jspace/results-loop/PROTOCOL_UNIFIED.md

Pre-registered protocol: unified adapter eval (written before any test numbers)

Date: 2026-07-13, after val@499, before step-799 completion. No test-set number for the unified adapter exists at time of writing.

1. Primary loop depth: k=2, for both tasks. Chosen on val CE with the tie-breaking rule: prefer the SMALLEST k whose hard-cell val CE is within 0.01 nats of the best k. (Current val: MBPP hard k2−k4 = 0.004, GSM hard k2−k4 = 0.006 → both ties → k=2.) The full k-curve is secondary/descriptive.

2. Checkpoint selection criterion (scalar, fixed now): mean of the two hard-cell val CEs at k=2, tasks weighted equally: crit = (gsm_hard_k2 + mbpp_hard_k2)/2. Lowest crit among saved checkpoints wins. (At writing: step 499, crit = (0.475+0.205)/2 = 0.340.)

3. Primary endpoints: (a) MBPP test pass@1 hard-bucket at k=2 vs k=0; (b) GSM8K test accuracy hard-bucket at k=2 vs k=0. McNemar, paired by item. Overall accuracy is secondary (known to be underpowered at n=250/256).

4. Same-harness rule: all k, INCLUDING k=0 baselines, measured by the prompt-only fast-path scripts (generate_frozen_prompt; k=0 = plain cached generate inside the same function). No numbers carried over from the full-position-loop harness.

5. Known missing control (not covered by this run): a same-size, no-recurrence adapter (h -> h + MLP(h) at the L13->L14 boundary, no loop, no band re-run) trained on identical data/objective. Until it exists, "the loop does the work (vs. 1.6M new weights anywhere doing it)" is NOT established. Queued as the next training run. Note the k=0 column is gated off by construction and is a sanity check only — it is not this control.

6. Symmetric interference check (missing): dedicated GSM8K prompt-only adapter as the reference for "unified costs GSM nothing". Queued. Until then the no-interference claim is one-directional (MBPP side only).

7. Band-location ablation (pre-registered 2026-07-13, before any arm ran). Arms, all else identical (adapter size/init, data, curriculum, k, scripts; MBPP): early L2-12, mid-narrow L17-27, late L24-34 (width-matched, 11 layers); shifted L6-22 (width-matched to the original 17). Reference: workspace L14-30 (already run, 3 seeds). Prediction: workspace-centered arms (L14-30, L17-27) exceed early/late on hard-bucket pass@1 at k=2-4 by a wide margin; shifted intermediate. Falsification: near-parity across arms demotes the lens claim from "locates where to loop" to "convenient discovery tool"; to be reported either way. Primary readout: hard-bucket pass@1 at k=4, e400 checkpoints throughout.

8. Language commitments for the writeup: the k0->k1 CE collapse (e.g. 4.36->0.18) is format/template learning expected from any trained adapter and must not be quoted as evidence of routing/planning; informative comparisons are within k>=1 cells only. Depth ordering k2 vs k4 deltas (0.001-0.006 nats) are inside checkpoint jitter and must be described as "k>=2 fits hard items equally well; k=1 slightly worse."

9. Anchor/entrance sweep (pre-registered 2026-07-14 ~03:00, before any arm ran). Arms: bands (13,30), (12,30), (11,30) — injection point shifted up from L14 at fixed tap L30; plus tap-23 = (14,23). All E2B/MBPP, same recipe, e400, primary readout hard-bucket pass@1 at k=4. Competing predictions: (a) "L14 special" (last full-attention KV-computing layer, lens boundary) → anchor-13 drops; (b) "KV-channel count" (anchors 11-13 add 1-3 extra KV-recomputing attention channels) → holds or improves. Body-length confound noted: earlier anchors lengthen the loop body; if results shift, run matched-length control (12,28) before interpreting.

10. L9 discriminator arm (pre-registered 2026-07-14 ~10:00, before running). Band (9,30): anchor at L9 — the only other full-attention, KV-computing layer below the boundary — deep in the lens's sensor regime, tap fixed at L30. Separates the two cliff explanations: (a) "lens boundary" predicts catastrophic (like anchors 11-13: 25-34% overall); (b) "full-attention KV-layer entry" predicts partial recovery (clearly above the L11-13 trend, i.e. >40% overall or hard >25%). Registered prediction: (a) — the sensor-region content dominates; layer type does not rescue it. Same recipe/checkpoint/eval as the anchor sweep (250 items, ks 0,2,4).

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Outcomes vs pre-registrations (scored 2026-07-14, after all arms completed)

1. k=2 primary depth — held. All primary comparisons reported at k=2; k-curves descriptive. k≥2 plateau confirmed (k=8 gen-eval flat).

