probe(D-TGA-5): squash the chain of origin into the most-updated lane, gated on contradiction; blame survives

.claude/board/FRUITS.md

@@ -4,7 +4,7 @@ Generated by `.claude/tools/fruits_index.py --write`. Do not hand-edit:
 add or change a `**Fruit:**` line on the ledger row and regenerate.
 CI fails when this file is stale.
 
-Open: 24. Closed: 1.
+Open: 25. Closed: 1.
 
 ## discovery torque
 
@@ -14,6 +14,7 @@ _none open_
 
 | tier | row | status | ledger |
 |---|---|---|---|
+| High-signal | 2026-10-23 — A certificate replaces the deltas: lane 0 keeps the delta, a receipt or seal, and in time a proof reference — never the operations | Open. | `IDEAS.md` |
 | High-signal | 2026-10-23 — Lumpability as the closure check: a palette composes under an operation only if its cells are lumpable for it, and purity measures that | Open | `IDEAS.md` |
 | High-signal | 2026-10-23 — One replay that checks proof, receipt and commit witness together | Open. | `IDEAS.md` |
 | High-signal | 2026-10-23 — OGAR #357's first kill test (TLAC-P01) is now buildable from real guards | Open. | `IDEAS.md` |

.claude/board/IDEAS.md

@@ -87,6 +87,120 @@ Agents filter by `@`-mention or domain to see what's theirs.
 
 (Prepend new ideas here with today's date. Format:)
 
