OI-PE-1: pseudoentropy, deterministic randomness and observer access (research plan) by amaybaum · Pull Request #923 · amaybaum/incompleteness

amaybaum · 2026-10-25T15:59:38Z

Guiding draft PR for the OI-PE-1 research thread (§A.43). This is exploratory research only. It is not a native V3 round, and the PR introduces no postulate, premise or manuscript change.

Branch: research/oi-pseudoentropy-20261025.
Drafting snapshot D: main at c37700ad7d1bf099c59010e941ca06ffc4c12e3d.
Head: 85096e3f8fb9f40dc23912c3a563ab95f6baff8b, tree eb4015d7. This is the PE-01 frozen preregistration.
Accepted thread plan: README.md`` at 66578f41, unchanged at the head. Its review is in `review/REVIEW.md` (commit `25e77a3c`).

Merge: not authorized.

PE-01 frozen preregistration

PE-01 is bounded tests on one fixed generator family.

Plan: pe01_bounded_tests_v1/PLAN.md,``` revision 5 (af38dc2d, sha256 `bf7b0cb9…e091`).
- The plan was pinned before any code: no code exists on this branch.
- It covers observer classes, exact advantages, controls, an invariant→checkpoint table (§A.41), the decision rule and outcome classes, scope, resources and literature.
Amendment A1: ['amendments/A1-owner-decisions.md'](https://github.com/amaybaum/incompleteness/blob/85096e3f8fb9f40dc23912c3a563ab95f6baff8b/verification/programmes/oi-qm/reconstruction/oi-pseudoentropy-20261025/pe01_bounded_tests_v1/amendments/A1-owner-decisions.md). Its final text is at 1e025b67. It records the owner's decisions of 2026-10-25, with their rationale:
- footprint cap θ = n + 1;
- K_LP(n) = 2^(n−1) − 1, with no post-result adjustment;
- the passive m = 3 sweep extended through n = 8, capped at the admissible region (K ≤ 15 at n = 7, K ≤ 31 at n = 8).
One decision rule for all observers (the owner's choice (a)). The m = 3 sweep is reported as its own cells, in its own CI jobs. Any control failure voids the whole stage.
Shard reporting. A shard never started is "not run". A shard started but not finished is "incomplete", with its completed cells and partial output kept.
Scope of results. Results are stated under θ = n + 1 only. θ = n is not tested as a decision rule.
Parameter enforcement. A1 carries a machine-readable parameter block, which the TH checkpoint reads and records. A run whose parameters differ from it refuses to start.
Review records: ['review/plan/'](https://github.com/amaybaum/incompleteness/blob/85096e3f8fb9f40dc23912c3a563ab95f6baff8b/verification/programmes/oi-qm/reconstruction/oi-pseudoentropy-20261025/pe01_bounded_tests_v1/review/plan/README.md), byte-identical to the reviewer's, with SHA256SUMS.

Commit	Verdict
`aa667c13`	BLOCK (R1–R5)
`6e5db447`	BLOCK (S1–S5)
`67a5cbe1`	BLOCK (admissible-region floor, attribution)
`fee98794`	ACCEPT WITH NITS
`1cbfba61`	ACCEPT WITH NITS (N6)
`af38dc2d` + A1 `ced675cc`	BLOCK (P1–P2)
A1 `7b8ca727`	ACCEPT WITH NITS (N-d, applied in `1e025b67`)

The reviewer's design-check scripts are retained, and each replays byte-identically. They check plan facts and drafting-time tables only; the AR checkpoint re-derives the tables at run time.
The author recomputed the admissible-region floor Z(φ) independently, and it agrees with the reviewer's in every cell.

Exact-head CI. workflow_dispatch run 40226975040 of verify.yml, on 85096e3f, is in progress. The branch stays at this commit until it completes. Execution begins only after it is green.

Pre-push checks:

artifact placement, voice, staleness, legacy_records_check (303 intact);
a scan of added lines found no secrets, e-mail or IP addresses, or local paths;
no push-triggered workflow matches these paths.

Question

This thread takes one fixed finite reversible realization and lets the horizon or protocol class grow. It asks:

for which observers the visible record is indistinguishable from a genuinely random reference source;
how far that holds, and at what resource cost;
whether it survives repeated and adaptive measurement.

The corpus claim under audit is book/ch18-beyond.md:114: randomness "is unpredictable by any embedded observer regardless of its origin". The thread treats it as a claim to test, not a premise. Finite observer classes can refute its universal form but cannot establish it.

Baseline already settled in the corpus (not restated as new)

Structure.md:1256: zero entropy rate. Recorded randomness is bounded by log|C_V×C_H| and exhausted at recurrence scale.
Main.md §3.4:
- finite-horizon dilation and gluing, with per-horizon realizations;
- the fixed-representation and fixed-N-state obstructions;
- ε-density.

Scope

Three notions, kept distinct:

Information-theoretic entropy.
Computational pseudorandomness and pseudoentropy, each use naming its distinguisher class:
- HILL with Shannon entropy: there is a Y that defeats every distinguisher (∃Y ∀D);
- metric: each distinguisher is defeated by some Y (∀D ∃Y);
- Yao.
OI observational indistinguishability, against a named reference law, with the quantifier order stated.

