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…ly; WIP / UNVERIFIED) Paper-only design unit authorized at #1032 comment 6649418760. Adds a new directory phase-b-design/ with the unit's README and a plan. No existing file in o-ret-routes-20261103/ is changed. No computation was run. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq
…(design only; WIP / UNVERIFIED) Completes DESIGN-PHASE-B.md: starting point with the 49/49 count checked against summary.json; Lemma PAD and Observation W1 (hand derivations, unreviewed); candidate NRR-1 (native ready-register retention) with K1 native under posit (vii) and the SM:112 ring rule as the unadopted F2 extension E-SDC; discrimination criteria with countercontrols; labelled assumptions; the five-requirement table; a proposed Phase B test with controls, decision rule, invariant-to-checkpoint table, output schema and outcome scopes; owner decisions G-1 to G-13; review packet; off-main reference classification. README headline filled in. No computation was run. No existing file in o-ret-routes-20261103/ is changed. Nothing is frozen, adopted or promoted. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq
Independent review of #1115 at
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…dacce5 (design only; WIP / UNVERIFIED) Applies the independent review at #1115 c.6649925951 (ACCEPT WITH CHANGES) and the owner's instructions relayed with it. R1: Observation D2-T1 (a consistent D2 implies DIL-exists and tau = infinity on W1, so the one-tick test is non-discriminating) and Proposition IP; the counting rule requires IP = false; DT-S13 is a concrete T = 2 failure under D2 with every declared assumption holding; DT-S1q a T = 2 pass that could have failed. R2: matched local signed-offset patterns for robustness; the impossible r = infinity outcome removed; Lemma NP; the reviewer's K1 argument re-derived as Proposition K1-NS with assumptions A1-A6 and its limits, unreviewed and not adopted; K1 kept; adoption is gate G-14. R3: D1 is Q8's lexicographic tie-break, quoted. R4: B-5 keeps T* and w* outside the per-tuple rule; B-6 handles the exit-4 case; coverage and Phase A rows rechecked. Non-blocking items applied. Gate items G-1 to G-16 restated with alternatives, consequences, tautology risk, new assumptions and labelled recommendations; none chosen. No computation was run. No existing file in o-ret-routes-20261103/ is changed. Nothing is frozen, adopted or promoted. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq
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Checkpoint 3 is pushed at Generated by Claude Code |
Second independent review of #1115 at
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| Item | Status | Where |
|---|---|---|
| R1: a consistent D2 implies DIL∃ and τ = ∞ on W₁; carried into G-4 and §4.4 | APPLIED | l.145–158, l.494–501, l.427–429, l.1001–1027 |
| R1 as extended by the owner (c.6649977592): a genuine discrimination test at T ≥ 2 | PARTLY | l.746–763: the IP flag is syntactic and misses guaranteed passes (B1) |
| R2: robustness for the finite rings | PARTLY | l.559–577, 759–762: well defined, but unreachable (B2) |
| R2: remove impossible outcomes | PARTLY | the r = ∞ row is gone, but l.818 and the STORAGE-ROBUST half of l.819 cannot occur (B2) |
| R2: K1 argument completed and kept unadopted; K1 kept in the controls | APPLIED in form, with a defect in content (B3) | l.207–254; G-14 |
| R3: Q8's tie-break in D1 | APPLIED | l.584–586. I confirmed the C-PAD D1 is the identity (the lexicographically least of identity and negation) |
| R4: T* kept outside ST and row 8 | APPLIED | B-5, l.612–615; counting, l.756 |
| W1 rescoped (D1′, restricted carrier), ELABORATING | APPLIED | l.186–205 |
| I-5G renamed (I-10) | APPLIED | l.608–611 |
| K1 described as the native step form on a toy graph | APPLIED | l.318–323 |
| E-SDC wording and the departure from ROUTES:462 | APPLIED | l.334–346 |
| "independent prediction" | APPLIED | l.926–931 |
| "smallest" | APPLIED | l.297 |
| PAD citations | APPLIED | l.115–120 |
| HC-K3 and C-PAD decoders | APPLIED | l.658–659, 664 |
| determinism invariant | APPLIED | l.851 |
| G-6(b) as HC-K4's pattern | APPLIED | l.1052 |
| locators | APPLIED | l.42, 76–77 |
| Lemma L stated conditionally | APPLIED | l.324–326 |
| §3.4 omissions | APPLIED | l.427–434 |
| G-10 split into replay, regression and import | APPLIED | l.1108–1126 |
| G-13 scope | APPLIED | l.1151–1169 |
| NK-K3 support restated | APPLIED | l.689–696 |
2. The new results
| Result | Status | Notes |
|---|---|---|
| Observation D2-T1 | verified | Consistency is checked per read configuration over every write-supported member of a ~₁-class, so g∘ρ is constant on each such class. supp R_{t₀+2} ⊆ f_R(supp R_{t₀+1}, supp Q_{t₀+1}), so no hit exists. IP = true at every T = 1 holds trivially. |
| Proposition IP | verified as a one-direction sufficient condition. Its use as the counting criterion is refuted (B1). | l.380–382 says "Only IP = false tuples carry a test that could have failed." That is false: see §3. |
| Lemma NP | verified, one correction | Proof correct. Checker over every written tuple (N = 5: 288 tuple×T; N = 8: 165): y₀ ∈ Q holds for all. C-NP-ALL-covered tuples (N = 5: 180; N = 8: 162): every written one fails J-i at t₀+1; rows {1, 3w} only. K1 at N = 8, r = 2: the written registers are {1}, {1,2}, {1,2,3}, {7}, {6,7}, {5,6,7}, each containing exactly one of sites 1, 7. Correction: l.431 says r = 2 constrains "five to seven" sites at N = 8. It is four to seven: Z₂({1}) = {1, 2, 3, 7}. |
| Proposition K1-NS | verified with correction (B3) | Join construction correct for general n_x, n; B e_{y₀} = b; the clean-write restriction is unnecessary (confirmed). The η ≥ 1/2 bound is correct, but A5 is not needed, and it is not an independent hypothesis: see below. Checker: every written K1 tuple with write-min ε ≤ ε* (N = 5: 129 tuple×T; N = 8: 66) has D2 undetermined and exact DIL∃ failing. Every one of those that passes J-1 at t₀+1 (12; 30) has η_{t₀+1} = 1 with G_status = empty, and none fails A5. |
| DT-S13 | verified | supp Q_{t₀+1} = {(0,0),(0,1)}, IP = false, ε 0, 0, 1/4, TV 1, 1, 1/2, DIL∃ fails, τ = 1, T′ = 2, J-1 holds at both hold ticks, SCH holds, G*_{W₂} = G*_{W₂′} = {p = 0} consistent, η 0, 1/2, row 2b, D2 consistent with g = r. Not a Phase A tuple: S1(3) was frozen at T = 1 only. |
| DT-S1q | values verified; its role is refuted (B1) | ε 0, 0, 0, DIL∃ holds, τ = ∞, SCH holds, row 5, syntactic IP = false. But f_R(·; (0,1)) = f_R(·; (0,0)) = id, so ~_{𝒬_{W₂}} = ~₁. The pass is guaranteed by D2 and the law. It is not "a T = 2 pass that could have failed" (l.666). |
K1-NS without A5 (the hand argument). Fix c. The two preparations σ₀ = (x₀ = 0, c) and σ₁ = (1, c) are both in P (A2).