+## 2026-10-23 — A certificate replaces the deltas: lane 0 keeps the delta, a receipt or seal, and in time a proof reference — never the operations
+
+`[P1 @thought-struct-scribe @truth-architect domain:thought-git D-TGA-5 D-TGB-4 D-TGB-7 D-DRMC D-CGW-4]`
+
+Operator direction (provenance): lane 0 is main, 1..63 are thoughts, and each
+lane may run on the order of 10^6 operations. Written with session 01G22yT6's
+mapping (EXO-50, 2026-10-23).
+
+**Storage arithmetic, not a measurement.** 64 lanes × 10^6 operations is
+6.4·10^7 deltas per cycle: 1–2 GB at 16–32 bytes each, or 33 GB at 512-byte
+rows. A few cycles a minute reaches terabytes within hours. A receipt per
+landed thought is about 64 × ~100 bytes per cycle. So deltas stay in RAM and
+die at squash; only the squashed delta, receipts and seals reach disk.
+
+**What exists.**
+- **D-TGB-4** (#1674, EXO-58 done) replaces history with a receipt. It
+  proves only the replay half, not admissibility.
+- **egglog** checks a proof for every admissible solution.
+- **DR64** refuses every recipe with `NoCertifiedCompiler`. That is the
+  certified-compiler-boundary row below, and its scope is the operator's call.
+- **The joint replay** (proof + receipt + lane read) is the 2026-10-23 IDEAS
+  row below.
+- **The causal verdict** is computed (`pearl.rs:259`) but promotes nothing
+  (ISS-D-CGW-4-PROMOTION-GATE).
+
+**The rungs.**
+1. **The gate:** squash every chain of origin into the most-updated lane,
+   refusing on contradiction or divergence, with blame kept over lanes.
+   MEASURED in `entries/2026-10-23-d-tga-5-squash-gate-preregistration.md`:
+   landing the squash equals landing the finals, and the delta stays N
+   cells while the history grows k·N. Update count is activity, not
+   insight, so the target choice is only a tie-free rule. Correctness comes
+   from the gate.
+2. **The determinism falsifier** (01G22yT6). The receipt replaces the
+   history only if every lane is deterministic given its seeds. Inject one
+   nondeterministic read (an outside read, thread timing) into the D-TGB-4
+   replay test. The replay must refuse, not reproduce different writes
+   silently.
+3. **Promotion at squash time.** CE64 bits 59..63 advance (correlation →
+   causality, MUL-calibrated rather than overconfident) only when the
+   squash is contradiction-free and blame shows independent lanes
+   (EXO-138's stamp condition).
+4. **Compiled thought.** An egglog / eggcc certificate replaces the order
+   list. Lane 0 then stores the delta plus a seal that points at the
+   certificate, and a certified thought is reusable by reference.
+
+**Outside grounding: the accumulation as a large Markov chain** (operator,
+2026-10-23). Source: Bittracher & Schütte, "A probabilistic algorithm for
+aggregating vastly undersampled large Markov chains", *Physica D* 416
+(2021) 132799,
+https://publications.imp.fu-berlin.de/2614/1/1-s2.0-S016727891930764X-main.pdf.
+The grades are per claim.
+
+- **[G] within the paper's assumptions (Def. 2.1, Lemma 2.3).**
+  - *Lumpable*: the probability of moving into an aggregate depends only on
+    the starting state's aggregate.
+  - *Deflatable*: within an aggregate, the end state is drawn independently
+    of where the chain came from.
+  - A chain that is both is *aggregatable*. Its N×N matrix then has exactly
+    R distinct columns, so it has rank R, and it equals
+    `P = Π · P̂ · Λ`.
+- **[G] (Alg. 3.1, Eq. 18).**
+  - Sample J columns, take an SVD and read the aggregates off the sign
+    pattern of the leading R left singular vectors (spectral clustering,
+    PCCA+ or SEBA).
+  - J depends only on R and the confidence p, never on N. With equal-sized
+    aggregates, recomputed here: R = 8 needs J = 51 for p = 0.99, R = 10
+    needs J = 66, and R = 16 needs J = 115.
+- **[G] (Prop. 3.9, Thm. 2.10).**
+  - The reduced matrix is recovered from the sampled columns alone:
+    `P̂ = Λ · P_K · Λᵀ_K · K⁻¹`.
+  - For an ε-almost aggregatable P, the L1 error is ≤ 4ε, also independent
+    of N.
+- **[H] mapping to thought-git.**
+  - The 64 × 10^6 operations are the trajectory of one large chain over
+    cell states. Each lane's run is an expensive sample from its starting
+    state.
+  - A knowledge-preserving squash is an aggregation. Lane 0 would store the
+    partition Ω, the R×R matrix P̂ and the in-aggregate distributions π: the
+    certificate is P̂, not the operations.
+  - With the 63 thought lanes as J = 63 column samples, recomputed with
+    Eq. 18: R ≤ 10 aggregates are recovered with p ≥ 0.987, R = 12 with
+    0.951, and R = 16 with only 0.758.
+  - The 4ε bound gives the squash gate a quantitative tolerance where it now
+    has a yes/no refusal.
+- **[H] where the mapping can break.** Each item is a falsifier, not an
+  assumption.
+  1. The paper's chain is time-homogeneous. Thought lanes are not, and the
+     aggregated process is in general non-homogeneous (paper §2).
+  2. Lanes are chosen thoughts, not uniform independent column draws, so
+     Eq. 18's p does not hold for them as written.
+  3. Deflatability is a strong extra condition, and nothing yet says
+     thought transitions satisfy it.
+  4. SVD / PCCA+ is a floating-point clustering step. It belongs only on the
+     cold, out-of-fold path (CLAUDE.md, the no-ms scoped exception), never
+     per query.
+- **Ties.** This is the stochastic form of EXO-132's lumpability, the
+  distinction GPT /08 asked for: almost-lumpability in L1, not deterministic
+  congruence.
+- ⊘ **Superseded 2026-10-23 (same day).** DECISION (operator): the substrate
+  is not probabilistic; a probabilistic model is a counterfactual that the
+  egglog/eggcc compiler must certify. The certificate is a checked proof, not
+  P̂, and the 64 × 10^6 folds are compilation material, not samples. The block
+  above is kept as the record of a withdrawn framing; see
+  `entries/2026-10-23-coresearch-thought-git-markov.md` § Correction.
+
+**Next probe:** rung 2, which is cheapest and guards the whole storage
+argument. **Kill:** a lane that is deterministic given its seeds cannot be
+defined for the planned writers (outside reads are essential). In that case
+receipts cannot replace deltas, and the arithmetic above stands against the
+design.
+
+**Fruit:** High-signal
+**Status:** Open.
 ## 2026-10-23 — Lumpability as the closure check: a palette composes under an operation only if its cells are lumpable for it, and purity measures that
 