Observer knowledge:

K0: neither φ nor μ is known, and one test is fixed in advance.
K1: φ and μ are known, but not the initial state.
K2: a priori knowledge of the initial state. This level is excluded.

An observer counts against the claim under audit only if it is embedded-realizable.

Stages:

PE-01 (frozen above);
PE-02: computational versus physical observers, each direction separately (§A.34);
PE-03 and PE-04: prospective.

First milestone: PE-01 and PE-02. It closes with at least one of:

a new bounded theorem;
a counterexample to the universal form of ch18:114 by an embedded-realizable observer;
a documented finding that existing OI mathematics already covers the distinction.

A failed control makes it VOID. Otherwise it closes OPEN.

Authority limits

This PR does not claim:

that OI guarantees cryptographic security;
that deterministic dynamics creates Shannon entropy;
that pseudoentropy reproduces quantum mechanics.

PE-01 execution is authorized by the owner once this preregistration is published and its checks pass. The job CI of §8 is workflow_dispatch-only, and each dispatch of it needs owner approval (§A.43). This PR carries no manuscript change, theorem or scientific-result designation, and no merge, without separate owner approval.

Related: #911 (bounded persistent memory; PE-03 coordinates with it and adopts none of its controllers), #910, #912, #917, #918.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…rver access) Opens the OI-PE-1 research thread from main c37700a. One file: the thread's question, its corpus anchors (book ch18:104-114 and FULL mirror, Main:78, :82, :172), three notions kept distinct (Shannon entropy, computational pseudoentropy in the HILL/metric/Yao sense, OI observational indistinguishability for a stated protocol class), stages PE-01 to PE-04 (PE-03/PE-04 prospective), decision rules stated before any computation, the literature to read before any closure claim, and authority limits. No computation, manuscript change or premise. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Addresses all eleven findings of the independent plan review of 80e4465 and the owner's two points: - HILL stated with Shannon entropy (min-entropy form BSW), metric with reversed quantifiers, Yao from Yao 1982; distinguisher model named. - Anchors restated in the corpus's own terms (Main:82 layers, Main:172 per-horizon fair coin, C3 on I*), and the baseline the corpus already settles added: Structure:1256 zero entropy rate, Main:476, :496-500, :536-538, :544-560, :576; related statements ch18:56-58, :110, appendix-c:58-62, Computation:15-17, Main:708. - OI advantage defined against a named reference law, with runs, settings, measurement independence and the observer's knowledge of phi stated; that knowledge is the first assumption-watch item. - Shannon bound given with its conditions; exact bound vs computational unpredictability (a PRG past the seed length) kept apart. - PE-01 tests three observer classes on one fixed generator, with a non-vacuous positive control and a negative control tied to its reason. - ch18:114 is a claim to test, refutable but not establishable by finite classes; the milestone is a question with an outcome rule. - #911 result pinned at bafb38d and scoped; references completed. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Owner review of 47d4f2b: - Knowing the law is not knowing the seed. Observer knowledge is now one of K0 (neither phi nor mu), K1 (phi and mu, not the initial state; prediction set by the posterior, computed rather than assumed; perfect from 2L symbols on by Fine-Wilf, L the maximal orbit length) or K2 (the initial state, i.e. reading h, outside the thread's classes). The unrestricted PE-01 observer is tested at K0 and K1. - The first milestone closes with one of three admissible outcomes: a new bounded theorem, a counterexample to the universal form of ch18:114, or a documented finding that the distinction is already covered by Structure:1256 and Main section 3.4. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Re-check of bd69acf (narrow block) resolved: - R2: Main:476/:536 say no fixed representation hosts generic combs; Main:538 is the fixed N-state realization obstruction for the qubit. - R3: a ranging reference class states its quantifier order (HILL-like min-max, metric-like max-min). - R4: K0 defined (test class fixed independently of phi, advantage over a named generator family); TV and the cryptographic notions are K1 by default. - R5: milestone closes with one or more of three outcomes, or OPEN, or VOID; a counterexample to ch18:114 needs an embedded-realizable observer (record memory and computation within C_V, measurement- independent settings); that memory bound is the first assumption-watch item; a bounded theorem needs a named class. - Nits: Main:498 removes the rationality restriction; TV 0 for the passive law, interventions for fixed finite families (Main:460, :536); record length n = K+1; HILL stated asymptotically in its source; Yao Shannon-type; exact all-circuit advantage only at tiny parameters; periodicity for the passive record only; K1 may infer the initial state, K2 excludes a priori knowledge; retained-seed escape when granted the target cuts. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