- Given
σ, the components ofQ_{t₀+1}other thany₀areG_j(y(t₀)) − x_j(t₀)forj ≠ 0. They do not involvex₀. y₀(t₀+1) = G₀(y_{≠0}(t₀)) − x₀.- So with
p_cthe law of(G₀, z)givenc,L(Q | σ₁)isL(Q | σ₀)translated bye_{y₀}. - A
Gthat is consistent contains no pair{q, q + e_{y₀}}; that is the join, together with A6. Henceμ(Q ∈ G | σ₀) + μ(Q ∈ G | σ₁) = Σ p_c(g, z)[1_G(g, z) + 1_G(g+1, z)] ≤ 1. - So
max_σ η_{t₀+1} ≥ 1/2with neither A4 nor A5.
The same argument shows two more things:
- A5 follows from A2 and A4. J-i (joint) makes
L(Q|σ)invariant under that translation, which is A5's equal-weight pairing. - The A5-failing tuples of l.248–249 ("through the wrap at
N = 5") fail J-i. For example, atA = {1,2},r = 1,Q = (y₄ − x₀, y₄)revealsx₀. They are row 1 and are covered.
Two further corrections to K1-NS:
- l.242–243 and B-6's rationale (l.618–619). K1-NS does not imply
G_status = inconsistent. On the instances checked, every J-1-passing written K1 tuple hasG_status = empty, which never raises exit 4. B-6 remains a reasonable guard, but its justification should say "may". - Scope is wider than stated. The proof uses only that
y₀entersy′_Aadditively with a state-independent coefficientb. That also holds for SMR registers containing site 1 and not siteN−1(y′₁ = y₀ + y_{R(1,y)} − x₁; no switch ofAreadsy₀).- On the
N = 8instances, every SMR tuple that is written with write-minε ≤ ε*and passes J-1 att₀+1is of this kind: {1,2} atr = 1, and {1,2,3} atr = 0andr = 1. - Each has DIL∃ failing and
η = 1, as the extension predicts. - The limitation "SMR … not covered" (l.250) should read: SMR registers containing site
N−1, orN−2with the conditionaly₀target, are not covered. - This extension is my hand derivation, unreviewed.
- On the
Also, D2 decides no written tuple of the family. On every instance checked, every written tuple has D2 undetermined, for both rules (the count of written tuples with D2 consistent is 0 at both N).
- Reason:
Pcontains bothx₀values, sosupp Q_{t₀+1}always containsqandq + e_{y₀}. - Wherever
y₀enters additively, the join merges a label-0 and a label-1 write-supported configuration inside~₁. - Consequence: under G-4 (a), every written NRR-1 tuple is decoded by the D1 fallback with
IP := false. G-4 (a) then coincides with G-4 (c) on this family, and the circulation that (a) is meant to keep testable (l.1025) is not exercised. The owner should know this before deciding G-4.
3. The owner's principle (a test must be able to fail with every declared assumption holding)
- DT-S13: yes. It is a configuration in which the
T = 2test fails under D2 with the declared law, access and decoder all holding. The failure comes from an input,p₁ = 1, that D2 never read. It is a toy calibration (E-reg). It shows that the classifier'sT ≥ 2step under D2 can fail. It does not show that any NRR-1 tuple has such a test. - The counting rule does not exclude every decoder-guaranteed pass (B1).
IP(l.746–749; l.372–373) compares input values. The guarantee in D2-T1 and IP depends only on the relation the inputs generate.- If every class of
~_{𝒬_{W_T}}that meets𝓛_{W_T}is a single~₁-class, the induction in IP's proof goes through unchanged and DIL∃, τ = ∞ and constant ε follow from D2's consistency, whatever new input values occur. - DT-S1q is such a case. So are 8 tuple×T cases at
N = 5and 50 atN = 8(K1 and SMR, all unwritten), whereIP = falsewhile the two relations coincide. Those cases never count; they show only that the flag mislabels them. - Proposed fix:
IP′ := every ~_{𝒬_{W_T}}-class meeting 𝓛_{W_T} is one ~₁-class. This is sufficient for a guaranteed pass. When it is false, two~₁-classes are merged by dynamics D2 did not read, so the check can fail. - Then replace DT-S1q's role. One example: a two-presence-bit
M_Fin which thet₀+2input swapsvinto an unread junk bitsinstead ofr. It merges only same-valued classes, so it is a genuine pass withIP′ = false. Without a replacement, the design has no positive-path control for a countable row.
- Other tautology risks under G-4/G-5.
- G-4 (b), G-3 (b) and G-5 (b)+G-4 (b) are flagged.
- Not flagged: G-5 (b) with G-4 (a). l.1038–1039 says nothing could count. That holds only for D2-consistent tuples: D2-fallback tuples carry
IP := falseand could count atT = 1, so the consequence needs re-derivation. If it did hold, the combination would be non-discriminating in the rejecting direction and should be flagged at l.1044. - Not flagged: STORAGE-ROBUST as defined (B2).
4. STORAGE-ROBUST and C-NP-ALL
- Well defined: yes. The nine local
N = 5patterns are exactly those of l.565–568 (C A; C A Z; C F A; C A A; A C A; and mirrors). Exactly eight have one matchedN = 8arc each, and{1, 4}has none. The checker's pattern enumeration agrees. Matched patterns give identical write-tick ε atN = 5andN = 8, as locality requires. - Non-vacuous: no (B2). Over the nine local
N = 5patterns withr ∈ {0, 1}:- SMR: every one is unwritten, or has write-min
ε(t₀+1) ∈ {1/4, 1/2} > ε*, or fails J-1 att₀+1. This holds under every decoder rule,Tand later dynamics. The matchedN = 8arcs behave identically. - K1: the written exact ones ({1} at
r = 1, {1,2} and {3,4} atr = 0, {4} atr = 1) are excluded by K1-NS. - Hence no matched pair can count, and STORAGE-ROBUST is unreachable for both rules. §6.7 l.818 ("NO-STORAGE on K1, STORAGE-ROBUST on SMR") and the ROBUST half of l.819 are impossible outcomes, the defect R2 asked to remove.
- Cause: on SMR, an exact write that passes J-1 needs at least one of the following, and neither fits in a local pattern at
N = 5(|I| ≤ 3):- a register of width ≥ 2 with readiness one step beyond it (
C A A Z,C A A A,|I| = 4); - a one-sided region (G-6 (c)).
- a register of width ≥ 2 with readiness one step beyond it (
- Candidate repairs, for the owner, not chosen here:
- pair
N = 8withN = 6orN = 7(|S| = 2¹²,2¹⁴), where those shapes are local; - and/or define patterns for G-6 (c)'s one-sided regions. Today
ris undefined for them, so they can only ever be ISOLATED.
- pair
- SMR: every one is unwritten, or has write-min
- C-NP-ALL as a halting control: sensible. Lemma NP is short and verified. Its covered tuples are predicted 1 or 3w by first-match precedence (gate, then RS at
t₀+1), and a failure would mean a lemma or implementation error. Halting there follows the "verdicts only over green controls" rule. Two notes:- Coverage is keyed by the label
r. Deduplicated laws equal toδ₀under another label (for exampleN = 5,r = 1,A = {2,3}) are not covered. NP also holds there, so the coverage could be widened cheaply. - With the extension above, C-NP-ALL could be complemented by a K1-NS/SMR-right-side check under G-14.
