# ET-8b — Accumulation: the loop, its gates and its readings (pre-registration)

*Registered 2026-09-19 (this commit is the timestamp). 8a §9 established why accumulation could not be tested on a
single fixed decision: the second generation's training states were byte-identical to the first's. 8b builds the
loop in which the prior's earlier choices shape the states it later reads, and asks whether a second generation,
trained on states its parent produced, beats its parent at held capability. It also carries the bridge to VII: does
the gain survive when the history is unverified?*

## 1. The loop

Episode = inspect → **decision 1** (head or base picks region × family) → patch → run tests → if red, inspect the
new state → **decision 2** → patch → run → if red, **decision 3** → patch → run. Up to three head decisions per
episode; the state at decision k depends on the choices at decisions < k. Same v3 task family, verifier, budget
accounting, per-problem logging and trajectory persistence as 8a. A budget in the prompt makes each budget a
different agent; the loop agent is a new agent and is compared only with itself.

## 2. Gates, in order, each with a number fixed now

- **G1 task gate** on the task draw used: distinct problems ≥ 0.9 of episodes (8a rule).
- **G2 prompt gate at EVERY decision the head touches:** distinct decision prompts / episodes ≥ 0.9 at decision 1,
  2 and 3 separately. A decision point that fails is not scored.
- **G3 state-dependence gate (the P9 failure, tested first):** run the base loop and the gen0-head loop on the same
  300; at decision 2, the fraction of episodes whose state differs between the two arms must be ≥ 0.30. Below
  that there is nothing to accumulate on and 8b reports that as its result.
- **G4 a base of its own:** the base-loop agent, no head, 300 episodes, same budget; every comparison is paired
  against it. The 8a single-decision numbers are never reused as this base.

## 3. Generations

- **gen0:** head fitted (layer 18, L-BFGS, read-only, 8a recipe) on the base-loop's verified history at all
  three decision points, one head per decision point or one shared head — chosen by held-out probe accuracy on
  base-loop states BEFORE any loop run, and fixed.
- **gen1:** head fitted on the states the gen0-head loop produced, with the verifier's outcomes. Same recipe, same
  three probe controls (permutation ×5, PCA-8, n=100 ×5 draws).
- **gen1-unverified (the VII bridge), defined 2026-09-20 after the first definition was found to name the verifier under
  another name (`agent_claims_pass` is the test verdict):** the label is an OFFLINE SELF-ASSESSMENT — for each patch step
  of the cross-fitted gen0 trajectories, the state is replayed and the frozen model is asked whether the tests now pass,
  with the verifier's answer withheld; the head is fitted on the same states with that yes/no as the label. The rollouts
  are untouched, so "everything else identical" holds exactly. A second arm, **gen1-self-stopped** — a rollout in which the
  verdict is never fed back and the agent stops on its own belief — is registered as OPTIONAL: it measures the arm and the
  changed rollout together, and if run it is read only beside the first, never instead of it.
- **Cross-fitting rule (added 2026-09-20, after gen0's memorised training trajectories contaminated gen1's fit):** every
  generation's trajectories used as a later generation's training data are produced under k-fold cross-fitting, so no
  episode is steered by a head that saw its task; each head file carries its training range and the chain refuses to
  launch a fold whose head overlaps it. A withdrawn number does not clean a corpus; the corpus is regenerated.