2. Checkpoint criterion — applied as written for the unified adapter. Separately reported: val-CE is a poor proxy for generation accuracy; later arms therefore pre-committed to fixed steps (e400) instead.

3. Primary endpoints (unified adapter, k=2 vs k=0) — (a) MBPP hard 3.6% → 28.6% (direction as predicted); (b) GSM hard 0% → 6.3%, overall 10.5% → 9.0% (no overall win — the math boundary result). Both reported.

4. Same-harness rule — held throughout (all final tables fast-path, k=0 included).

5. Missing weights control — run: trained FF adapter = 17.9% hard, exactly the untrained-loop level. Loop-vs-weights gap established.

6. Symmetric interference check — run (dedicated GSM adapter); mixed-task training regressed both tasks; reported as negative result.

7. Band-location ablation — prediction CONFIRMED with a caveat: L14-30 hard 43.6% ≫ early L2-12 (23.6%, overall destroyed 22.8%) and shifted L6-22 (21.8%, overall 29.0%). Caveat discovered: L17-27 and L24-34 are structurally null (KV sharing; k>0 ≡ k=0 bit-identical), so the "mid-narrow beats late" half of the prediction was untestable at E2B; the 12B replication (no shared KV) carries that weight instead.

8. Language commitments — honored in PAPER.md (k0→k1 CE collapse not cited as planning evidence; k2-vs-k4 nats described as jitter).

9. Anchor/entrance sweep — prediction (a) "L14 special" CONFIRMED: anchor-13 hard 17.9%/overall 34.4%; 12: 28.6%/30.8%; 11: 25.0%/25.2%; monotone collapse below the boundary. Tap-23 arm died in training (never rerun); exits 27/30/32/34 within seed noise, so exit choice is free. Matched-length control not needed (results did not shift with body length in the informative direction).

10. L9 discriminator — registered prediction (a) CONFIRMED: band (9,30) overall 14.0-21.4%, hard ≤21.4% — catastrophic, like anchors 11-13, despite L9 being a full-attention KV-computing layer. The lens boundary, not layer type, gates the retrofit.

11. Recurrent-regime arm (pre-registered 2026-07-15, before training). Huginn-style retrofit on the frozen E2B band: RecurrentAdapter (learned A,B init α·I/(1−α)·I + zero-init MLP), h0 = norm-scaled noise, log-uniform random depth k∈[1,16], bptt=4, same data/steps/ checkpoint rule (e400 primary) as all merge arms. Eval ks 0,2,4,8,16,32 on the 250-item MBPP set. Competing predictions: (a) "amortization is intrinsic to frozen-band retrofits" → performance plateaus by k≈4 at or below the merge arm's level, no depth-monotone gain; (b) "fixed- point behavior was an artifact of our fixed-shallow-k training" (Huginn regime transfers) → monotone hard-bucket improvement past k=8 and reduced noise-seed sensitivity after training. Secondary readout: path independence (two noise seeds → output agreement rate) at e400. Known risk, stated in advance: 600 steps may be far too little for this regime (McLeish et al. use ~50B tokens); a null here bounds the cheap-retrofit budget only, not the regime.

12. Parcae-constrained recurrent arm (pre-registered 2026-07-15, before training; Prairie et al. 2026 parameterization). Same as item 11 but A = exp(−Δt·exp(a)) diagonal → ρ(A) < 1 by construction; init exactly the α=0.3 merge (verified bit-equal at init). ρ(A) logged every 10 steps in BOTH arms. Theory-derived predictions, stated in advance: (a) contraction ⇒ fixed point is a function of e ⇒ the Parcae arm SATURATES in k (no depth-monotone gain) and its converged performance is amortizable — if so, our deflationary result is a corollary of ρ<1, and our observed k≈3–4 convergence is the geometric rate 0.3^k; (b) the UNCONSTRAINED item-11 arm either drifts toward ρ≥1 (watch the ρ log: divergent runs should show ρ≥1 before loss spikes) or, if it gains monotone depth-performance, does so with ρ near 1 — the edge of stability is where genuine iteration must live. Either outcome formalizes "the anchor coefficient is the stability dial" as "the anchor coefficient is the spectral radius".