- Coverage is keyed by the label
5. Phase A (R4, B-5, B-6)
- Freeze untouched. No Phase A file changed (
git diff --name-only f5c281ae 5839e064lists only the two design files). The design reads PREREG §2.10 correctly: T*/w* stay unset and unused. - Rows unchanged, by inspection of PREREG §3.2 and
PHASEA-EXPECTED.json.- B-2: every
TV(t₀+1)is 1, or 9/10 for SC. - B-4: every storage tuple has
E ≠ ∅: S1(2) and R3{p₁, v₁}; S1(3); SW{p₁…v₂}; MC(2){u₃, u₄}; MC(3){u₄, u₅}; HC-SKk ≥ 5, other channel cells. - B-1 and B-3 do not apply. B-5 restates §2.10. B-6 is moot, since exit 4 was never raised.
- B-2: every
- First-match coverage intact. B-2 is a new first step. B-4 maps a storage outcome to one row. B-6 sends the halt case to steps 7–8, which are exhaustive.
- Non-blocking (§A.41). "Every Phase A row is preserved" (l.924–925) is an asserted invariant with no checkpoint; the reviewer confirms it by inspection. Under G-10 (c) no tuple ever measures it. That argues for G-10 (b).
6. Gate items
Every item gives alternatives, consequences, tautology risk, new assumptions and a labelled recommendation, and none is chosen (l.949–952). Exceptions are noted in the table.
| G | Alternatives (exact?) | Tautology risk (flag correct?) | New assumptions listed? | Writer | This review | Justification |
|---|---|---|---|---|---|---|
| 1 | a/b/c, exact | none; correct | yes | (a) | (a) | K1 as native-form control, SMR as the only enumerable state-dependent rule. Note (§2): both are largely predicted negative by K1-NS and its SMR-right-side extension. |
| 2 | a/b, exact | none | E-SDC, yes | (a) | (a) | Testing a named, unadopted hypothesis is not adopting it. CONDITIONAL[E-SDC] is carried. |
| 3 | a/b/c, exact | (b) flagged: rejecting-direction non-discrimination, correct | yes | (a), (c) affordable | (a) only | (b) is RS by construction at T ≥ 2, so reporting it beside (a) adds no information. |
| 4 | a–e, exact | (b) flagged. (a) under-flagged: syntactic IP leaves guaranteed passes (B1) | yes | (a) | (a) with IP′; otherwise (c) | IP′ enforces the owner's principle. On this family D2 is undetermined for every written tuple, so (a) and (c) coincide there; the choice matters only for the controls and future families. |
| 5 | a–d, exact | (b)+G-4(b) flagged. (b)+G-4(a): consequence (l.1038–1039) wrong for D2-fallback tuples; re-derive and flag | none; correct | (a) | (a) | Every counted test then includes a hold tick after the first, under any decoder rule. |
| 6 | a/b/c, exact | (b) at T = 1 and the r = ∞/2 re-supply-only laws flagged, correct | yes | (a) + (c) for SMR | (a) + (c) for SMR, with (c) given a pattern/radius so it can enter robustness; K1 under (c) optional, as a K1-NS check | Without (c) or G-9's repair, SMR's only candidates fall to K1-NS's extension or J-1. Left-side, nonlinear-injection registers are where SMR is not covered by any paper result. |
| 7 | a/b, exact | none | none | (a) | (a) | Prevents TR/EX labels on blind registers. Changes no Phase A row. |
| 8 | a/b/c, exact | none | margin, yes | (a) | (a) | Robustness, once repaired, carries the locality burden. |
| 9 | a/b/c, exact | "None" is wrong: (a) and (b) are unreachable for both rules (B2) | yes | (a) | (a) after repair (pair 8 with 6 or 7, and/or one-sided patterns) | A criterion that no tuple can meet does not discriminate. |
| 10 | a/b/c, exact | none | yes | (c) | (b), authorized by name; (c) alone leaves Phase A row preservation unmeasured | §A.41. (b) is a regression test of the new tool, not a Phase A result. |
| 11 | a/b/c | none | yes | (a) | (a) | Scope discipline. |
| 12 | a/b | none | none | (a) | (a) (administrative) | As for Phase A. |
| 13 | a/b/c | none | none | (a) | (a), adding IP′ and the corrected K1-NS (without A5, with the SMR-right-side extension) | §A.46 item 7. |
| 14 | a/b, exact | correct | yes | (b) | (b) | A refutation should not void the SMR half. Revisit after the G-13 record, with the corrected statement. |
| 15 | a/b, exact | none; correct | none | (a) | (a) | Only withholds storage. Its rationale should say K1 tuples may reach the step. |
| 16 | a/b, exact | none; correct | yes | (a), conditional on G-13 | (a), conditional on G-13 | Verdicts only over green controls. NP is verified here; PAD was verified by the first review. |
The gate classes at l.954–957 are reasonable. G-14 and G-15 are scientific; G-16 is partly scientific.
7. Scope and §A.42 item 8
- Scope. Only the two design files changed. No Phase A file, frozen record, merge, freeze, dispatch or computation by the writer.
- New references.
INTERFACE-CONTRACT.md:35–36,MR-star.md:464–465andphasea.py(blob3d5edd97) are onmain: support onmain.- research(#1032 O-RET): Phase B native-retention design (design only; WIP / UNVERIFIED) #1115 c.6649925951: provenance. K1-NS is re-derived in the file.
- O-OBSMU
f67b9f0c: provenance. E-SDC rests on SM:104 and SM:112 onmain. - research(#866 O-OBSMU): observer-interface sourcing, paper assessment (WIP / UNVERIFIED) #1110 and ARROW-1: is the arrow of time derived, or inherited from time-asymmetric initial conditions? (cross-document disagreement) #1112: provenance.
- The classifications in §9 are correct.
- Missing. The governing principle (l.10–13) is attributed to "owner, relayed with the review". The record is O-RET: physical one-step retention and carrier-sensitive native readout (F2 planning) #1032 c.6649977592 (amaybaum, 2026-11-05T04:49:59Z). Quote it with author and time (§A.42 item 7) and list it in §9.
- Name collision (non-blocking). K1-NS's "(A5)" collides with Main's "(A5)", linearity of the update, cited at l.319. Rename, for example H-1 to H-6.
Required revisions
Blocking:
- B1. Redefine
IPat the level of the relation (IP′), in §3.1, §6.4, §6.9 and §6.12. Restate l.380–382. Reclassify DT-S1q asIP′ = true. Add a positive-path control withIP′ = false. - B2. Make STORAGE-ROBUST reachable, by a change the owner chooses at G-9/G-6. Remove or re-derive the §6.7 rows that cannot occur (l.818, and the ROBUST half of l.819), and correct G-9's tautology line.
- B3. Restate K1-NS on A1–A4 and A6. A5 is implied by A2 and A4, and the bound needs neither A4 nor A5. Then:
- delete the l.248–249 limitation;
- correct l.242–243, B-6's rationale, §6.7 l.819, §6.8 item 7, G-6 l.1062, G-14 l.1175–1193, the review packet item 6 and README l.74–75;
- narrow the SMR limitation (l.250) to registers that contain
N−1(orN−2with the conditional target); - add the D2-always-undetermined consequence to §4.4 and G-4.
Non-blocking:
- l.431: four to seven, not five to seven.
- Flag G-5 (b)+G-4 (a).
- G-10 (b) for the §A.41 checkpoint.
- Cite c.6649977592.
- Rename A1–A6.
- Widen C-NP-ALL to all
δ₀-equal laws. - Give G-6 (c) a pattern definition.
Standing
Established: nothing physical. Verified on paper and by my exact check:
- D2-T1;
- IP, as a sufficient condition;
- Lemma NP, with one count corrected;
- K1-NS, in a stronger form than stated;
- DT-S13's values.
Refuted: the claim that IP = false marks a test that could fail, and DT-S1q's role.
Shown unreachable: STORAGE-ROBUST under the current family.