 `[P2 @palette-engineer @truth-architect domain:codec/palette]`

.claude/board/STATUS_BOARD.md

@@ -385,7 +385,7 @@ Plan: `.claude/plans/ce64-hypothesis-layers-v1.md`. Plateau: `.claude/knowledge/
 | **D-TGA-2** | Read plane R and status | Queued | a read outside R is never reported stale |
 | **D-TGA-3** | rebase (four masks, no data moved) | Queued | rebase-then-squash == from-scratch re-run on v+1, including a deletion in main (retract then re-derive); disables: no stale re-run, no conflict check, no retraction |
 | **D-TGA-4** | land through the revision gate into the next Lance version (D-HL-8) | Queued | landing a thought that is behind is refused |
-| **D-TGA-5** | squash_into (partial squash) and blame | Queued | blame returns original sources after slot reuse |
+| **D-TGA-5** | squash_into (partial squash) and blame | In PR (lab precursor: `crates/thought-git-probe/tests/squash_gate.rs`, `entries/2026-10-23-d-tga-5-squash-gate-preregistration.md`; most-updated target, contradiction/divergence gate, blame over lanes, 5 disables red) | blame returns original sources after slot reuse (slot reuse not yet covered) |
 | **D-TGA-6** | MergeQueue | Queued | independent thoughts == landed by hand in FIFO order; a thought reading another negated lands after it; a cycle through negation refused at enqueue |
 | **D-TGB-0** | thought git basics: fixtures per write-intention outcome, squash-stack and anomaly fixtures, absent-not-zero fixture, from-scratch oracle (`thought-git-basics-v1.md`) | Shipped (lab, #1630; probe `crates/thought-git-probe`, 19 tests; `PREREGISTRATION.md`) | 5 oracle disables verified red-then-green; every signal has a can-fire and a can-stay-silent case on real contract code; the pearl half on edges moves to D-TGB-3 |
 | **D-TGB-1** | slot pool, autonomous: taken by `branch`, freed by `squash`/`discard`/`land` (the write is the Rubicon decision, 2026-10-20) | Shipped (lab, #1630/#1631; `crates/thought-git-probe/src/slots.rs`). Slot pool only: no production land, rebase or persistence (D-TGB-2..5 Queued) | at 63 taken `branch` picks a FIFO or least-used candidate, squashes it along its dependency chain if it has one, else evicts it (DECISIONS 2026-10-20; was: squash unremarkable first, else refuse); stale handles refused; 6 tests |