## 4. Readings, written before the runs

All on an independent 300, paired, exact test, interval reported; capability = problems solved at the loop
budget; cost = total tokens with head inference counted; the matched-compute point reported as in 8a §7.6.

| result | reading |
|---|---|
| gen1 > gen0, interval excludes zero, at ≤ gen0's cost | **accumulation** — the frontier moved twice; 8b's claim |
| gen1 ≈ gen0 (interval contains zero) with gen0 > base | **one-shot** — experience moves the frontier once and stops; the series says so |
| gen1 < gen0, interval excludes zero | **dogma** — the prior's own choices narrowed what it later learned from; reported at full prominence |
| gen1-unverified ≈ gen1 | the verifier's bits were not what carried the gain; VII's bound is NOT what limits accumulation here |
| gen1-unverified ≈ gen0 or < gen0 while gen1 > gen0 | **the external bits are the gain** — VII's Internal-Improvement Bound observed inside 8b |
| G3 fails | nothing to accumulate at this budget; 8b reports the state-dependence fraction and stops |

Selection rules fixed now: no budget ladder; the loop budget is 12 model actions total across the three decisions;
no re-fit after seeing the independent set; exclusions as line items.

## 5. Cost

Harness 2 days. Base loop 300 ≈ 4 h. gen0 fit + 300 ≈ 5 h. gen1 fit + 300 ≈ 5 h. Bridge arm ≈ 5 h. One box, one
week, after 8a's R7.

## 6. Record, 2026-09-21

- gen0 (single fit, tasks < 226) on held-out 75: +17.3 [+5.3, +29.3]. Its training trajectories were memorised (true region
  found at decision 1 on 100% of training tasks) and contaminated gen1's first fit; that arm read −12.0 vs gen0 and is
  recorded as the defect's signature, not as accumulation.
- Cross-fitted gen0 (3-fold, head on 150 tasks each) on all 225: +18.7 [+12.9, +24.9], p 3×10⁻⁹ — a lower bound on the
  full head, reported as its own arm.
- gen1 (fitted on cross-fitted gen0 trajectories) on held-out 75: vs gen0 −2.7 [−12.0, +6.7], p 0.77; vs base +14.7
  [+2.7, +26.7]. Interval 18.7 points wide at n = 75: consistent with one-shot and with an increment it cannot see. NOT
  filed as §4's one-shot. The independent 300 decides (running).
- gen1-unverified: closed by its precondition. The frozen model's own judgment of success is a constant — 0 of 568 patch
  points called "pass", including all 83 that passed; agreement with the verifier 85.4% = the base rate of failure; four
  prompt wordings × two temperatures, said-pass never above 3.3%. No positive class, no head. Reading, bounded to one
  model and one setting: there are no internal bits about success to improve on — VII's Internal-Improvement Bound
  observed one level earlier than the arm built to test it. The optional self-stopped arm is not run: an agent that never
  believes it has succeeded never stops.

## 7. Accumulation, measured 2026-09-21 — and gen2 pre-registered before it runs

**Result.** On two independent 300s, reported seed by seed and not pooled: gen1 vs gen0 +5.7 [+0.7, +10.7], p 0.040
(seed 73) and +9.7 [+4.7, +15.0], p 0.0004 (seed 47); model tokens per episode +0.1% and −3.0%; controller cost
identical by construction. §4 row 1 fires: the frontier moved twice. gen0 vs base +13.7 / +13.0; gen1 vs base +19.3 /
+22.7. The n = 75 screen had read −2.7 [−12.0, +6.7]; both 300s lie inside or at the edge of that interval — an
underpowered screen, not a contradiction — and it was not filed as one-shot because the reading note fixed that before
the number existed. Bounds: one model, one environment family, gen1's heads fitted on fewer rows than gen0's (2,824 vs
4,052), so the comparison is conservative and not matched-data. Instrument by hash: model, three task-set signatures,
six head md5s, disjointness measured zero. One-command reproduction: `experience/reproduce_8b_accumulation.sh`, both
gates exercised by making them fail.