Not checked:
- W1/NK-Wq, NK-W, NK-K3 and the C-PAD values (unchanged and accepted in c.6649925951);
r = −1atN = 8by computation;- the OI ↔ QM equivalence: proof gate (dependency index; carries #885) #914 quotations;
- run time.
Generated by Claude Code
…iew of 5839e06 (design only; WIP / UNVERIFIED) Applies the second independent review at #1115 c.6650383732 (ACCEPT WITH CHANGES), under the owner's decision #1032 c.6649977592. B1: the syntactic IP flag is replaced by IP' (every class of the window's relation that meets the supported set is a single class of D2's relation). DT-S1q is reclassified as a decoder-guaranteed pass that must not count; new control DT-S2s (two-presence-bit M_F, IP' = false, row 5, counts) is a pass that could have failed; DT-S13 rechecked (IP' = false, fails). B2: STORAGE-ROBUST shown unreachable under the current family by hand, per matched pattern and rule; the impossible 6.7 rows are replaced; G-9 now presents four repairs (pair N=8 with 6 or 7, one-sided patterns, both, none) with consequences and tautology risk; none chosen. B3: K1-NS restated on KN-1 to KN-4 without the independence hypothesis; the false wrap limitation is deleted; the exit-4 claim, B-6 rationale, 6.7, 6.8, G-6, G-14, review packet and README are corrected; the SMR limitation is narrowed; the second review's SMR extension is recorded as unverified; D2 is undetermined on every written K1 tuple, so G-4 (a) falls back to D1 on this family (4.4, G-4). Non-blocking items applied. No computation was run. No existing file in o-ret-routes-20261103/ is changed. Nothing is frozen, adopted or promoted. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq
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Checkpoint 4 is pushed at Generated by Claude Code |
Delta review of #1115 at
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| Item | Status | Lines |
|---|---|---|
| B1 (flag at the level of the relation; DT-S1q reclassified; new positive control) | APPLIED as asked, but my B1 was partly wrong (see §2) | l.160–204, 416–417, 842–849, 991, 1069–1071 |
| B2 (unreachability recorded; §6.7 has no unlabelled impossible row; G-9 tautology line corrected) | APPLIED | l.485–487, 863–888, §6.7, l.1260–1310 |
B3 (K1-NS on KN-1 to KN-4, without A5 or J-1; false limitation removed; G_status; SMR limitation narrowed; D2-undetermined consequence added) |
APPLIED | l.227–297, 555–565, 680–685, 972, 1230, 1390–1410. README l.77 |
| "four to seven" sites | APPLIED | l.481 |
| G-5 (b) + G-4 (a) | APPLIED | l.1180–1195 |
| G-10 (b) for §A.41 | APPLIED | l.704–707, §6.9 row, 1321–1343 |
| c.6649977592 quoted with author and time | APPLIED | l.10–13, §9 |
| KN rename | APPLIED | l.235 |
C-NP-ALL keyed by computed G0_uniform |
APPLIED | l.731, §6.9 |
| G-6 (c) pattern definition | APPLIED | l.1206–1215 |
The writer's refinement that the SMR extension also needs A ∌ N−2 is correct. R(N−2) = 0 when y_{N−1} = 0, so y₀ enters there with a state-dependent coefficient. My c.6650383732 wording omitted that case.
2. New material
| Result | Status |
|---|---|
IP′ definition and sufficiency proof (l.160–180) |
verified: consistent D2 + IP′ ⇒ DIL∃ on W_T, τ = ∞, constant ε |
"IP′ = false ⇒ D2 does not guarantee the pass; the check can fail" (l.185–188, 416–417, 845–849, packet item 4) |
refuted (below) |
| DT-S2s hand values (l.736, 780–798) | verified: injective; Q = (p₀, p′₀, v₀); supp Q_{t₀+1} = {(0,0,0), (0,0,1)}; 𝒬_{W₂} adds (0,1,v); ε 0, 0, 0; TV 1, 1, 1; DIL∃; τ = ∞; T′ = 2; J-1 + at both ticks; SCH P, P; (R-a), (R-b); D = 3; E = cells 1, 2; row 5; IP′ = false |
| DT-S2s "a pass that could have failed" (l.200–202, 798, 1069–1071; README l.73) | refuted (below) |
DT-S13 IP′ = false; DT-S1q IP′ = true |
verified. Syntactic IP: DT-S13 false, DT-S1q false |
| K1-NS as restated (KN-1 to KN-4) | verified on paper. The join needs KN-4's differently decoded pair. Translation by x₀ gives `L(Q |
| Reachability note, pattern by pattern (l.863–888) | verified by hand. Every SMR line matches my derivation, including {1,2}: y₁′ = c + y₃ and y₂′ = (1 if y₃ = 1, else y₄). Every SMR write-tick ε matches my earlier check at both N. |
Why IP′ does not track decoder guarantee.
- It depends on unread cells in
R.- In DT-S2s, the only new link
(r,0) ~ (r,1)lies inside one fibre of the read map. Every decoder ofrpasses it. - Take the same dynamics and law with
R = (r). Thenp′ ∉ Par(r),Q = (p₀, v₀), the window's inputs are thet₀+1set, and syntacticIP = true: a strict D2-T1-type tautology (checked). - So DT-S2s's
IP′ = falsecomes only from adding the never-read bitsto the register. The physics of the record inris the same as in DT-S1q.
- In DT-S2s, the only new link
- It treats identical decoders differently.
- In DT-S1q,
~₁is trivial and every read configuration is write-supported, so D2's table equals D1's (g = r). - §6.4 (l.847–849) counts a D1-decoded tuple because D1 reads no hold-tick data. The identical table, labelled D2, is barred by
IP′ = true.
- In DT-S1q,
- I withdraw my c.6650383732 §3 claim that DT-S1q is decoder-guaranteed.
- Its pass is decided by
f_R(·; (0,1)), a map D2 never read. - Strict decoder tautology, a pass implied by D2's inputs alone, is exactly the syntactic
IPof5839e064. IP′ = truewithIP = falsemarks a weak but dynamics-dependent test, not a guaranteed one.
- Its pass is decided by
Proposed repair (for the owner, not chosen). D2 can guarantee a pass only through values it sets that D1 would not. So:
- count a D2-consistent storage tuple iff its D1 row is the same storage row, or
- some window link joins members of
𝓛_{W_T}with different read configurations lying in different~₁-classes ("IP* = false").
Under this rule:
- DT-S1q and DT-S2s count as D1-equivalent static storage;
- D2-only passes need a cross-fibre test;
- the flag no longer moves when unread cells are added to
R.
A positive control that is genuine under every reading above (checked):
- the setting: a two-presence-bit
M_Fwith register(r₁, r₂), both read; - the write:
r₂uniform,r₁ready, and the writer₁ ← r₁ ⊕ v₀ ⊕ r₂; - the decoder:
r₁ ⊕ r₂, which is D1 and also D2; - the hold:
p′ = 1swapsr₁ ↔ r₂, first possible att₀+2; - the law: uniform on
{p₂ = p′₂ = 0, p₁ = 0, r₁ = 0}.
It gives ε 0, 0, 0, TV 1, 1, 1, DIL∃, τ = ∞, J-1 +, SCH P, row 5, IP′ = false and IP* = false. The swap links write-supported 10 and 01, both labelled 1, across distinct ~₁-classes.
3. Evidence for "D2 undetermined on this family" (§A.46 item 7, §A.42)
My counts are an unretained, unreviewed check and support nothing. I recommend two things:
- State it only where it is proved on paper.
- K1: KN-4, l.273–275, as now.