.claude/board/entries/2026-10-23-coresearch-thought-git-markov.md

@@ -0,0 +1,114 @@
+# Coresearch 2026-10-23: thought-git accumulation as a large Markov chain
+
+**Status:** exploration map. Nothing is adopted; the operator chooses.
+**Question (operator):** "Consider that giant thought-git accumulation as a large Markov chain."
+Sources: Bittracher & Schütte, *Physica D* 416 (2021) 132799, read in full;
+Askarian, Xu & Faragó, *Algorithms* 9(3):50 (2016), arXiv 1809.06564, read in full.
+
+## Frame (what the scouts established)
+
+- **F1.** A version is a deterministic function of the givens, the prior
+  version and the landing thought set (`oracle.rs:46-108`, verified in code).
+  Thought-git is therefore a transducer, or a Markov decision process; it is a
+  Markov chain only once the policy that chooses thoughts is fixed.
+- **F2.** No ruling grants the Markov property to lane accumulation.
+  E-SUBSTRATE-1 covers bundles and E-MARKOV-TEMPORAL-STREAM-1 covers stream
+  order. Last-writer replace is neither, and the seal is an order-dependent
+  fold (`seal-vs-temporal-ordering-information.md`).
+- **F3.** Lanes are measured not independent: they share the manuscript, the
+  tokenizer and the model (`ISSUES.md:3852`).
+- **F4.** No code in `crates/` estimates transition probabilities, tests
+  lumpability or bounds an aggregation error. The search space was a closed
+  `git grep`; ndarray/hpc was not searched.
+- **F5.** Two earlier rejections apply here.
+  - #1703: a replay capsule is not proof authority, and population evidence
+    only nominates.
+  - TORQUE T-2026-10-23-1 (killed): a learned PaletteLut aggregation did not
+    compose.
+
+## Where the papers stop applying
+
+- **B&S Algorithm 3.1.** It needs a restart from any state to draw a column.
+  A trajectory log cannot do that. Trajectory-only estimation needs about
+  p·r samples (Zhu et al., arXiv 1907.00113, Thm 3, section-read), so "J
+  independent of N" does not transfer [S]. It also requires homogeneity
+  (fails per F1) and independent samples (fail per F3).
+- **AXF Theorem 2.** It needs an irreducible, aperiodic chain. Accumulation
+  over versions is a transient DAG with no recurrence, so the theorem does
+  not apply.
+- **What survives** without the Markov property and without independence:
+  - min/max L/U bounds over counts (AXF Def. 3);
+  - deterministic congruence found by partition refinement;
+  - the type split: certificate (replay + seal) versus model.
+
+## Exploration map
+
+| idea | verdict | why / probe |
+|---|---|---|
+| Squash folds only committed writes | **ADOPT-NOW, done** | Found by the falsifier: `Lane::final_state` folded Prune/Veto/Plan writes. Fixed in #1736 with P8 (red before the fix, green after; disable D6 turns only P8 red). |
+| D: squash equals chain for every later read | PROBE (S) | Fixtures: (b) contradiction then rewrite; (c) intermediate divergence then agreement; (d) the same value 3× vs 1×. Predicted: the intermediate contradiction and divergence records, and the multiplicity, are lost. Decide whether that loss is acceptable before building a certificate on the squash. Silent twin: `clean_lanes`. |
+| D-59..63: the squash preserves the epistemic promotion | PROBE (S), blocked | The promotion reader must be pinned first. Blame is a lane bitmask, not a count, so a multiplicity-reading promotion breaks. |
+| I3: counted ε-spread L/U gate | PROBE (M) | Bridge: R2 is ε = 0 with a point mass per lane. Count lanes per (cell, value class) from the blame bitmask; refuse when U−L > ε by integer cross-multiplication. With ε = 0 it must reproduce R2 (the p2/p4 tests). It is a BOUND only when the counts are exhaustive; otherwise it is an empirical interval, a gate annotation and never proof authority. |
+| I7: coarsest congruence by partition refinement | PROBE (S–M) | Integer, cold. It supplies I3's blocks. Kill if the reduction is below 2× on real traces. |
+| F1: is the process Markov at all, over a chosen state space | PROBE (M), needs real traces | First the revisit rate: below 1% means untestable on that state space, so coarsen. Then an order-1 vs order-2 contingency test against a Jirak band; kill if more than 10% of states differ. A synthetic policy decides the answer in advance, so it does not count. |