- N8: K0 chooses one test for a named generator family; worst-case (max_D min_phi) and average-case (max_D E_phi) forms stated; per-phi choice over all tests would collapse K0 into K1; average case is not folding phi into the seed. - N9: the embedded-realizability sentence is conditional on 2L log2|A| exceeding the observer's share of visible memory; L depends on phi. - N10: a failed control makes the milestone VOID regardless of other outcomes; otherwise OPEN if no outcome is reached. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Adds review/REVIEW.md, byte-identical to the separate-agent internal review of the plan (sha256 be943f7d5b5cce0cbfe3ee6e40d5cdc7785cb63e51ea56ea18dd5321da4e348d): the first review of 80e4465 (BLOCK, eleven findings), the re-check of 47d4f2b with its update for bd69acf (BLOCK, narrow: R1-R5), Addendum 2 on e49c3b0 (ACCEPT WITH NITS: N8-N10) and Addendum 3 on 66578f4 (ACCEPT). Every reviewed commit is on this branch. Line numbers in the review refer to README.md at the commit each part reviews. Scanned before commit: no tokens, keys, signed URLs, e-mail or IP addresses, and no local paths; nothing redacted. The accepted plan (README.md) is unchanged. The review is internal review, not a research result, external validation or owner adoption. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Fixes the PE-01 objects (skew-product generators G_lin / G_filt / G_clk over primitive LFSR maps, with control generators G_dec, G_tape and a reciprocal-polynomial sibling), the inline definition of adv_D(phi), the reference law, knowledge levels, the three observer classes (unrestricted calibration, structured bounded classes B1-B4, embedded reversible observers P^emb(m)), positive/negative/exactness controls, the A.41 invariant-to-checkpoint table, and the decision rule with the COUNTEREXAMPLE criterion for the universal form of ch18:114. No code, no results. Local draft only. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Applies the independent review of aa667c1 (narrow BLOCK) before any code: - R1 a counterexample witness may be K1, and its K0 status is reported; - R2 the readout clock is charged in a witness's footprint, and the prediction advantage must hold on a fixed window w = 3; - R3 G_tape(K) with N = K, x_0 uniform, fully enumerated for K <= K_tape = 20; - R4 new checkpoint EX8 (no hidden-sector access), and EX7 rests on it; - R5 K0 is fixed per subclass, the deterministic worst case is labelled a lower bound, and T3 uses the average-case or exact randomized LP form; - N1-N14: G_filt specificity, the B4 counting horizon, an independent DP check of the LC count, the B4 weight method and K0, the U average-case K0, IM6, the Main:560 scope and table size, realization conditions in the verdict, workflow_dispatch-only CI with JSON shards, literature before candidate-NEW tags, the stage-outcome label, vectorisation, and K_delta = null; - section 10 lists the seven owner decisions, with the review's recommendations. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Applies the re-check of 6e5db44 (narrow BLOCK) and the owner's decisions, before any code: - S1 EX8 checks each observer map (rho-step, a-step, clock tick, readout) for identity on h and independence from h, and checks that phi is the identity on (v, clk, out); - S2 the G_filt specificity rule is <= at every injective K, and < at some such K, for each n; - S3 new CX checkpoint: the JSON-only evaluation of (a)-(f), with three mutant witnesses each refused on its own condition; - S4 footprint = m + ceil(log2(K+1)) + 1 everywhere; new FP checkpoint; curves labelled "evaluation time uncharged"; the table size includes the trigger constant; the overcharge is noted as conservative toward the claim; - S5 the resource-model limitation sentence and the admissible-region tables (theta = n and n+1, per generator) in section 7 and in the verdict text; - A4: a candidate covered by a section 9 paper is tagged COVERED-literature; - dual-form randomized LP with K_LP(n) = 2^(n-1) - 1, plus a section 8 row; the B1 K0 nit; - section 10 records owner decisions 1-7 as decided. The admissibility threshold theta is the one open decision, and no run starts before it is fixed. The plan's own purpose statement is added. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…tribution) Applies the re-check of 67a5cbe (narrow BLOCK), before any code: - defines the universal zero horizon Z(phi) and states why it holds for every observer, adaptive included; the window floor is now K >= Z(phi) + 4 for all three generators. The section 7 tables are rebuilt per generator for theta = n and n+1, with Z values independently recomputed at drafting, and the consequences restated in sections 7 and 10. "Design-checked" is removed. - new checkpoints: AR (Z computed exhaustively, Z(G_lin) = n cross-checked against PC, the region recomputed and equal to the tables, and printed recomputed by the verdict) and TH (theta, K_LP and the fixing amendment recorded in the JSON and checked like PIN); - attribution rule: unpredictability is attributed to resources iff some witness meets (a)-(e) but fails (f); otherwise the verdict says "no witness within the enumerated scope at any footprint"; - CX also reads the EX1/EX7/EX8/IM3 flags and the global control flag; VG's self-test checks the limitation sentence; runs are gated on both theta and K_LP. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Nits only, from the re-check of fee9879 (accept with nits). No code. - N1: the readout clock starts at 0. - N2: AR also checks that mu factorises with uniform h and that every observer register starts at a fixed value. - N3: the linear-filter sweep runs n = 3..8. - N4: the attribution rule is applied per (generator, n, observer subclass); the section 7 consequences heading is reworded. - N5: the scope of the passive m = 3 sweep is a new open owner decision in section 10: (i) n <= 6 as comparison data only, or (ii) extend to n = 7, 8, capped at the admissible region, with its own section 8 row. Runs are gated on this decision as well as on theta and K_LP (TH). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

- N6: section 6 item 4 now says that theta and the m = 3 scope are the open owner decisions, and that K_LP awaits confirmation. No other "one open owner decision" phrasing remains. - Cosmetic: rewraps the over-width section 6.4 lines, and fixes the lazy continuation line at the end of the attribution bullet. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