13. Per-depth adapter arm + free-ACT probe (pre-registered 2026-07-15, before training). (a) PerDepthAdapter: one merge adapter per iteration (n=4, Bae-style depth-wise relaxation at the entrance; breaks time-invariance — LTV, no fixed-point guarantee), standard curriculum, e400, eval ks 0,2,4,8. Prediction: lands at or below the distill/rung-2 amortization ceiling (~46% hard) because depth-indexed weights add content, not state-evolution; exceeding it would show per-iteration expressivity was binding and amend the deflationary claim. Depths >4 reuse adapter 4 (stated: k=8 cell is then fixed-point-like by construction). (b) Free-ACT probe on the standard merge arm: record per-item convergence depth (cos>0.9995) at k=8 cap. Predictions: accuracy unchanged vs fixed k (post-convergence no-ops); mean k_conv ≈ 3; hard-labeled items converge SLOWER than easy ones (adaptive compute allocates like ACT without any learned halting parameter).

--- Outcome, item 11 (scored 2026-07-15, k=16/32 cells cancelled by decision after k<=8): PREDICTION (a) SUBSTANTIALLY CONFIRMED, with one twist. The unconstrained arm left contraction immediately (rho(A): 0.3 -> 3.4 by step 100, plateau ~4.5) yet trained smoothly — per-iteration norm-matching converts magnitude explosion into directional churn, so "rho>=1 => divergence" becomes "rho>=1 => divergence OR stationary churn" under a norm projection. Consequences as predicted: substrate damage (easy 98.4 -> ~69% at all k>0, far exceeding any contractive arm's tax), val CE flat k=1..16 (stationary, not progressive), hard bucket at merge level (35.7/39.3/42.9% at k=2/4/8 — a one-item-per-depth-doubling crawl that at k=8 reaches what the contractive merge reaches at k=4, never approaching the amortization ceiling from above). 4x parameters bought nothing. Depth-monotone computation did not emerge at this budget.

14. Tied-alpha arm (pre-registered 2026-07-15, before training). TiedAlphaAdapter: x = (1−a)⊙e + a⊙ŝ + MLP([e;ŝ]), a = σ(â) per-dim learned, init a=0.3 everywhere (bit-equal to MergeAdapter at step 0, verified). B tied to (1−a): convex combination keeps the LTI fixed point on the e–ŝ segment (substrate-anchored by construction), ρ = max(a) < 1 guaranteed, +d≈1.5K params. Standard curriculum, s0 = band(e), e400, eval ks 0,2,4,8 on 250 items. This is the one untested cell combining parcae's learnable decay with the merge's anchoring. Predictions: (a) substrate fidelity preserved (easy ≈ merge's 88%, unlike both rec arms' ~70%) because anchoring, not ρ, controls fidelity; (b) hard-bucket at merge level (no significant gain — per-dim constant α is not where capability lives, per the adaptive-α E2B result); (c) learned a drifts slightly DOWN from 0.3 (as in parcae). If (a) holds while rec arms failed it, the fixed-point-location dial is causally isolated: same learnable-decay freedom, only the tie to (1−a) differs from parcae.

--- Outcome, item 12 (scored 2026-07-15): prediction (a) CONFIRMED in its dynamics half, REFUTED in its fidelity half — and the refutation is the finding. Dynamics: rho stayed in (0,1) throughout (0.300 -> 0.292, the optimizer drifting MORE contractive when confined to the stable region); loss trajectory as good as or better than the unconstrained arm at every checkpoint (the rec arm's flight to rho~4.5 was epiphenomenal — all fit lives in the MLP); eval saturates completely (hard 42.9/42.9/39.3/39.3/ 39.3 at k=2/4/8/16/32, easy flat ~71%). Fidelity: easy items were NOT preserved (71% vs the merge's 88.5%) despite guaranteed contraction — substrate fidelity is controlled by fixed-point LOCATION (anchored B + curriculum), not by rho. Conclusion: stability and fidelity are independent dials (fig_phase.png); the Parcae constraint delivers exactly what it promises (robust training, convergence, certified tail gradients) and exactly nothing more. Item 14 (tied-alpha) is the causal isolation of the fidelity dial.

15. Fidelity factorial + capacity control + seed (pre-registered 2026-07-15 ~03:15, before any of these arms ran; overnight batch). The fidelity loss of both rec arms (easy 88.5 -> ~71%) confounds three deltas from the winning merge: (i) learned B, (ii) random-depth training instead of the difficulty->depth curriculum, (iii) noise s0. Item 14 (tied-alpha) tests (i) with anchoring. New single-variable cells, everything else = standard merge recipe (fixed B, band(e) s0, curriculum, e400, eval ks 0,2,4,8 on 250 items): a. merge+randk — only (ii) changed (log-uniform k in [1,16], bptt 4). b. merge+noises0 — only (iii) changed. c. merge h=2048 — capacity control for the per-depth arm (6.4M shared vs 6.4M depth-indexed): if per-depth beats the ceiling but h2048 does not, time-variation (not capacity) is credited; if both do, it was capacity all along. d. parcae seed 1 — robustness of the fidelity refutation. Predictions: (a) and (b) each cost a few points of easy at most (anchored fixed point dominates); neither reproduces the ~17-point drop — the culprit is the learned/free B (with item 14 as the positive control). h2048 stays at the ceiling (hard <=46%), fidelity intact. parcae s1 reproduces easy ~71% within seed noise.