- SMR registers containing site 1 and not
N−2orN−1: the K1-NS join applies verbatim, withb = e₁. This is unreviewed, so cite it as a hand derivation, not as established.
- Label the SMR left-side part as "reported by an unretained, unreviewed check; not established".
That requires changes in three places:
- l.477–479 (§3.4), which states it unqualified, must be narrowed;
- the bold G-4 consequence, "the choice between (a) and (c) does not matter" (l.1156–1161), must be restricted to K1 (and SMR right-side, labelled);
- the B-6/G-15 mentions of my
G_status = emptycounts (l.684, 1420) may stay as context, since neither recommendation rests on them.
4. G-9: would (c) with N = 7 make the criterion reachable?
No, on the following paper argument. It is my hand derivation and unreviewed. Its outcome cases are confirmed by my unretained check.
Write registers as arcs. In SMR, y₀ is a parent of y′_i only for i ∈ {1, N−2, N−1}. So a written arc contains 1 (right side) or N−2/N−1 (left side), never both, at width ≤ 3.
- Right side (
A ∋ 1,A ∌ N−2, N−1):y′_A = q₀ e₁ + H′(y, q_rest) − x;- K1-NS's join and
x₀-translation apply withb = e₁; - so there is no ST under any decoder rule.
- Left side, any law in which every non-carrier site is either ready (both slices 0) or free, independently. This covers
ν_rand G-6 (c) for everyr_far, r_opp. Each case fails the write or J-1 att₀+1:- (i)
A ∋ N−1,A ∌ N−2.- A write ≤ ε* needs site
N−2ready andy₁ = 0, so site 1 is ready andx₁ = 0. - Then
y₁ ∈ Q, withy₁′ = c + y_{R(1)}. - If site 2 is free,
y₁′ = c+1whenevery₂ = 1: J-i fails. - If site 2 is ready,
G₀ = y_{N−1} + y₂ = 0: J-i fails throughy₀′ = −x₀.
- A write ≤ ε* needs site
- (ii)
A ∋ N−2,A ∌ N−1.- The write needs site
N−1ready. - Then
y_{N−1}′ = (y₁ if c = 0, else 1) ∈ Qleaksc, whether site 1 is ready or free: J-i fails.
- The write needs site
- (iii)
A ⊇ {N−2, N−1}.G₀ = (y₂ if y₁ = 0, else y₁)is uniform only if site 1 is ready and site 2 free, or site 1 free and site 2 ready.- In the first case
y₁′leaks, as in (i). - In the second,
y′_{N−1} ∈ Requalsy₁whenc = 0, andy₀′ = y₁ − x₀, so J-ii fails. My check confirms that J-ii fails.
- In the first case
- (i)
- Check. Every G-6 (c) left arc at
N ∈ {7, 8}withr_far, r_opp ∈ {0, 1, 2}: none passes write-minε ≤ ε*and J-1 att₀+1.
Consequence. Together with K1-NS and the reachability note, no tuple of ν_r ∪ G-6 (c) on arcs at N ∈ {7, 8} can count, for either rule. The same holds at N = 5 for ν_r: my earlier check found no SMR tuple there that passes the write and J-1.
- STORAGE-ROBUST stays unreachable under (a), (b) and (c).
- STORAGE-ISOLATED is also predicted unreachable.
- The planned run would test K1-NS, its SMR extension and this case analysis. It cannot discover storage unless one of them is wrong.
- l.1286–1289 ("left-side SMR shapes …
|I| = 5, local atN = 7") is incorrect: such shapes fail J-1 att₀+1. - The (c) row "no known tautology" (l.1304) and the recommendation's rationale (l.1307–1308) need revising.
Where SMR is genuinely open. The one shape I found that passes the exact write and J-1 at t₀+1 uses slice-level readiness: A = {N−1}, site N−2 ready, y₁ = 0 with x₁ free, and site 2 free (checked at N = 7 and N = 8: write-min ε = 0, J-1 + +). Its pattern spans offsets −2…1 (|I| = 4), so it is local at N ≥ 6. It lies outside both ν_r and G-6 (c). Whether it stores is open. Adding it would be a new imposed shape (H-sel), to be decided before any run (§A.29).
5. Gate items, refreshed
Every item gives alternatives, consequences, tautology risk, new assumptions and a labelled recommendation, and none is chosen. Missing or wrong flags are bold.
| G | Alternatives | Tautology risk (in the file → this review) | New assumptions | Writer | This review |
|---|---|---|---|---|---|
| 1 | a/b/c | none; (b) predicted → (a): the SMR half is also predicted negative (§4), so neither rule's half discriminates storage | E-SDC; rule h | (a) | (a), presented to the owner as a test of K1-NS, its SMR extension and the left-side analysis |
| 2 | a/b | none | E-SDC | (a) | (a) |
| 3 | a/b/c | (b) cannot pass; flagged | locus | (a), with (c) affordable | (a) only |
| 4 | a–e | (b) flagged → (a)'s IP′ neither excludes exactly the guaranteed passes nor admits only failable ones (§2) |
t₀+1 support | (a) | (c) for this family (D1, Q8 exactly; D2 rows recorded), since (a) acts as (c) on K1 (paper) and the flag is unsettled. Otherwise (a) with the D1-row-or-IP* rule |
| 5 | a–d | (b)+(b) flagged; (b)+(a) weak, flagged | none | (a) | (a) |
| 6 | a/b/c | flagged correctly → (c) for SMR is also predicted negative (§4, cases i–iii) | carrier restriction; one-sided H-sel | (a) + (c) for SMR | (a). Add a slice-level alternative for SMR's left side, if the owner wants SMR tested at all; (c) as defined adds only predicted negatives |
| 7 | a/b | none | none | (a) | (a) |
| 8 | a/b/c | none | margin | (a) | (a) |
| 9 | Part 1 a–d; Part 2 a/b | (d) flagged → (a), (b) and (c) are also unreachable under the current law families (§4) | pairing; one-sided shapes | (c), N = 7 |
(d), reporting STORAGE-ROBUST as unreachable, under the present families. If the owner admits a slice-level family: (a) with N = 7, which makes that shape local; reachability then open. Part 2: (a) |
| 10 | a/b/c | none | import fidelity (c) | (b) | (b) |
| 11 | a/b/c | none | LA method | (a) | (a) |
| 12 | a/b | none | none | (a) | (a), administrative |
| 13 | a/b/c | none | none | (a) | (a), adding the IP repair. If G-1, G-6 or G-9 consequences are to rest on them, also the SMR extension and the §4 case analysis |
| 14 | a/b | flagged | promotion of an unreviewed result | (b) | (b) |
| 15 | a/b | none | none | (a) | (a) |
| 16 | a/b | none | relies on G-13 | (a), conditional on G-13 | (a), conditional on G-13 |
Not every alternative can now fail under its declared assumptions.
- Under the present law families, every G-9 repair and G-6 (c) cannot pass, and the whole family can produce only NO-STORAGE or VOID if the paper arguments hold. The file should say so in G-1, G-6 and G-9.
- G-4 (a)'s flag needs the §2 repair before its "never counts a guaranteed pass" claim is correct.
Required revisions
Blocking:
- C1. Replace or qualify the
IP′rationale (l.181–188, 416–417, 845–849, 991, 1069–1071, 1148–1149; packet item 4; README l.69–73).- DT-S2s is D1-equivalent static storage, not a failable D2 pass.
- DT-S1q is not a strict tautology.
- Present the counting flag to the owner as a G-4 sub-choice: syntactic
IP,IP′, or D1-row-or-IP*, each with its consequences. - Adopt a control that is genuine under all of them, for example the
r₁ ⊕ r₂swap control above.