… only) Adds pe01_bounded_tests_v1/review/plan/: the independent review of the stage plan from aa667c1 to revision 4, with its addenda (REVIEW.md, RECHECK-67a5cbe1.md, RECHECK-fee98794.md), byte-identical to the reviewer's records, and the reviewer's design-check scripts with their outputs. Every script was replayed and reproduces its retained output byte for byte. README.md indexes the verdicts and maps the working paths; SHA256SUMS covers the directory. No plan text changes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…eeze) Adds pe01_bounded_tests_v1/amendments/A1-owner-decisions.md, fixing the values PLAN.md (revision 5, af38dc2) leaves open, as decided by the owner on 2026-10-25: - theta = n + 1; - K_LP(n) = 2^(n-1) - 1, with no post-result adjustment; - the passive m = 3 sweep under option (ii), extended to n = 7 and 8 with K <= 15 and K <= 31. The plan's text, conditions (a)-(f), thresholds and controls are unchanged. The extended sweep adds observers only, is reported as its own cells and runs in separate CI shards. Results are stated under theta = n + 1 only. A machine-readable parameter block is read and recorded by the TH checkpoint. This commit is the frozen preregistration; code commits follow it. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Applies the pre-freeze check of ced675c: - P1: records the owner's clarification of the "separate" safeguard, reading (a): one decision rule for all observers, with the m = 3 sweep reported as its own cells in its own CI jobs. - P2: a shard never started is "not run"; a started, unfinished shard is "incomplete", with its completed cells and its partial output kept; neither status is a verdict; a checkpoint failure in an m = 3 shard voids the whole stage. - Nits: per-n values in the parameter block, checked against the formulas; K_LP applies at n <= 6 only; the review README now covers up to revision 4 and points to the A1 check. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

… (nit N-d) The checker compares each formula with its explicit values only where the block gives them: theta at n = 3..8, K_LP at n = 3..6. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…(evidence only) Adds review/plan/PRECHECK-A1.md, the independent check of revision 5 and of A1 (ced675c: BLOCK narrowly, P1-P2; 7b8ca72: ACCEPT WITH NITS), byte-identical to the reviewer's record, and indexes it in README.md and SHA256SUMS. Its nit N-d is applied in 1e025b6; N-e is this commit. Touches review/plan/ only. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

amaybaum · 2026-10-25T19:59:06Z

Checkpoint: the PE-01 frozen preregistration passed CI at its exact head.

workflow_dispatch run 40226975040 of verify.yml ran with head_sha 85096e3f8fb9f40dc23912c3a563ab95f6baff8b. It completed with conclusion success, and all 40 jobs succeeded.
The branch stayed at 85096e3f for the whole run.
With the preregistration published and its checks green, the owner's condition for execution is met. Implementation now proceeds on this branch, in commits after 85096e3f.
Before the §8 CI sweeps are dispatched, the code will get an independent review, and the owner will approve the dispatch (PLAN §8, §A.43).
No result exists yet.

Generated by Claude Code

…U, B1-B4) PLAN.md §1-§3 as written, in exact arithmetic (Python ints and Fraction; numpy on integer arrays only): - gf2: polynomials, primitivity by the order of z, packed GF(2) elimination. - generators: phi = tau_f o kappa_sigma for G_lin, G_filt, G_clk, G_dec, the K0 families over all primitive p, and the mutant G_tape(N) with its prior. - laws: record laws by full enumeration through the bijection; U at K1 (TV, Bayes predictor) and K0 (the D_union / min-TV and mixture / mean-TV intervals); complement invariance (SY). - lc: Berlekamp-Massey, the length-count closed form, the independent DP and its Markov premise by enumeration (IM1, IM2). - bclasses: B1 by integer WHT (K <= 23) and the affine-hull tests beyond; B2; B3 k-wise (K <= 127) and windows (w <= 16); B4 by exact elimination, binary search for the least K, Dickson reduction (d <= 2) and enumeration (d = 3, K+1 <= 24) over annihilator spaces of dimension <= 20. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

… registry - params: the run parameters and the TH and PIN checkpoints. TH parses A1's pe01-parameters block, evaluates each formula at every n with an explicit value (theta: 3..8; K_LP: 3..6), compares the block with the parameters the code runs with, records A1's blob and requires 1e025b6 to be an ancestor of the run commit with A1's blob unchanged. PIN records PLAN.md's blob, requires it unchanged since af38dc2, that commit an ancestor of the run commit and of every commit touching the code. Either failing refuses the run. - ar: Z(phi) by exhaustive equidistribution over all control sequences, K_cx from the orbit census (median uniqueness checked), the admissible region recomputed from Z, K_cx and theta, compared cell for cell with the §7 tables parsed from PLAN.md. - pending: the points where the plan as written does not determine the computation (B3 window K0; the setting map of linear-filter observers). A run in result mode refuses to start while any is open. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…dual LP - observers: all observers with m <= 2 (16 and 9216); passive m = 3 in the canonical BFS labelling of the component reachable from v_0 (306432 forms, equal to Hall's subgroup counts of F_2 for k = 1..8); linear filters rho_x(v) = A v + x b, every (A, b) and their behavioural classes (the minimal polynomial of b under A). - composite: the composite bijection on C_V' x C_H from register-level maps (readout gated by the clock, rho, a, phi, clock tick); EX1, EX7, EX8, FP; the full-state path of IM3; the clocked witness composite. - embedded: the aggregated transfer sweep. Q_p exactly as integers Q_K = 2^K q_K per (rho_0, rho_1); every maximum (K1 optimal F, K1 prediction, K0 worst and average over all tests, K0 over prediction tests) is decided by integer bounds and exact Python-int evaluation; windows of the same O and chi at K-3..K are tracked for the primary and the family. - lp: the randomized K0 worst case for m <= 2 in its dual form, by cutting planes over an exact simplex, with both certificates checked. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…t.py - cx: conditions (a)-(f) of §6 item 4 evaluated from a witness record's fields alone; the self-test's three mutants (one window value at 1/8 - 2^(-K-2), footprint theta+1, K = K_cx + 1) must each be refused on exactly its own condition, and the base record accepted. - collect: merges shard outputs into measurements.json; a shard is complete, incomplete (started, not finished; A1) or not run. Cross-shard controls: EX3 over every shard, TH and PIN consistency, NC-2 specificity (G_filt against G_lin at every K where both records are injective), CX, RP from the replay records. A checkpoint is green only if evaluated and passing; a missing primary shard leaves its checkpoints unevaluated. - verdict.py: generates the verdict text from measurements.json alone, VOID first and naming the failed checkpoints; per (generator, n, subclass) witness classification and attribution; the resource-model limitation sentence and the recomputed admissible region. VG self-test: regeneration identical, every control flag flipped yields VOID naming it, and the text check rejects a text without the limitation sentence. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