+| F3: lane independence after conditioning on shared inputs | PROBE (M), needs real traces | Conditional mutual information against a time-shuffled null. Precondition for any cross-lane convergence gate. |
+| I12/I13: lossless op-log encoding, tags plus cleanup | PROBE (S) | Use Lance's own column encodings and version tags; no parallel store. This answers the terabyte concern without any Markov assumption. |
+| I2 P = Π P̂ Λ; I5 defect; I6 interval propagation; I10 Chapman-Kolmogorov; I11 VAMP; I16 MarkovTripletState | PARK | Each needs F1 to pass (homogeneity) or the dormant VAMPE+Jirak track. All are cold-path and report-only. |
+| I1 J-column SVD; I4 AXF convergence; I14 Nova IVC | SKIP | I1: no restart oracle and dependent lanes. I4: transient DAG. I14: licence unknown, far outside the ns law. |
+| I8 causal state; I9 certificate vs model | ALREADY-HAVE | `final_state()` is the causal state of a deterministic lane; replay plus seal is the certificate. |
+
+## Head selection (operator follow-up)
+
+Recency is not the criterion. The gate-grade parts are subsumption (R1/R2)
+and the exact L/U spread. The others are not:
+
+- cross-lane convergence (R̂) presumes independent lanes, which F3 refutes;
+- stability (ρ) and predictive sufficiency are cold-path and report-only.
+
+## Not searched
+
+- ndarray/hpc (clam_compress, cam_pq);
+- GOLDSTAUB, identity-temporal-evidence-primer, holographic-temporal-access-projection;
+- the IDEAS joint-replay row;
+- Buchholz and Franceschinis-Muntz bounding-aggregation papers (not located);
+- bisimulation metrics (abstract only).
+
+## ⊘ Correction 2026-10-23: the probabilistic premise was a category error
+
+DECISION (operator, 2026-10-23): the substrate is not probabilistic. SPO-FC
+being probabilistic today is legacy. Every probabilistic model counts as a
+**counterfactual** and must be certified by the egglog / eggcc reasoning
+compiler before anything rests on it. The 64 lanes × ~10^6 folds run per
+second are the **material** a thought is compiled from, until it is a proof
+that later operations can call by reference. They are not a population to be
+aggregated statistically.
+SCOPE: this map and the IDEAS row "A certificate replaces the deltas" (its
+Markov block). BASIS: the operator's statement; consistent with F1 (versions
+are deterministic), #1703 (population evidence only nominates) and
+`dr-math-binding-probe` (`admit_recipe` ends in `NoCertifiedCompiler`).
+REVISIT WHEN: never on statistical grounds.
+
+What this changes in the map:
+- The Bittracher/Schütte and Askarian papers describe at most the **search
+  over counterfactuals**, never the admission and never the certificate.
+  All their rows (I1–I6, I10, I11) drop to PARK as counterfactual-layer
+  descriptions. The certificate/model split (I9) holds and is sharpened: the
+  certificate is a checked egglog proof, not a replay witness and not P̂.
+- The premise gate failed. Phase 0 split certificate from aggregation but
+  never asked whether the substrate is stochastic at all. F1 (versions are
+  deterministic) already said it is not; the brief should have stopped there.
+- Head selection: the head is the thought whose compiled proof is admitted.
+  The children's folds are the search trace. After admission they are
+  discarded, except the seal and the refuted branches the proof cites.
+- What actually blocks this: no certificate exists for DR64 (`dr-math-binding-probe`,
+  `NoCertifiedCompiler`). The open items there are a typed relational statement
+  language, egglog laws with checked proofs, and a lowering check. The candidate
+  first law is associativity of Boolean relation composition. `crates/egglog-r2il-probe`
+  holds the cold compile path; `.arxiv/2026-10_eggcc_effect_safe_extraction_statewalk_r2il_map.md`
+  holds the effect-safe extraction lesson.
+- Still valid: the P8 fix (only committed writes squash) and probe D
+  (squash = chain for every later read). Both are deterministic.
+
+## Closeout
+
+`coresearch | STATUS: open | OUTCOME: one defect fixed in #1736 (P8); probabilistic premise withdrawn (category error) | OPEN: DR64 certified compiler (typed statement language + checked egglog laws + lowering check); probe D; promotion reader unpinned`