- C2. Revise G-9 (l.1260–1319), G-6 (c) and G-1 to record the §4 argument, labelled as an unreviewed hand derivation with an unretained check. Delete the
|I| = 5left-shape claim. State that, on that argument, the planned family can yield no counting tuple.
Non-blocking:
- C3. Scope "D2 undetermined" as in §3.
Standing
- Verified: K1-NS as restated; the
IP′sufficiency proof; DT-S13, DT-S1q and DT-S2s values; the reachability note. - Refuted: DT-S2s's role, and
IP′ = falseas a sign of a failable test. - New: a paper argument (unreviewed) that no tuple of
ν_r ∪G-6 (c) can count for either rule. - Nothing physical is established.
Generated by Claude Code
Independent review of #1115 at
|
| Control | ε | DIL∃ | τ | J-1 | IP |
IP′ |
D1 = D2? | Strict tautology? |
|---|---|---|---|---|---|---|---|---|
| DT-S13 | 0, 0, 1/4 |
false | 1 | ++, ++ |
F | F | yes | no; fails |
| DT-S1q | 0, 0, 0 |
true | ∞ | ++, ++ |
F | T | yes | no (the file says yes) |
DT-S2s, R = (r, s) |
0, 0, 0 |
true | ∞ | ++, ++ |
F | F | yes | no |
same dynamics, R = (r) |
0, 0, 0 |
true | ∞ | ++, ++ |
T | T | yes | yes, but D1 passes independently |
replacement (r₁, r₂), T = 2 |
0, 0, 0 |
true | ∞ | ++, ++ |
F | F | yes (XOR) | no |
- DT-S2s "could have failed" in the free-map class, as the file says at l.798. The delta review's refutation applies the decoder-attribution reading, not the tautology reading.
- Both DT-S1q and DT-S2s are genuine, use-novel passes. DT-S1q's role, "must not count" (l.737, 923, 1069–1071; §6.9), is wrong.
- The replacement control is valid (values as stated in c.6650681094), with three notes:
- (a) Every single cell is independent of
κatt₀+1andt₀+2(checked). So SCH holds only vacuously, and a swapped record gets row 5 ("static"). The control exercises SCH's joint-information blind spot; it does not separate static from circulating storage. - (b) It is valid at
T = 2only. AtT = 3the carrier returns, J-i fails att₀+3, and ε att₀+4is 1/2. - (c)
D = 4bits (p₂,p′₂,p₁,r₁).
- (a) Every single cell is independent of
Recommended counting rule (for the owner). Count a storage row iff it is reached by a decoder that read no hold-tick data (D1), or its window holds an input D2 never read (IP = false). Both clauses are use-novel. The rule
- excludes HC-SW-type D2-only passes at
T = 1; - counts DT-S1q, DT-S2s and the replacement control;
- is unchanged when the unread
sis added toR.
G-4 (c), D1 only, meets the principle with no flag at all.
This matters for no NRR-1 verdict. Every written tuple of the family has D2 undetermined:
- K1: K1-NS.
- SMR on the right of the carrier: the same join.
- SMR on the left: no written tuple passes J-1 (Task 2).
The flag acts only on the controls.
Task 2. The K1-NS extension to SMR, and the left-side case analysis
SMR's update. y′_i = y_{i−1} ⊕ (y_{i+1} ∨ y_{i+2}) ⊕ x_i. So y₀ is a parent of y′₁ (additively, coefficient 1), of y′_{N−1} (through y₀ ∨ y₁) and of y′_{N−2} (through y_{N−1} ∨ y₀).
Right side: VERIFIED, and wider than stated.
- Scope:
A ∋ 1,A ∌ 0, N−2, N−1,q = 2, two-slice locus, current-slice read,Pall four values,μ = μ_Σ ⊗ νfor anyν. EveryT, every decoder rule. - Write.
y_A(t₀+1) = c·e₁ + n, wherenandn_x = y_A(t₀)do not involveσ. - Join.
f_R((x, y); q) = (y, H(y, q_rest) + q₀e₁ − x), withxentering additively. Soℓ* = (H(n_x, q_rest) + q₀e₁ − n, n_x)maps to(n_x, n)underqand to(n_x, n + e₁)underq + e_{y₀}. The nonlinearity ofHplays no role. - Translation.
Q_{t₀+1}'s components other thany₀do not involvex₀, andy₀(t₀+1) = G₀ + x₀, whereG₀reads neithery₀norx₀. SoL(Q | σ₁) = L(Q | σ₀) + e_{y₀}, andη ≥ 1/2. - This holds even where
Qcontainsy_{N−1}(atN = 5,A = {1, 2}), becausecis fixed in bothσ₀andσ₁. - Two more facts: registers containing none of
1, N−2, N−1are unwritten (row 3w) under any product law, and D2 is undetermined on every written right-side tuple.
Left side (cases i–iii): VERIFIED, with one repair, under site-level laws.
- Site-level laws: every non-carrier site is independently ready (both slices 0) or free (both slices uniform). These are exactly
ν_r(r ≥ 0) and G-6 (c).π₀is Lemma PAD's case. - Repair. In (i), and in the first sub-case of (iii), "
y′₁leaks" is false when site 3 is ready: theny′₁ = c ⊕ y₂is marginally uniform. J-i still fails jointly, throughy′₀ ⊕ y′₁ = (y₂ ⊕ x₀) ⊕ (c ⊕ y₂) = c ⊕ x₀. - (ii): an exact write needs site
N−1ready, because a freey_{N−1} = 1maskscin the OR even when another register cell readsy_{N−1}. Theny′_{N−1} = y₁ ∨ c ∈ Qleaks. ✔ - (iii), second sub-case: a write needs site
N−3ready or inA. ThenRfixescand, whenc = 0,y₁, andy′₀ = y₁ ⊕ x₀violates J-ii. ✔ N = 5has registers outside the arc cases. I derived them by hand: no counting tuple anywhere atN = 5.- Under
r = 0:{1, 3}: least write error 1/2.{1, 4}: least write error 1/4.{2, 4}: least write error 1/2.{1, 2, 3}and{1, 3, 4}: J-ii fails, sinceRfixescandy₄(respectivelyy₂), andy′₀then revealsx₀.{1, 2, 4}and{1, 2, 3, 4}:G₀ = 0, so J-i fails.
- Under
r = 1, every register containing 1 and 3 or 4, and{2, 3}and{2, 4}, has the lawδ₀(Lemma NP).
- Under
- Not covered:
- slice-level readiness (one slice fixed), readiness to the value 1, correlated laws, G-6 (b),
q > 2; - non-arc registers at
N ≥ 7.
- slice-level readiness (one slice fixed), readiness to the value 1, correlated laws, G-6 (b),
- Check. At slice level, write and J-1 at
t₀+1are reachable on the left. AtN = 7, out of 4096 laws:{5}152,{6}96,{5, 6}220,{4, 5, 6}142. The three-case conclusion therefore depends on site-level readiness.
Task 3. Under the planned laws, can any tuple count? No, and on my check no tuple can even reach a storage row.
On paper, no tuple of ν_r ∪ G-6 (c) counts, for either rule, at N ∈ {5, 7, 8}, for any T, decoder rule or G-9 repair.
r = −1: PAD.- K1: K1-NS (any product law).
- SMR: the right-side extension, the left-side cases and the unwritten rest.
A more elementary obstruction, which the file and the reviews have not examined.