… job - shard: the computation split by (n, family), with the passive m = 3 sweep in its own (n, family) shards (A1), plus the controls and G_tape shards. Every §5 checkpoint is evaluated where its data are: EX1-EX8, IM1-IM6, PC, NC, SY, MO, FP, K0, AR, and the per-witness CX fields (full-state simulation of the clocked composite, its aggregated twin, K_cx, FP, EX6, EX1/EX7/EX8/IM3, K0 status). Smoke mode is the §8 local row: n <= 5, U, B1-B4, passive m <= 2, and the controls. - run.py: shard / replay / collect / list. TH and PIN run before any work; result mode also refuses while an open plan item has no amendment. A shard writes a deterministic <id>.json (commit, recipe, preflight, controls, measurements) and a separate <id>.provenance.json (run id, timings), so a replay can be compared byte for byte (RP). - .github/workflows/pe01-bounded-tests.yml: workflow_dispatch only (no push or pull_request trigger); plan, primary and m3 matrices from run.py list, a replay job per shard, collect and the verdict; shard and result JSON uploaded as artifacts for commit after review. Dispatch needs owner approval (AGENTS.md §A.43 item 4). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

The VG flip test now flips only passing controls to failing (an already failing control leaves the verdict VOID and named), the limitation-sentence check is exercised on a probe text when the verdict itself is VOID, and a VG failure keeps the original failed checkpoints in the VOID line. Found by running collect and verdict on a copy with one control flag injected false. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

amaybaum · 2026-10-25T21:49:24Z

Checkpoint: the PE-01 implementation is published as WIP / UNVERIFIED.

Head: 0f1391cd470ec5c8513de05ced1bad3c61050c08. It is six code commits after the freeze 85096e3f. PLAN.md and A1 are unchanged.
The code implements every §5 checkpoint. During development each was broken deliberately and caught the break; those mutants were not committed.
The CI job .github/workflows/pe01-bounded-tests.yml is workflow_dispatch-only and has contents: read permissions:
- 20 primary shards;
- 18 separate m = 3 shards (A1);
- a replay job per shard;
- a collect job whose VOID marker reads structured verdict data.
Local smoke (§8 row 1) took 382 s. Every control in its scope passed. Its output is a smoke run, not a result, and it is not committed.
Result mode refuses to start. Two open points, which the plan does not determine, need an amendment first:
- exact K0 for B3 windows beyond w = 4, which is infeasible;
- the control map of linear-filter observers.
Independent code review is in progress. Owner decisions on the amendments and on the CI dispatch come after it.
No result exists yet.