--- Outcome, item 13a (scored 2026-07-15): prediction CONFIRMED — per-depth lands below/at the ceiling, never above. Detail is instructive: fidelity preserved throughout (easy 88.5/89.3/86.9 at k=2/4/8 — anchored B), but hard-bucket content is DEPTH-STRANDED: 17.9% at k=2 (adapters 3-4, which hold the hard-trained content, never execute), 35.7% at k=4, 42.9% at k=8 — where depths 5-8 reuse adapter 4, i.e. the architecture reverts to shared-map iteration and the fixed-point mechanism collects the remaining gain. Time-variation adds a fragility (content unavailable except at its training depth) and no capability; map-sharing is load-bearing for the anytime-usable gain. Depth-4 adapter overfit visible in val (hard k4 CE 0.188@99 -> 0.371@599) — LTV concentrates small-pool overfitting into single depths.

--- Outcome, item 13b (scored 2026-07-15): accuracy prediction CONFIRMED (k=8 halt run 52.0/90.2/42.9 = plateau level); convergence predictions REFUTED. Per-item state-cosine (thresh 0.9995, k=8 cap): k_conv distribution 4:3, 5:57, 6:47, 7:17, never-within-8:126 — mean 7, and NO difficulty gradient (easy 7.01 vs hard 7.00). The earlier "bit-exact by k3-4" was the single dynamics-probe example, not the population: outputs plateau by k~2-4 while the state keeps drifting at 1e-3..1e-4 cosine scale; the fixed point is an OUTPUT-stable orbit (suffix layers + decode wash out residual state motion), not a literal state fixed point for most prompts. Free-ACT via state-cosine therefore yields no early exit at this threshold, and no ACT-like difficulty allocation falls out for free — output-level halting signals would be needed. Paper's dynamics claims softened accordingly.

--- Outcome, item 14 (scored 2026-07-15): ALL THREE PREDICTIONS CONFIRMED. (a) Fidelity fully preserved: easy 93.4/91.0/90.2 at k=2/4/8 (merge: 92.6/88.5; parcae with identical decay freedom but untied B: ~71%) — the free B is causally isolated as the fidelity culprit, the anchoring tie as the protection. (b) Hard at merge level exactly (35.7/42.9/39.3 = merge's k-curve within noise); no gain from the freedom. (c) Learned a essentially unmoved: mean 0.298, range [0.285, 0.310], 0/1536 dims moved

0.05 from init — the anchor coefficient is not a useful learnable DOF; hand-tuned 0.3 was already optimal. Recipe consequence: fixed-alpha anchored merge is the recommended design; learnable-alpha safe but pointless, learnable-B harmful, per-depth strands the gain.

16. Code→GSM8K cross-task transfer (pre-registered 2026-07-15 ~14:10, before running). The MBPP-trained loop adapter (adapter_code, s0) and the noise-s0 variant evaluated on GSM8K test (n=256, prompt-only loop, same harness as eval_gsmonly). Extends the transfer-distance ladder (HumanEval tie -> LCB trained-hurts) across tasks. Predictions: (a) hard-bucket gain ~0 (plan content is task-local; GSM8K needs evolving state, not static plans); (b) easy items damaged at k>0 (~93 -> 50-70%), comparable to or worse than the GSM-trained merge — substrate damage on GSM8K is perturbation-driven and content-agnostic; (c) overall at k>0 below k=0 (no rescue). If instead hard gains appear (>5 points), plan-shaped content is partially task-general — would weaken the task-local claim from LCB.

--- Amendment to item 15 (2026-07-15 ~13:15): noise-s0 arm EXCEEDED prediction (b) upward: hard 50.0/53.6/50.0 at k=2/4/8 with easy 88-90% — nominally the best hard cells of the project (merge best 46.4; seed mean 37.5±5.5). Paired vs tied-alpha (only same-day per-item baseline): discordants 5-1/3-0/3-0 in noise-s0's favor, each k p≈0.22-0.25 at n=28 — consistent direction, not individually significant. Denoising interpretation: training the loop to reach the fixed point from noise regularizes the content. SEED ARMS QUEUED (s1, s2, same recipe/eval, pre-registered here): if seed-mean hard(k=4) > 46.4 (the merge's best single cell), the recommended recipe gains noise-s0; if seed mean falls back into 37-46, it was a lucky seed.

