translation has p(τ) = 1.

• r3_comparator.py: reads.

  • The native Z/X reads with kicks, plus the Y read as S†, X read, S, give 2,380 cases with 0 failing for each of the 4 S.
  • Copy-only reads give 588 cases with 138 failing (C-B2).

• r4_H_R.py: Lemma R and A3.

  • For all 4 S, the encoded actions of L and of τ each have determinant −1.
  • z_2 += 1 acts as Y ↦ −Y.
  • There are 4 encoded H solutions, 2 of them in the NNB group, all with p(τ) = 1, and H flips p pointwise.
  • The Pauli translations preserve p.
  • T_1 and T_2 send all 6 states to the maximally mixed state.

• r5_T12_full.py and r6_Sleak.py: parity-cell traces of T_2 and S (Q2).

• r7_adaptive_probe.py and r7b_control_nnb.py: the adaptive probe and its NNB countercontrol (Q1).

• r8_offsets.py: offsets. All 256 offset pairs generate groups containing S and an encoded reflection. This reproduces c8 under my reading of it.

• Composite. The Mermin–Peres identities (X⊗Z)(Z⊗X)(Y⊗Y) = +I and (X⊗X)(Z⊗Z)(Y⊗Y) = −I hold, and for Φ⁺, ⟨XX⟩ = ⟨ZZ⟩ = 1 and ⟨YY⟩ = −1. The model's ⟨YY⟩ = 0 with uniform p_A + p_B was derived on paper.

• Literature. I fetched and read LWE (arXiv:1802.06121v2):

  • Theorem 1;
  • eq. (5), T_2(ρ) = H T_1(ρ) H;
  • eqs. (6)–(7), the parity-preserving and parity-reversing maps;
  • "a Pauli operation preserves the parity xyz and the Hadamard swaps it (as does the phase gate P)";
  • the Discussion on the toy theory and on two-qubit preparation contextuality;
  • the measure-theoretic appendix.

  All are as cited. LWE's operational equivalence is relative to the subtheory (Q2).

• Sources read first-hand at b1d782f9.

  • Substratum L48 and A1–A6. A4 has two senses: translation invariance, which P3 already departs from, and no self-copy.
  • SM: the form lemma at L224, the scope remark at L226 (NNN couplings are compatible with A3), the invariants at L296 (u·v is not among them; E mod 2 = Σu + Σv + u·Av), Theorem 3, and §4.8.
  • Main: the Definition, Lemma 3, and the screened Bell theorem at L366.
  • Apparatus-1: §1.3, §3, §4 (Lemma 3, Lemma 5 with its adaptive clause), §5, and the three accepted review records on Apparatus-1: embedded reciprocal registration and the one-observer test (#1169 steps 1–2) #1183 (6711876301, 6712087746, 6712228186).
  • The two-system leak (§4) and correlation recombination (§3), against which Lemma Q is consistent: recombined relations there have Q* = 0.
  • The Lean files ReadWriteControl.lean (readWriteSourced_not_qm, L174) and SubstratumInterface.lean (monomialSource_not_qm, L192).

• Links. Every pinned blob/b1d782f9…#Lnn link resolves, and its target line matches its use.

• Not reproduced. c2's 75,556-case count and c1's random grading runs. G1 and G2 were checked on paper instead.

---

Generated by Claude Code

[amaybaum]

Review record after the first review. It is condensed from the same separate independent reviewer's delta reports; that reviewer is separate from the author and read only. The full text is kept in the session record.

Delta review at b9c61b95: ACCEPT WITH CHANGES.

• Q1–Q9 are resolved.
• New paper arguments re-checked:
  • the A2 induction over uniform level-set laws, which agrees with the 2,380-case control;
  • L = Na ∘ C12 (f_x∘L = f_y, f_y∘L = f_x, p∘L = p);
  • S = τ ∘ L (f_x∘S = f_y + 1, p∘S = p + 1);
  • separate availability;
  • "Lemma Q protects absolute, not relative, parities";
  • the Lemma Q extension to record feedback.
• Required:
  • D1. The C-CP case split under R1 was false; the native Z read is a measurement branch with α = β = 1. The conclusion holds: the minimum Choi eigenvalue is 0 over 7,642 branch maps, and the controls give −1.
  • D2. The kernel positioning needed an explicit containment in permTheory, a monotonicity transfer of ¬control and ¬QM, and a finiteness scope. monomialSource_not_qm was dropped (Fin 2 only; no MonomialSource lemma for permTheory). The citation of the vacuous readWriteSourced_not_qm was replaced by permTheory_not_control / permTheory_not_qm, since permClass admits unit scalars (KERNEL-VAC-1: ReadWriteSourced is vacuous; repair or retire readWriteSourced_not_qm/_not_control and repoint their citations #1188).
  • D3. Separate availability scoped to N_na.