Generated by Claude Code

… (review R9) - pending: each open item lists the readings the code implements (B3W-K0, LF-A, WIT-A, TAG-L, D-SIGN); open_items() returns the items A2's block does not resolve with a listed reading. - params: amendment A2 carries a machine-readable pe01-resolutions block. TH pins it as it pins A1: A2_COMMIT (unset until A2 lands), its blob unchanged at the run commit and in the tree, A2_COMMIT an ancestor of the run commit, A1's commit an ancestor of it. TH records the A2 blob and the resolutions. Result mode refuses while any item is open. A test mode reads an unpinned local stub (PE01_TEST_A2) and is never a result. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…coding - ar (review R3): K_cx is checked against independent values: the closed form 2^(n-1) - 1 for G_lin and G_filt (two fixed points (x, 0); every other state on a cycle of length 2^n - 1), and a separately coded scalar orbit census for G_clk. l_med is recorded. The unused theta argument is removed. - bclasses (open item B3W-K0): window marginals are checked stationary for every window used; the K0 average is exact by sign-pattern decomposition over the union of supports (checked against all tests for w <= 4); the deterministic worst case is exact for w <= 4 and the D_union / min-TV interval for 5 <= w <= 16. B1's lower bound beyond K = 23 is monotone in K (review N4). - exact (review R6): run-length encoding and a lossless complement form 1-p/2^e for dyadic values near 1. - composite: a map leaving the declared state space fails EX1 and FP cleanly instead of crashing; FP's reference clock width is written independently (review N1); the window-reading note (N12). - lc: the tautological length-rule sub-check is removed (review N2). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…IM3 (review R1, R4, R5) - embedded: prediction windows are tracked under both readings of (d) (open item D-SIGN): 'abs' |Pr - 1/2| >= 1/8 and 'signed' Pr - 1/2 >= 1/8 with the same chi at every K' in K-3..K; per K the subclass count, the family-wide count and the count per family member. - shard, R1: embedded_bruteforce compares the window counts (both readings, primary and family-wide) with an independent scalar Fraction path; pred_bruteforce does the same for the 'pred' path (K1 prediction, the K0 worst and average maxima, windows) on passive linear filters and a passive m = 3 sample. The '>=' -> '>' window mutant is now caught. - R4: the m = 3 shard checks m = 3 <= U, prediction <= distinguishing and its K0 records; K0 <= K1 is checked pointwise for every K0 class against the named generators' K1 curves (where K1 is exact); randomized K0 lies between the deterministic worst case and the average. - R5: the passive-linear sweep carries the full-state IM3 path at n <= 4, and the class reduction is checked per (A, b) by the multiset of cells (C[v,0], C[v,1], Q_K(v)) and of linear-prediction hit counts. - Open items: B4 at degree d takes the lower-degree values where only the 2^-d bound is known, with MO d <= d+1; the B3 window K0; passive linear filters named so (plin_m*); witnesses per reading, plus the first family-wide window (N6); mechanical L1-L4 tag inputs (TAG-L). - N3: PC firing also asserted on the sweep's m = 1 curves on G_dec at K = 1. N9: the canonical m = 3 forms are pairwise distinct and fixed by an independent BFS relabelling. Curves and per-K lists are run-length encoded losslessly (R6); progress is reported after every block for partial outputs (R8). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…rements (review R2, R6-R8) - verdict.py, R2: horizons are printed from the shards' exact and determined flags. Only exact, determined statements stand under PROVED (exhaustive finite); lower bounds print as "K_delta <= K" or "undetermined", intervals as ranges, in their own section. INCOMPLETE (no verdict) when a checkpoint or primary shard was not evaluated; VOID only for a failed checkpoint. Condition (d) under the reading A2 selects, or both when none is selected. Mechanical tags L1-L4 with COVERED-corpus first (N5); theta from the measurements (N8); per-combination region cells (N10); family-wide window counts (N6); the conservative reading of (a). - cx: (d) under a named reading; a malformed value refuses (d) instead of crashing (N7); the self-test covers both readings, a sign-alternating window and a malformed value. - collect, R6-R8: measurements.json holds only verdict inputs and each shard file's sha256, with run id, attempt and job per shard and for the run; incomplete shards keep their completed cells and controls; a missing replay record is unevaluated, a differing one fails RP; cross-shard MO for m = 3; witness K_cx checked against AR; a 20 MB budget per file. verdict.json records the sha256 of measurements.json and the run id. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…fixed before reading) Owner decision 2026-10-26: extend tagging to relevant prior work without changing PE-01's frozen verdict. A3 adds prior work on self-clocked and clock-controlled generators (Rueppel 1987, Gollmann-Chambers 1989, and works found from them) to the citations productivity tags may use, and fixes the tagging rule before any of it is read: first-hand reading only, quoted passage and covered parameters, "covered in kind" kept distinct, no candidate-NEW while any listed work is unread. Verdicts, measurements, controls and the A2 mechanical tags are unchanged; nothing is re-run. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…terature corrected review/literature/ holds the tag annex (r2, in force; r1 kept as the reviewed object), the independent review of r1 (ACCEPT WITH CHANGES), the re-check of r2 (ACCEPT WITH NITS, nits RN1 and RN4 applied), the author's check script with its outputs, and the reviewer's probes. - The counterexample cell is covered in kind, not in its parameters, by a 2006 clock-control fault attack on the shrinking generator. - Passive horizons of linear statistics on the linear generators are covered in kind by AGHP's mechanism. - No candidate-NEW tag is assignable while the listed works are unread. REPORT.md's Literature section is replaced to match: it corrects the Rueppel comparison (G_clk's step is selected by the visible parity bit, which the observer's action modifies; Rueppel's by the register state) and the Agievich-Solovey description (a restatement, not a confirmation), and states PE-01's contribution as a verified bounded counterexample under its declared model, with no new cryptanalytic technique claimed. Verdicts, measurements and the A2 mechanical tags are unchanged; nothing in results/ was re-run or edited. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Planning checkpoint for PE-02 (Issue #934): charged and uncharged observer tables, active against passive observers, clock ablation. Plan and notes only, with two design-only arithmetic checks (the polynomial rule for n > 8 reproduces PE-01's polynomials for n = 3-8; the footprint formulas). No code computing results; nothing run; no execution authorized. Independent plan review next. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

… not frozen) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Applies R1-R5, R7-R15, R6's reporting change and the UX cross-check of the independent plan review; CHANGES-r2.md maps each item. Owner decisions O1-O10 (including the stage name and the charge scope) are marked as placeholders with the review's recommendations. Design scripts replay byte for byte; no experiment run, no PE-01 cell recomputed. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…4-N7 nits) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