--- Outcome, item 15c (h2048 capacity control, scored 2026-07-15): the per-depth exoneration is CLEAN — shared 6.4M params reach hard 42.9/53.6/ 50.0 at k=2/4/8 vs per-depth's 17.9/35.7/42.9 at the same capacity; time-variation is strictly worse than weight-sharing at matched params. Fidelity prediction confirmed and exceeded (easy 95.1% at k=2 — best looped fidelity of the project; 90.2% at k=4/8). Ceiling prediction (hard <= 46%) REFUTED UPWARD like noise-s0: k=4/8 at 53.6/50.0. Two independent variations (noise s0, 4x MLP) now sit at 50-54% where the original merge reached 46.4 — suggests 46.4 was an UNDER-estimate of the recipe family's level, not a ceiling it defined. The distill-parity deflation claim is unaffected statistically (53.6 vs 45.7 at hard n=28 is within noise) but the language "every regime tops out at the same ceiling" should become "at the same level within noise" — pending the noise-s0 seed arms.

--- Outcome, item 15d (parcae seed 1, scored 2026-07-15): CONFIRMED — the fidelity refutation replicates. easy 70.5/73.0/72.1 at k=2/4/8 (seed 0: 72.1/71.3/70.5); hard 32.1/39.3/35.7 (seed 0: 42.9/42.9/39.3, ordinary seed spread at n=28). Two-seed conclusion: contraction-with- free-B loses ~17 points of easy items regardless of seed; the phase diagram's Parcae point is solid.

--- Outcome, item 16 (code->GSM8K transfer, scored 2026-07-15): ALL THREE PREDICTIONS CONFIRMED, emphatically. MBPP-trained loop on GSM8K: hard 0.8-1.6% at every k (prediction a: ~0 gain — plan content is task-local); easy 93.1 -> 27.6-44.8% (prediction b: damaged, in fact WORSE than the GSM-trained merge's 48%); overall strictly below k=0 at every k>0 (prediction c). noise-s0 variant identical (easy 34.5, hard 1.6). The transfer-distance ladder ends cleanly: near (HumanEval) tie, far-code (LCB) trained-hurts, cross-task (GSM8K) trained-content actively toxic while gaining nothing. Task-locality of the learned content is now a three-point monotone result.

--- Closure of the item-15b/15c "ceiling nudged upward" question (2026-07-15, after ns seeds): LUCKY SEED, per the pre-registered rule. noise-s0 hard(k=4) across seeds: 53.6 / 39.3 / 35.7 -> seed mean 42.9, inside the 37-46 band. Fidelity across seeds intact (easy 90.2-94.3 — the factorial conclusion is seed-robust); the 50-54% cells (ns seed 0, h2048 single seed) were upper-tail draws of the same distribution the merge's 46.4 came from. No recipe amendment; the abstract's original "same level within noise" framing stands; single-cell records are not levels — only seed means are.

17. GSM-only, current recipe (pre-registered 2026-07-15 ~20:45, before running). train_merge_unified.py --tasks gsm: MergeAdapter, prompt- only loop, curriculum, GSM8K data ONLY — removes the mixed-task interference confound from the adapter_uni run, completing the "winning recipe trained on GSM" question. Eval: prompt-only, n=256, ks 0,1,2,4, e400. Predictions: (a) hard <= 10% at every k (supervision density is structural: ~3 answer tokens; the recipe's dense-output ingredient cannot exist here); (b) easy damaged at k>0 (to 40-70%); (c) overall never beats k=0. If hard exceeds 15% or overall beats k=0, task interference in the mixed run was masking a real GSM capability — would reopen the GSM chapter.

    Scope note (item 17): the design-space arms of items 11-15 are NOT crossed with GSM8K, deliberately. Exclusion by dominance: fidelity- failing regimes (rec, parcae) cannot improve on a task MORE fidelity- fragile than MBPP; architecture-failing (per-depth) and equivalent (tied-alpha -> merge) and k-placement-only (randk) and same-family (noise-s0, h2048) variants have no mechanism by which task change could invert their MBPP verdict. Only the recipe family's best member (this item) is informative on GSM8K.

--- Outcome, item 17 (GSM-only, current recipe, scored 2026-07-15): predictions (a) and (b) CONFIRMED, (c) nominally exceeded but not meaningfully. hard 8.7/5.5/4.7% at k=1/2/4 (below the 10% bar; nowhere near the 15% reopen threshold); easy 93.1 -> 48-52% at k>0; overall 11.7/10.9/10.2 vs k0's 10.5 — the k=1 cell is +1.2 points nominal (~3 items at n=256, not significant), the rest below. Removing the mixed-task interference bought ~2 points over adapter_uni (9.4 -> 11.7 at k=1) — interference was real but marginal, not masking a capability. The GSM8K chapter is closed: the recipe family's best member, trained on GSM alone in the correct regime, delivers no usable gain and the standard fidelity damage; combined with the scope note, the boundary claim (structural: supervision density + state-evolution bottleneck) is fully supported.