- Lemma SS-2 (paper, unreviewed). Take a copy-form, centre-free rule and a single-site register
A = {i}whose current slice is ready att₀(y_i(t₀)constant). If J-i holds att₀+1, theny_i(t₀+2)is independent ofκ. SoTV_{t₀+2} = 0and every decoder hasε_max(t₀+2) ≥ 1/2.- Proof.
y_i(t₀+2) = G_i(y(t₀+1)) − x_i(t₀+1).G_ireads onlyQ's cells (centre-free), andx_i(t₀+1) = y_i(t₀)is constant. Soy_i(t₀+2)is a function ofQ_{t₀+1}, which is independent ofκ. ∎ - Since
t₀+2 ∈ W_Tfor everyT ≥ 1, no width-1 register underν_ror G-6 (c) has a storage row at anyT, whatever the decoder. - Classification (§A.31): ELABORATING Lemma PAD, one tick later.
- Proof.
- Check (not support). Screen: J-1 at
t₀+1, and some fixed decoder of the current slice withε ≤ 1/20at botht₀+1andt₀+2. This is necessary for any storage row at anyT.- Over every register and every law of
ν_r ∪G-6 (c), for both rules atN ∈ {5, 6, 7, 8}, no tuple passes. - Every tuple that is written and passes J-1 at
t₀+1has a best window error of 1/2, or 5/16 (SMR{1, 2, 3}), or 1/4 (K1 width 3). - SMR at
N = 5, 6has no written, J-1-passing tuple at all.
- Over every register and every law of
What the run can and cannot establish.
- Its possible verdicts are NO-STORAGE (both rules) or VOID. STORAGE-ROBUST is unreachable under G-9 (a), (b), (c) and (d), and so is STORAGE-ISOLATED.
- On the check, the decision rule's storage step (step 6) is never reached by an NRR-1 tuple. Its outputs reduce to the failure-mode tally: 3w (blind), 1 (RS), 2a/2b, and 3.
- Could establish: that the implementation agrees with PAD, NP, K1-NS, its extension, the case analysis and SS-2 on these instances, which is consistency-axis evidence and could catch an error in them; and which failure mode removes each record.
- Could not establish: anything about retention, or any negative beyond what the paper results already derive.
Owner's question (#1032 c.6649977592). On the planned family the run cannot distinguish retained information from information passing through.
- That is not because the classifier cannot: DT-S13 against the replacement control, and HC-TS against S1, show that it can.
- It is because the family contains no candidate whose outcome the paper results leave open. The negative is fixed in advance.
- The run is a test that cannot pass, which is the rejecting-direction non-discrimination the design itself flags for G-3 (b) and G-9 (d). It should be presented to the owner as a confirmation run, not a discriminating test.
- Corrections needed:
- §6.7 (l.947 and the ISOLATED rows);
- G-1, G-6 and G-9, where l.1286–1289's
|I| = 5left-shape claim and l.1307's rationale fail; - l.1069–1071 ("the test can fail with its assumptions holding"). That holds for the controls, not for the family.
- Open (theorem recovery, not concession): whether SS-2's
t₀+2obstruction extends to every width under J-1. The check finds no counterexample at slice level for SMR atN = 7(best window error ≥ 1/4 for every register). No proof is given.
Task 4. The slice-level shape (A = {N−1}; site N−2 ready; y₁ = 0 with x₁ free; site 2 free)
It fails at t₀+2, so the claim that SMR is "genuinely open" there is refuted.
y_{N−1}(t₀+2) = y_{N−2}(t₀+1) ⊕ (y₀ ∨ y₁)(t₀+1) ⊕ y_{N−1}(t₀).y_{N−2}(t₀+1) = y_{N−3}(t₀) ⊕ (y_{N−1}(t₀) ∨ c) ⊕ x_{N−2}(t₀).- Site
N−3lies outside the pattern (offsets −2…1), soy_{N−3}(t₀)is free. - For
N ≥ 7it enters nothing else in that expression. AtN = 6it also entersy′₁, butx₁padsy′₁independently. - So
y_{N−1}(t₀+2)is uniform givenσ, andε(t₀+2) = 1/2for every decoder. That gives row 3 (or 2a/2b), never storage. - With the register's current slice ready, this is SS-2 directly. The check agrees: at
N = 7,{6}has 96 slice laws that pass the write and J-1 att₀+1, all with best window error 1/2. - The delta review checked only
t₀+1.
Premise status (§A.29).
- It is the same kind of resource as H-sel (imposed readiness, here at slice resolution), not a new dynamical premise.
- But it is a law shape outside the preregistered families, proposed after those families were shown unable to pass. Adding it would be a variant chosen to fit, carrying no independent prediction. It would have to be frozen before any run, with its
Dreported.
Can a test including it fail under its assumptions? It can only fail: it is predicted non-storage. Including it would add one more confirmation, not a discriminating case.
Required revisions
- D1. State the counterfactual class. Restore syntactic
IPas the strict-tautology flag, with the write-input caveat. Withdraw "guaranteed" forIP′ = true. Remove DT-S1q's "must not count" role.- Lines: l.160–204, 415–430, 735–737, 842–849, 923, 951, 969, 1069–1071; §6.9; packet item 4; README.
- Offer the owner the D1-or-
¬IPrule, or G-4 (c). - Adopt the replacement control at
T = 2, with its SCH note.
- D2. Record the SMR right-side extension (any product law), the left-side cases (site-level, with the joint-leak repair), the
N = 5hand cases and SS-2, all labelled unreviewed.- State in G-1, G-6, G-9, §6.4, §6.7 and §6.12 that the planned family can yield only NO-STORAGE or VOID.
- Delete the l.1286–1289 claim and the G-9 (c) rationale.
- D3. Re-frame the run for the owner as a confirmation of paper negatives plus an implementation calibration. A discriminating Phase B needs, before any run, a family that no paper argument (including SS-2) decides. None is identified here, and the slice-level shape is not one.
Standing.
- Verified: D2-T1; the sufficiency of
IPand ofIP′; the values of DT-S13, DT-S1q and DT-S2s; the replacement control (atT = 2); the SMR right-side extension; the left-side cases, as repaired. - Refuted:
IP′ = trueas a sign of decoder guarantee;- DT-S1q's role;
IP*as a tautology flag;- the open status of the slice-level shape;
- G-9 (c) as a route to reachability.
- New (unreviewed): the strict-tautology characterization, Lemma SS-2, and the
t₀+2screen result (a check only). - Nothing physical is established.
Generated by Claude Code
… NRR-1 obstruction (WIP / UNVERIFIED) Applies the owner ruling #1032 c.6651202161 (Option 1) and review #1115 c.6650968100. Paper derivations only; nothing run, frozen or adopted; no Phase B run is planned. Phase A records untouched. - Theorem N: no tuple of the NRR-1 family (K1, SMR; N in {5,7,8}; declared registers; nu_r and one-sided site-level laws; all four carrier preparations; any fixed decoder; any T) takes a storage row. Built from Lemma PAD, Lemma NP, Proposition AE (additive carrier entry: K1 and SMR right side, any product law), Proposition LS (SMR left side, site-level laws, with the joint-leak repair), Observation U, the N = 5 cases, Lemma SS-2 and the slice-level shape. All proofs written out; all labelled not independently reviewed. - Counting criterion: the syntactic flag IP restored as the strict- tautology condition relative to the stated free-map class, with both directions proved and caveats (write-tick inputs, realizability). IP' and IP* shown not to be tautology flags. Control roles corrected: DT-S1q, DT-S2s and the new DT-SX are informative passes; DT-S2s with R = (r) and every T = 1 D2 pass are strict tautologies. Corrected criterion recorded (D1 row or IP false), not adopted. - Scope stated exactly; not a universal no-go for OI retention. - Open families and the smallest unresolved ingredient recorded. - The run specification and gate items G-1 to G-16 are dropped from the record; they remain at 4337057. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
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Checkpoint (WIP / UNVERIFIED): paper-only negative record at Files changed: only Content: every derivation is by hand and labelled "not independently reviewed". No probe, enumeration, simulation or Lean build was run.