G_clkfix_u searched over its own theta = n+2 region (and the passive m = 3 caps raised to it); NOT_IN_SEARCH_RANGE status, and NO_WITNESS_IN_SCOPE only over a searched non-empty cell; dependent parameter values tagged with the decisions they assume, refused on mismatch, with each option's effect on the search ranges stated; O4b (the m = 0 cut) split out as its own owner placeholder; the linear class-code arithmetic for O3 added as a design script; nits N4-N7. All four design scripts replay byte for byte. Owner decisions O1-O10 and O4b remain open. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…ozen) Records the owner's approval (amaybaum, 2026-10-26) of all eleven decisions O1-O10 and O4b as recommended. P1 brings every option-dependent control under the stop-on-mismatch rule (24 dependent entries; TH emulation passes with no OPEN); P2 drops the stale status line; P3 fixes the schema identifiers. The O8 rename is held: "PE-04" already names the quantum-reconstruction stage in the thread README, so applying it would collide; an unused identifier is put to the owner. Design scripts replay byte for byte. Not frozen. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Owner decision O8 (amaybaum, 2026-10-26): "rename the new stage to PE-05. PE-04 remains reserved for quantum reconstruction." The stage directory moves to pe05_charged_tables_v1/; PLAN, NOTES, CHANGES and the design scripts' header docstrings name the stage PE-05; the parameters block records O8 = PE-05. The thread README gains a PE-05 entry after PE-04. Retained review files are byte-unchanged; review/README.md maps their old paths. Verbatim owner quotes and the other stage named PE-02 are untouched, and the fixed identifiers (pe02-shard/1, ...) are unchanged. Checks: the four design scripts replay their committed outputs byte for byte from the new path; the TH emulation passes (11 decisions, 24 dependent entries, no OPEN value). No experiment was run. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

The independent confirmation of 7b46918 is ACCEPT WITH NITS. This commit applies them: - C1: the PE-05 README entry moves to the end of the thread README, so lines 1-277 stay byte-identical and PE-01's frozen line citations still resolve at the head. - C2: status lines are timeless; no freeze SHA is written into the files. - C3: the owner's "exact-version checks" are applied in both readings: a fixed PE05_env (Python 3.12, numpy 2.2.6, ubuntu-24.04 x86_64) that TH and collect enforce, and a freeze record naming the exact commit and the digests of PLAN, NOTES and the parameters block. - C4: owner quotations are verbatim; summaries are marked as such. - C5: CHANGES-r3 records #934's retitle. The design scripts replay byte-identically, and both TH emulations pass. No experiment was run. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

…e candidate) The confirmation of 7736a1c found the C3 environment pin inconsistent: - E1: one rule everywhere. Result mode refuses unless Python is 3.12, numpy is 2.2.6, ImageOS is ubuntu24 and RUNNER_ARCH is X64. ImageVersion and sys.version are recorded, never compared. - E2: ENV applies in result mode only. Smoke and test runs record the environment and are never results. - E3: the stdlib-plus-numpy claim becomes checkpoint IMP. Each shard records its non-stdlib top-level modules, excluding __main__ and the stage's own package; collect refuses a result shard unless the set is exactly {numpy}. The owner's O8 table row is quoted as its two cells. CHANGES-r3 is headed "Change log (r3)". The design replay is byte-identical, both TH emulations pass, and README lines 1-277 are unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

The confirmation of d6fc056 recommended IMP-1: interpreter startup (site, .pth files, sitecustomize) can load non-stdlib modules that -I does not prevent. IMP now measures only the top-level names added after a snapshot taken at the entry module's first statement, still excluding __main__ and the stage package. The startup set is recorded and never compared. Every loaded stage-package module must also lie inside the stage's code directory. In result mode, collect refuses a shard unless the measured set is exactly {numpy} and the location check passes. Typo fixed in PLAN 9. The design replay is byte-identical, both TH emulations pass, and README lines 1-277 are unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

Four confirmation reports (7b46918, 7736a1c, d6fc056, 7d90b32), the last CONFIRM FOR FREEZE at 7d90b32. Review records only; PLAN, NOTES and the parameters block are unchanged from 7d90b32. One local scratch path is redacted from the first report. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

amaybaum · 2026-10-26T20:25:30Z

PE-05 specification freeze record

The PE-05 specification is frozen at 7d90b3234093d95d62213d772dd3c3af318c66c0.

Authorization. The owner (amaybaum, 2026-10-26) said "Proceed with freeze at 7d90b32 only if CI and the independent confirmation pass on that exact commit. No experiments authorized." Earlier the same day: "Approved: rename the new stage to PE-05. … This authorizes the specification freeze, not experimental execution." No experiment, run or dispatch is authorized.

Frozen object

Path: verification/programmes/oi-qm/reconstruction/oi-pseudoentropy-20261025/pe05_charged_tables_v1/ at 7d90b323.

Object	Identifier
`PLAN.md`	sha256 `dedd129a48e53935410f0b6f428f30aed40b809526f6e1aa422baff869ca7022`
`NOTES.md`	sha256 `cfddbdcf51e7261c8f1ba8d2a5e214fb723cd78deca9180375eca2042630841a`
`pe02-parameters` block, from after the opening fence line to the closing fence	7412 bytes, sha256 `d89d3ce49c865ec31e44ff7554008fb4ce5355f0297a7d8fb8938f758ecc3a96`
stage directory	git tree `fe71fe7aaf813a3e09f9efa2d85d3eaa6e7de01e`

The pe02-parameters tag is a fixed identifier, kept through the rename.