18. E1: learned per-prompt halting gate (pre-registered 2026-07-16 ~00:20, before any arm runs; PLAN_SELFPACED.md). HaltingMergeAdapter: frozen-recipe merge + ACT-style halting head on the last prompt position's workspace state; soft state-mixture training, CE + lambda * E[iters], penalty warmup at step 100; NO difficulty curriculum (mixed batches — the gate must discover the allocation). k_max=4, e400/e600 checkpoints, deploy = sequential halting at 0.5 cumulative mass, generation via frozen-prompt at per-item k*. Arms: lambda in {0, 1e-3, 1e-2}, seed 0. Eval: 250 items, vs anchors k=0 (0.488), uniform merge k=4 (0.512/0.885/0.464), probe-gate E0 (0.520/0.975/0.286). Predictions: (a) some lambda gives overall >= 0.512 at mean E[k] <= 2.4 (60% of uniform-4); (b) easy >= 0.95 at that lambda; (c) k*-vs-hard point-biserial r > 0.3; (d) hard >= 0.286 (beats E0's frozen probe). Collapse (E[k] pinned at 1 or 4 for all lambda) falsifies E1 and triggers the plan's kill criterion. lambda=0 control isolates whether the CE gradient alone moves the gate (expected: barely — penalty provides the pressure).

    Item 18 amendment (2026-07-16 ~23:45, before results): arms run on a rented 4xH100 node in parallel instead of the Spark queue; a fourth arm (lambda=1e-3, seed 1) is added for immediate seed replication of the expected-winner penalty. Spark's queued gate jobs will be dropped to avoid duplication. Everything else per registration.

--- Outcome, item 18 (scored 2026-07-16 ~00:40): predictions (b), (c) REFUTED, (a) marginal miss, (d) trivial pass. All arms converge to UNIFORM depth (lambda 0/1e-3/1e-2 -> E[k] 4/2-or-4/1; the two 1e-3 seeds picked different plateaus — degenerate penalty landscape), r = 0.000 everywhere. Mechanism identified and consistent with prior findings: teacher-forced CE is depth-flat (stationarity), so CE provides no per-item depth gradient; the penalty alone cannot teach selectivity. The state DOES carry the signal (E0 probe: train acc 1.0) — the failure is the training signal, not the representation. E1-as-designed is dead; kill criterion NOT fully triggered (E2 untested, and the mechanism points at a repair).

19. E1b: label-supervised halting head (pre-registered 2026-07-16 ~00:45, before running). Freeze the curriculum merge (adapter_code s0); train ONLY the halting head (BCE): target halt=0 at iterations below the label's depth (easy->1, hard->4, per STaR label), halt=1 at or above it. 300 steps, mixed batches, head-only params. Eval: gated eval as item 18, n=250. Predictions: (a) r(k*, hard) > 0.5 (the head is a trained difficulty classifier now); (b) easy >= 95% at k*=1 (near-E0's 97.5); (c) hard >= 35.7% (>= best uniform arm, via better recall than E0's frozen probe: more than 18/28 hard items routed deep); (d) overall >= 52.0 at E[k] <= 2.2. If (c) fails while (a,b) hold, halting-head recall saturates at probe level and gate quality, not gate training, is the binding constraint.

--- Outcome, item 19 / E1b (scored 2026-07-16 ~01:15): prediction (c) CONFIRMED (hard 39.3 >= 35.7 at mean k* 2.18), (a) FAILED at r=0.217 (selectivity real — hard routed 2x deeper than easy (2.18 vs 1.08), the program's first nonzero gate correlation — but weak at deploy), (b,d) FAILED for a traced design reason: halted_k_per_item lacked k*=0, so easy items were forced through >=1 iteration and landed on the merge's WORST easy depth (k=1: 85.2%); E0's 97.5% came precisely from k=0 routing. E1c amendment (pre-registered before running, same session): pre-loop halt consult on s_0 enabling k*=0; targets easy->0, hard->4; threshold 0.5 unchanged (calibration deferred unless E1c misses). Predictions: easy >= 95%, hard >= 35.7%, r >= 0.4, overall >= 51.2 at E[k] <= 1.5.