**gen2, registered now (this commit precedes the run).** gen1 trajectories on tasks 1–225, 3-fold cross-fitted (no
episode steered by a head that saw its task); gen2 heads fitted on them with the same recipe and controls; gen2 run
on both independent 300s, paired vs gen1, vs gen0, vs base; cost condition as §4. Readings, fixed before the run:

| result | reading |
|---|---|
| gen2 > gen1 on both seeds, intervals excluding zero, at ≤ gen1's cost | accumulation continues; the series asks in VIII-b's paper what bounds it |
| gen2 ≈ gen1 (intervals contain zero) on both | the loop reaches a plateau at generation 1 — reported as such, with the verifier's ceiling named as the candidate bound |
| gen2 < gen1, interval excluding zero | consumption: a head steering the search removes the signal its successor needs; reported at full prominence with the already-found-at-decision-1 fraction printed beside it |
| seeds disagree in direction | the disagreement is the result; no pooling |

No gen3 without a ruling; VIII-b's experimental package closes after gen2 whichever way it falls, and the paper is
written backward from there.

**E5 under amendment 2.** The arm asks whether a specific person's stated preferences transfer. With a model rater
there is no person unless the author supplies the K preferences. Ruled 2026-09-21: E5 is PARKED unless the author
writes K statements of his own poetic preference; the version that elicits the judge's own preferences is not run,
because it measures a model learning a model, not the registered question.

## 8. gen2, measured 2026-09-21 16:35Z — accumulation stops at generation 1

Seed by seed, not pooled: gen2 vs gen1 −2.0 [−6.3, +2.3], p 0.44 (seed 73); −7.0 [−11.0, −3.0], p 0.0015 (seed 47).
Cost flat (−0.2%, +0.4%). gen2 vs base +17.3 / +15.7 — between gen0 and gen1 on both. §7's plateau row fires on one
seed and its consumption row on the other; the fourth row does not fire, since both estimates are negative and the
intervals overlap on [−6.3, −3.0]. **Ruling (2026-09-21 17:1xZ):** the paper reports both rows as they fired, per
seed, and the sentence established on both is: *a third generation does not improve on the second; on one seed it is
significantly worse; the series' best head is generation 1.* The consumption mechanism is reported as consistent, not
demonstrated: the d1 and d2 heads are byte-identical between gen1 and gen2, so the whole difference is the d3 head,
which learned from trajectories where the region was already found by decision 3 in 48.8% of surviving episodes
(41.5% for gen1's). One moved point is not a mechanism. A gen3 would be empty by construction — the loop has three
decisions and gen2 moved the last — independently of the stop rule. **VIII-b's experimental package is closed.**
The frontier moved twice — base → gen0 → gen1 — and did not move a third time on this loop; the paper is written
backward from that sentence.

## 9. Pre-registered 2026-09-21 18:1xZ — the loop base at the generations' compute

The loop's generations spend about 30% more model tokens per episode than the loop base (≈3,800 vs ≈2,950). The
accumulation limb (gen1 vs gen0) is equal-cost by construction and needs no control; the loop's gain over base does.
Arm: on each independent seed, a small ladder of base action budgets on slice 1, the budget whose mean tokens per
episode is nearest 3,800 chosen by absolute distance before the ladder is read, then that budget on the full 300,
paired against gen0 and gen1. Readings: base-matched below gen0 by more than the interval → the loop's gain is
experience, not compute; base-matched ≈ gen0 → generation 0's gain was bought with compute and only the gen1-vs-gen0
increment stands as the frontier claim. Printed either way.

**Outcome (2026-09-21 19:1xZ): the arm is unbuildable, and that is the finding.** The action budget does not bind on the
loop — base tokens per episode are flat from budget 14 to 24 (≈2,880 and ≈2,930 on the two seeds) because the
three-decision cap ends the episode first; the selection rule then chose on noise (budget 14 on one seed, 20 on the
other). The generations' extra compute is endogenous: fewer actions (7.7 vs 8.2) at 37% more tokens per action,
because the head's choice of where to look lengthens the context the agent carries. It cannot be matched with a knob,
and a base with a raised decision cap or a forced-inspect policy is a different agent. VIII-b therefore reports the
loop's gain over its base with the per-action decomposition and does not claim it as a frontier shift; the
accumulation claim (gen1 over gen0) is at equal cost by construction and stands on its own.