Local checks: legacy records (303 intact), citation roles, duplicate, staleness and artifact placement all exit 0. Next: independent review of the derivations and of the negative conclusion, using the §9 review packet. Not authorized: Phase B freeze, enumeration, execution, new physical premises, or promotion. Generated by Claude Code |
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Independent review of Verdict.
Derivations verified by hand:
No step depends on an unrecorded computation. The writer's two departures from the source review are correct:
Needed:
Smaller:
Optional:
Labels and hygiene:
Next: the writer applies these corrections, and the same reviewer runs a delta check. No Phase B freeze, run, enumeration, simulation, Lean work or promotion. Generated by Claude Code |
… (E1-E11; WIP / UNVERIFIED) Applies #1115 c.6651949245 (negative ACCEPTed; record ACCEPT WITH CHANGES). Paper record only; nothing run, frozen or adopted; no Phase B run planned; every derivation still [D], not independently reviewed. - E11: section 7.2 restated as failure of at least one hypothesis of each of PAD, NP, AE, LS, U and SS-2 (U's condition added; NP under its hypotheses; LS no longer a necessary condition). Escape routes O1, O5, O4 (excluded, full-carrier-support reason, R:163-168) and O6 listed; "smallest" qualified (O1 and O5 not ranked; D-SML). Propagated to the summary and README. - E4: exit-4 halt and rows 7/8 not excluded for AE case (b) tuples. - E5: DT-SX polarity of IP* fixed; c.6650681094 convention recorded. - E8: IP stated as two directions plus the undecided case (A.34). - E1, E2, E6, E7, E10; optional E3, E9; E-SDC judgment labelled [D]. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
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Delta check
Three corrections remain, all in §7.2. Theorem N is unaffected.
Next. The writer applies C1–C3, followed by a final delta check. Throughout: no Phase B freeze, run, enumeration, simulation, Lean work or promotion. Generated by Claude Code |
…79acca (C1-C3; WIP / UNVERIFIED) Section 7.2 only; Theorem N unaffected; every derivation still [D], not independently reviewed; nothing run, frozen or adopted. - C1: AE and LS escape conditions add q > 2; LS adds P not all four values; AE notes both x0 values are needed for only some c. - C2: O5 stated under nu_r, r >= 0 (pi_0 is decided by PAD). - C3: O4 not proposed as a candidate, on RET-st's full-support reason (a route-analysis criterion, R:33-34; HC-K4, R:46-50, R:163-168) and requirement 2; admissibility left to the owner. W1's mechanism stated correctly (x0 = 0 silences y0 at t0+1; J-i fails at t0+2). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
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Final delta check,
Status.
Generated by Claude Code |
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Owner decisions on the O-RET record at amaybaum, Claude Code session chat, 2026-11-05:
Next
Unchanged. #1115 stays open as provenance and is not merged or closed. There is no Phase B freeze, run, enumeration, simulation, Lean work or promotion, and no universal no-go claim. Generated by Claude Code |
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Accidental close and reopen. GitHub closed this PR automatically at 08:43:55Z, two seconds after #1120 merged (08:43:53Z). The cause was the coordinating session's error: the #1120 body quoted an owner instruction containing "close #1115", and GitHub reads that phrase as a closing keyword. No one decided to close this PR. The coordinating session reopened it, and it is open now. Its branch, commits and content were not touched. The bodies of #1121, #1122, #1123, #1114 and #918 were scanned and contain no closing keywords. From now on, PR bodies quote such instructions without the "close/fix/resolve #N" pattern. Generated by Claude Code |
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Board card corrected (administrative, not a scientific disposition). The owner approved one
The PR stays open. Generated by Claude Code |
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Review-status reconciliation (owner ruling, #1031 c.6676219154). This is an administrative record. It changes no scientific status and authorizes no work. Owner ruling. amaybaum, Claude Code session chat, 2026-11-06; recorded at #1031 c.6676219154:
The two readings
Reading adopted. The classification above applies to the derivations of
Authoritative result. This settles completion criterion 2 of #1032 c.6666791018 and the open question in #1031 c.6667027319. Not authorized: Phase B freeze, run, enumeration, simulation, Lean work, promotion or merge. Phase B execution is not reopened. Generated by Claude Code |
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Retirement: closed without merging. Owner ruling: #1031 c.6676219154 (amaybaum, 2026-11-06). This is administrative and changes no scientific status. The accountable Issue is #1032. What landed.
Branch-only content, and where each obligation now lives
No claim on Preserved. Nothing is deleted or rewritten. The heads were checked with
Not authorized: Phase B freeze, run, enumeration, simulation, Lean work, promotion or merge. Phase B execution is not reopened. Generated by Claude Code |
WIP / UNVERIFIED. Design only. Guiding draft PR (
AGENTS.md§A.43) for the paper-only O-RET Phase B design unit of #1032. Not for merge.Historical draft, not the landed result.
DESIGN-PHASE-B.mdat this head (4b4cacc9) is the historical design draft. The result is onmainasverification/programmes/oi-qm/reconstruction/o-ret-routes-20261103/phaseB-negative/THEOREM-N.mdwithREVIEW.md(#1120, mergeb606ee41, #1120 c.6653830179). It is an extract of this head, accepted at exact head82e146d8, and it records O4 under owner ruling (a) (c.6652197336). See six-PR audit finding 4, recorded at #1032 c.6666791018.writer-oret. Branchresearch/o-ret-phaseb-design-20261105, drafted frommainf5c281ae10a913ec68fa41b3b839ad0b164979cd.4b4cacc93884039afadd0069373b0ac448761a6b. The final delta check returned ACCEPT (c.6652150358).fdacce54: ACCEPT WITH CHANGES (c.6649925951);5839e064: ACCEPT WITH CHANGES (c.6650383732);43370576: ACCEPT WITH CHANGES (c.6650681094), and separately REVISE (c.6650968100);250ab402: ACCEPT for the negative conclusion, ACCEPT WITH CHANGES for the record (c.6651949245);179acca3: ACCEPT WITH CHANGES (c.6652079353);4b4cacc9: ACCEPT (c.6652150358).250ab402and179acca3(the negative record),43370576(checkpoint 4),5839e064,fdacce54and189ef6e2.49f0bd41);main);main).Contents
A new directory,
verification/programmes/oi-qm/reconstruction/o-ret-routes-20261103/phase-b-design/, with two files. Nothing else is changed.README.mdDESIGN-PHASE-B.md. At this head it is the paper-only negative record of the NRR-1 obstruction, with these sections:main.Up to checkpoint 4 (
43370576) it was the design draft: (a) starting point; (b) the candidate NRR-1; (c) discrimination; (d) assumptions; (e) sourced versus imposed; (f) the proposed test; (g) gate items G-1 to G-16; the review packet and off-mainreferences.Checkpoint 4 changes (historical; superseded by
250ab402,179acca3and4b4cacc9)IP′replaces the syntacticIP: every class of the window's relation that meets 𝓛 is a single~₁-class.IP′ = false, passes and counts; it could have failed.IP′ = false, and it fails.Limits
o-ret-routes-20261103/is changed, and Phase A's frozen evidence is only read.