--- Outcome, item 19 / E1c (scored 2026-07-16 ~01:50, Spark re-run): prediction (b) CONFIRMED — easy 95.9% with mean k*=0.11 (the k=0 routing fix worked perfectly for easy items); (a) FAILED (r=0.220, unchanged); (c) FAILED HARD — hard 21.4% at mean k*=1.5: with the pre-loop halt consult, weakly-discriminated hard items now exit at k*=0/1 where before they got >=1 iteration; the recall problem became more expensive, not better. (d) FAILED (overall 50.0 at E[k]=0.74). Net Pareto: E1c = (50.0 overall, 95.9 easy, 21.4 hard, 0.74 mean iters — 82% compute saved); E0 probe-gate = (52.0, 97.5, 28.6, ~2.2) still dominates on accuracy. The learned-head line has ONE identified un-tried knob: deploy-threshold calibration on val for hard-recall (the 0.5 threshold is arbitrary; raising it routes more items deep, trading easy tax for hard recall — a tunable curve E0 cannot offer). E1 arc summary for PLAN_SELFPACED: gating machinery works end-to-end, easy-item protection and compute savings are demonstrated and cheap; difficulty-selective DEPTH allocation remains unsolved at 3K-param-head scale — binding constraint is classifier quality on the k=0/s0 state, exactly where E0 started. Next per plan: threshold sweep (cheap) before any E2.

20. E1 threshold curve + oracle bound (pre-registered 2026-07-16 ~02:15, before running). Phase 1: record E1c head's halt probabilities per test item (one GPU pass). Phase 2: per-item outcomes for the frozen curriculum merge at k=0/1/2/4 (four generation sweeps, tag merge_lut — doubles as the reusable gate-evaluation lookup table and supplies the long-missing per-item logs for the canonical merge). Phase 3 (offline): gated accuracy at thresholds .3-.99 by composing k*(theta) with the lookup; plus the ORACLE gate (best k per item) = the ceiling any gate can reach with this merge. Predictions: (a) some theta gives hard >= 32% with easy >= 93% and E[k] <= 2.2 (dominating E0 on compute at comparable accuracy); (b) the curve is monotone in theta; (c) oracle overall >= 55% — if so, gate-quality headroom is large and further gate work is justified; if oracle < 53%, gating this merge is nearly saturated and the program pivots to E2 or closes.

--- Outcome, item 20 (scored 2026-07-16 ~02:35): (b) CONFIRMED — clean monotone threshold curve (hard 7->50%, easy 96.7->87.7%, E[k] 0.43->2.63 across theta .3->.99). (a) FAILED — no theta reaches easy>=93 AND hard>=32; at matched easy the E0 frozen probe dominates the entire learned-head curve: the BCE-trained 3K head is strictly worse than the class-balanced logistic probe it was meant to replace. (c) CONFIRMED, emphatically: ORACLE gate = 59.6 overall / easy 100% / hard 64.3% at E[k]=0.24. Key insight: hard items are DEPTH-DIVERSE — 18/28 solvable at some k in {0,1,2,4} but no single k solves more than 13; a third of the hard bucket lives in per-item depth selection. Program continues per rule; binding constraint quantified: gate quality is worth ~9.6 overall points (50.0 deployed vs 59.6 oracle). Also noted: the LUT re-run of the canonical merge shows small systematic drift vs the Jul-13 eval (k4 hard 46.4 identical, k1/k2 hard 3 items lower) — the LUT (per-item, single harness run) is now the canonical reference. Next candidates, in cost order: (i) deploy E0's probe AS the gate against the LUT (free, offline); (ii) stronger classifier (multi-position features, more data, calibrated threshold); (iii) oracle-gap error analysis on the hard items no fixed k solves but some k does.

21. E2 stage A: dense short-CoT supervision through the carry whiteboard, GSM8K (pre-registered 2026-07-16 ~02:55, before running; PLAN_SELFPACED E2 / the hybrid from the internalization discussion). Prep: harvest TERSE verified CoTs ("at most 3 short steps", answer- verified, STaR filter) for GSM train. Arms: (A) carry regime (k=2 prefill, pauses easy p=2 / hard p=6) trained with CE on scratchpad+answer (~30-60 dense tokens — the ingredient every latent GSM arm lacked); (B) CONTROL: identical supervision, feedforward adapter, no recurrence. Eval: GSM test 256, grid 0:0 (base), 2:2, 2:6; e400 checkpoints. Predictions: (a) arm A beats every previous GSM arm's overall (>12.1%) — dense supervision is the binding fix; (b) the A-vs-B delta isolates the whiteboard: if A > B by >=3 points overall, recurrence adds value beyond visible-scratchpad training; if A ~= B, the scratchpad text alone carries it (deflation, GSM edition); (c) easy-bucket damage smaller than answer-only carry's (83->45%) because training and deployment output formats now match. Honest note: arm outputs are VISIBLE tokens (~40) — this is the budget-CoT-with-loop hybrid, a scope change from latent planning, run at Nils's explicit direction ("do gsm8k and such").