Final check at 2d666ab4: ACCEPT WITH CHANGES.

• D1–D3 resolved, and D2's positioning is sound.
• Required:
  • F1. Masked reads belong in the uncorrelated case.
  • F2. Trace 2 must not assume both parity-cell slots known, which Lemma Q excludes.

At a0429851: F1 and F2 resolved, and the ReadWriteSourced clause names its reason correctly. Remaining: the masked-read example described the opposite meter.

At 2649bd0d: ACCEPT. Only the masked-read parenthetical changed, and it is correct. Q1–Q9, D1–D3 and F1–F2 remain resolved.

CI at 2649bd0d: run 42416235712, 25 successful jobs and one conditional skip.

---

Generated by Claude Code

[amaybaum]

Independent paper/source review at 2649bd0dff6b49d521edc91d733729c135895c44: REVISE

Reviewer: /root, this separate Codex session; not the author. Authority: owner's current instruction. I read the complete 995-line DESIGN (blob 95c30ef93fdfbe6aa274e4d395bb4fd46a4fe139), its main-source hypotheses and relevant kernel statements, the previous review/corrections, and LWE v2 first-hand. I acknowledge the other reviewer's ACCEPT; the findings below concern remaining written arguments. No scientific program, enumeration, simulation, Lean build or dispatch was run.

CI is green at this exact head: ordinary run 42416235712, 25 successful jobs and one conditional skip, checked through structured run/job records. This does not resolve paper-proof gaps.

R1 — Required: repair the conditional-noise step in the R1 C-CP proof

Lines 695–711 infer from records being uncorrelated with the input that the displayed ancilla offsets (e,o) are independent of it. That inference needs a conditional affine normal-form argument; it is false for the raw offsets of the process.

A hand-derived example within N_na, using the same single carrier cell as output:

1. Let the carrier have coordinates (z,x). Attach an opposite-colour neighbour with (z_B,x_B)=(w,0), w independent uniform (P2).
2. One even coupled tick gives (z_A,x_A)=(z,x+w) and (z_B,x_B)=(w,z) in the paper's fixed frame. This is the displayed native symmetric edge; P3/E-iso supplies its scheduling.
3. At the odd tick, make a native X read of A with a fresh ready meter. It records r=x+w and kicks A by an independent uniform k, leaving A as (z+k,x+w). Register only that meter and discard B. No feedback is used.

For every input law, r is uniform and independent of the input. But given r, the raw offset o=w=r+x depends on input x. Here the displayed coefficients are alpha=beta=1; nevertheless the conditional carrier law is uniform on x_A=r, independent of the input. It is a constant preparation channel, not a Pauli mixture (a Pauli mixture is unital).

This is not a counterexample to C-CP: the branch itself is CP, with probability 1/2 and output X_r. It is a counterexample to the written inference/classification. Recover the theorem by explicitly reducing each conditioned affine branch to an effective kernel with fresh independent residual variables, allowing its effective input coefficients to change after conditioning. The proof must use the entire joint record, not merely independence of each record separately. Then show that the resulting branch normal forms are CP. A finite Choi check is not a substitute for this general step. Preserve the unrefuted C-CP conclusion as a recovery target while repairing its proof.

R2 — Required: put the remaining availability arguments on paper

The A3 pass uses availability of an encoded H (lines 601–608); only its desired action and a description of its factors are written. The c6 group check is expressly not evidence. There is a short recovery, so no withdrawal is needed:

• Let Nb be the other-parity NNB shear, z1+=x2, z2+=x1.
• The word Na o Nb o Na sends (z1,x1,z2,x2) to (x2,z2,x1,z1).
• Follow it by the graded cell swap W=C12 o C21 o C12, obtaining R:(z1,x1,z2,x2)->(x1,z1,x2,z2).
• Then translate z2 by 1. This gives f_z o H=f_x, f_x o H=f_z, f_y o H=f_y+1, p o H=p+1.

The mediator construction in node 1 and free scheduling supply W; no search is needed. Include this or another explicit available word.