Exact-version checks. Both readings of the owner's condition are applied:

(a) A pinned result-mode environment, PE05_env: Python 3.12, numpy 2.2.6, ImageOS ubuntu24, RUNNER_ARCH X64. TH and collect enforce it.
(b) This record names the exact commit and the digests above.

Independent confirmation. The final verdict is CONFIRM FOR FREEZE at 7d90b323, with no remaining findings. It covers:

P1–P3;
the rename;
the frozen PE-01 references: PE-01's trees are unchanged since a611f943, and README lines 1–277 are byte-identical, so every historical line citation resolves;
the digests;
the reviewer's TH emulation, which passes.

The four confirmations are retained in review/CONFIRM-*.md at cd406481. That commit adds review records only; the frozen files are unchanged.

CI. Run 40393320363 on head 7d90b323 is green: 25 checks pass and 1 placeholder job is skipped. It is a pull-request run, which tests the merge with main b64919cd. main does not touch the thread directory between the branch's base c37700ad and b64919cd, so the frozen files are identical in the tested tree. No exact-head workflow_dispatch run was made, because a dispatch needs separate authorization.

After this freeze

PLAN, NOTES and the parameters block do not change. Any change is an amendment with its own independent review.
The code commits that implement the specification come next. They are verified against it.
Execution needs separate owner authorization.

Generated by Claude Code

amaybaum · 2026-11-04T10:48:01Z

Closing without merging (§A.43 item 6; PR-AUDIT-1, #1088)

Owner decision (amaybaum, Claude Code session chat, 2026-11-04):

I approve the #923 disposition, with option (a), inclusion of A1–A3, and conditional authorization to close #923 without merging.

This is an administrative retirement, not a scientific adoption. Nothing on this branch is adopted by closing it, and no claim is promoted or reclassified. The PE-01 evidence has not landed on main. Until the separate landing PR merges, the evidence supporting book/ch18-beyond.md:106 is on this branch only.

The PR description is superseded. It names head 85096e3f, the PE-01 preregistration. The live head is cd4064818fe2cff1ee4b147a9761ed157bcf990c, and the comments above record the work since then.

Retained.

Branch research/oi-pseudoentropy-20261025 at cd4064818fe2cff1ee4b147a9761ed157bcf990c, and refs/pull/923/head.
Nothing is deleted, and every SHA cited on this PR stays resolvable.

Where each part now lives.

Part	Home
ch18:114 correction	On `main`: #933, merge `687e885b` (`book/ch18-beyond.md:106`, FULL:4919)
PE-01 evidence supporting that sentence (§A.42): 16 records (A1–A3 included) plus a replay pin, option (a)	Accountable Issue: #1088, comment 6628737033. Work: a separate landing PR, to be prepared and independently reviewed; merging it needs the owner's explicit approval
PE-01 full run, shards and code	This branch (provenance; needed for PE-05)
PE-05 frozen specification (`7d90b323`), its freeze record, the exact-commit CI caveat, and its execution dependencies	#934, comment 6628747635
#933 nit N3 (ch18:106, 10⁻³²)	#1028, comment 6628749107
PE-02 (computational versus physical), PE-03, PE-04, milestone 1	#1092
OI-PE-1 coordination with NP-AVG-1, and the PE-02 → PE-05 label correction	#929, comment 6628749955
OI↔QM gate	#914: no direct row, no change

Recorded as not needing a home. PE-01 code-review nits N17 and N18 (review/code/REVIEW.md:665–672). The reviewer marked both as not needed before dispatch, and the run completed with a non-INCOMPLETE verdict.

Authority. This closure authorizes no execution, dispatch, F/E designation or merge.

Generated by Claude Code

claude added 6 commits October 25, 2026 15:37

amaybaum mentioned this pull request Oct 25, 2026

States and dynamics: exactness, sourcing and finite-approximation audit (research record) #911

Merged

claude added 11 commits October 25, 2026 18:33

claude added 6 commits October 25, 2026 21:42

claude added 4 commits October 25, 2026 22:53

amaybaum mentioned this pull request Oct 26, 2026

ch18: scope the unpredictability sentence to what PE-01 leaves standing #933

Merged

amaybaum mentioned this pull request Oct 26, 2026

PE-05: separate active from passive observers and charged from uncharged lookup tables (OI-PE-1 follow-up) #934

Open

claude added 13 commits October 26, 2026 08:18

research: PE-02 plan independent review (ACCEPT WITH CHANGES, R1-R15;…

2bb45e0

… not frozen) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

research: PE-02 plan r2 re-review (REVISE narrowly: N1-N3 required, N…

5b2ae24

…4-N7 nits) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

research: PE-02 plan r3 re-check (ACCEPT WITH NITS: P1-P3)

7a283d3

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

amaybaum closed this Nov 4, 2026

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OI-PE-1: pseudoentropy, deterministic randomness and observer access (research plan) - #923

OI-PE-1: pseudoentropy, deterministic randomness and observer access (research plan)#923
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PE-01 frozen preregistration

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Baseline already settled in the corpus (not restated as new)

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PE-05 specification freeze record

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