Likewise lines 723–727 and 828–830 use the uncommitted 256-offset check to reject welding by fixed affine offsets. In the stated N model all constant slot translations are already available, so an offset a of G=t_a o L can be removed by the available t_{-a}, giving L. State that paper argument for the actual resource class and retain c8 only as a control. If the weaker class with only encoded Pauli translations is intended, its separate all-offset assertion still needs proof/evidence and must not be silently substituted for N.

Also replace the sentence at lines 682–684: an affine output does not by itself imply that the realizing protocol used no feedback. The separate-availability result is correctly limited to a non-adaptive realization; keep that explicit hypothesis.

R3 — Required: narrow the traced-out-sector closure

Node 4's verdict, §4.2 and the classification at line 929 still say the traced-out sector cannot host the parity / closes the suggested branch.

The evidence is narrower. G2 covers non-adaptive S. Reciprocal access makes each individual slot readable; it does not make its sum readable. Indeed Lemma Q itself protects u_h+v_h (Q*=1) on an extra native cell, even though either slot can be read individually. A shared-cell signalling example excludes that sharing arrangement, not every distributed hidden-sector realization. Masking without randomization and adaptive S remain explicitly open.

Retain the valid conclusions: no non-adaptive S under G2's hypotheses; no independently unreadable slot under the stated reciprocal-access protocol; failure of the displayed shared parity; no complete native A1–A3 construction supplied. Do not turn those into a general exclusion of an inaccessible parity functional or all adaptive/hidden-sector routes.

Content that survives

The center-free quadratic invariant/conditional knowledge result, the explicit L=Na o C12 and S identities, the level-set induction for the displayed read/S sequences, the parity-flipping translation's non-CP action in U-prime, the distinction between encoded and physical control, and the finite-scope permTheory positioning retain their stated conditional roles. I checked the actual partial-permutation class and closure/type statements; I did not rely on the vacuous ReadWriteSourced predicate.

Disposition: three bounded paper repairs and a fresh exact-head review are needed. No author file/ref changed here; Claude remains the sole writer of DESIGN. This review adopts no premise, authorizes no execution or merge, and claims neither a native mechanism nor full equivalence. The bare adaptive-S question remains open; its complete-target assessment must also retain C-CP and the full accessible history.

[amaybaum]

Merge record.

• Merge: 499463f, a normal merge. Parents are main d186eee and the reviewed head 2649bd0. Its only change from d186eee is quarter-phase-native-20261107/DESIGN.md, blob-identical to the reviewed head.
• Approval: owner, Claude Code chat (amaybaum, 2026-11-07, about 22:10 UTC), recorded on OI-QM-EXT-1: establish conditional equivalence with explicit added conditions, then minimize and source them #1169 c.6713519633.
• Post-merge CI on main at 499463f: green, 25 successful jobs and one conditional skip, run 42418102685.

The reviewed scope is unchanged: a paper-only stop. No premise is adopted, and no OI–QM equivalence or V3 certification is claimed. Open: adaptive native S, a native derivation of posit I, and masking without randomization.

---

Generated by Claude Code

[amaybaum]

The three bounded findings in this session's additional review have a forward recovery in draft #1189, exact head 1f9922466584c4114a1439010a8253606948b3c6. A separate reviewer ACCEPTed the complete patch, with no remaining paper-proof correction.

The patch preserves the construction and supplies the full conditional affine/record-isotropy proof under R1, explicit H and offset arguments, and the narrowed hidden-sector conclusion. A separate self-contained note proves the combined S+C-CP obstruction for the stated linear encodings/common lift/translations while keeping bare adaptive S open.

These corrections are reviewed on the forward draft, not yet on main. #1189 remains unmerged with ordinary CI running. The original #1184 branch and approved merge history are untouched; no premise, V3 execution or manuscript claim is adopted. Claude's separate conditions-status trace remains independent.

[amaybaum]

The forward recovery is now complete in draft #1189 at 8ca8ce30ff1fd65a21768fe875c36b9bf1f58f31. The independent delta ACCEPT carries the full paper review forward with the fixed active-output scope explicit. Ordinary CI 42420079198 passed at that same head (25 successful jobs, one conditional skip).

The original construction is preserved. The patch supplies the conditional-noise/terminal-record CP proof, explicit H/offset arguments and narrowed hidden-sector conclusion, plus the separate scoped feedback/control result. Bare adaptive S and physical sourcing remain open. #1189 is still draft/unmerged; these forward repairs are not yet on main. No merge, physical premise or manuscript promotion is implied. Accountable closeout.