--- Outcome, item 21 (scored 2026-07-16 ~06:30). Harvest: 427 verified terse CoTs (292 hard, 135 easy; 73.5% yield, ~3 min). Grid (n=256, base 10.9/93.1/0.8/0.0 overall/easy/hard/drop): arm A carry 2:2 53.9 (82.8 / 60.6 / 37.0) arm A carry 2:6 57.4 (72.4 / 63.8 / 45.0) control FF 2:2 49.6 (79.3 / 59.8 / 28.0) control FF 2:6 54.7 (82.8 / 66.9 / 31.0) (a) CONFIRMED, dramatically: best cell 57.4% vs the previous best GSM arm's 12.1% — a 5x jump to full-CoT territory (~53%) at ~1/4 the visible tokens. Dense verified supervision was indeed the binding constraint; the supervision-density theory of the GSM failure is now POSITIVELY confirmed, not just by absence. (b) MIXED: A-vs-B delta +4.3 at p=2 (clears the >=3 bar), +2.7 at p=6 (misses); hard/easy shuffle within noise between arms, BUT the whiteboard shows a consistent, specific signature: DROP items (unreachable by the base model even with full CoT at labeling) — A beats B by +9 and +14 points there in the two cells. Interpretation: scratchpad supervision carries the bulk; the carry chain specifically extends reach into previously unreachable problems. McNemar (scored 2026-07-16 morning): overall A-vs-B not significant in either cell (2:2 discordants 34-23 p=0.185; 2:6 33-26 p=0.435), but the pre-identified drop-bucket signature IS: 2:6 drop discordants 20-6, exact McNemar p=0.0094 (survives Bonferroni x4 = 0.038); 2:2 drop 16-7, p=0.093 (same direction, marginal). Verdict: the whiteboard's edge is real and specific to extending reach into drop items, not a general lift over matched supervision. (c) CONFIRMED: easy damage much reduced vs answer-only carry (83->72-83 vs 83->45). Ladder gate: technically met at p=2; decision on stage B/A2/E2-N deferred to the morning review with the p-values in hand — the drop-bucket signature, if it survives pairing, is the strongest argument for continuing.

22. E2-L rung B: internalization ladder, front-first step deletion (pre-registered 2026-07-16 ~10:40, before running; Nils chose stage B over A2/E2-N at the morning review. Gate state: pre-registered +3 overall met on points (+4.3 at p=2); paired McNemar overall ns, but the drop-bucket signature significant, 2:6 p=0.0094). Design: delete the first d scratchpad lines of each verified terse CoT (d=1,2,3 — front-first: the deleted computation must ride the pause-chain before the visible remainder), each deleted step replaced by 10 pauses (median step = 10 tokens, compute-matched); unparseable cots (14/427 without exactly one Answer line) pass through intact. Step-count distribution 1/2/3/4/5+: 11/164/196/27/15 — so d=3 is effectively rung C (pauses only) for ~87% of items. Each rung warm-starts from the previous (d=1 from rung-A e400), brief retrain: 200 steps, LR 3e-4 cosine, seed 0. Eval: GSM test n=256, cells 0:0 (k=0 sanity, expect ~base 10.9), 2:(2+10d), 2:(6+10d); e200 checkpoints; per-item logs kept so rung-vs-rung McNemar is offline. Known approximation, stated in advance: items with fewer than d steps train at smaller effective p than the eval cell (ndel=min(d,n_steps)). Predictions: (a) d=1 best cell within 5 points of rung A's 57.4 — one step fits the recurrence budget (the drop-bucket reach evidence says the whiteboard already carries step-sized computation); (b) monotone decline across d; (c) at d=3 accuracy stays above BOTH base (10.9) and cold answer-only carry (9.4) — curriculum beats cold training even where the ladder breaks. Deliverable: the break rung = first d whose best cell falls >=5 points below the previous rung's best — the measured capacity of this recurrence budget to absorb computation. Job: scripts/jobs/zzz_m_gsm_rungb.sh (single submit, ~3x(40min train + eval) on the Spark).

--- Outcome, item 22 (scored 2026-07-16 ~15:30). k=0 sanity row reproduced base exactly in all three rung evals (10.9/93.1/0.8/0.0). Ladder (best cell overall, n=256): rung A 57.4 -> d=1 31.6 (2:12) -> d=2 18.4 (2:26) -> d=3 19.1 (2:32). (a) FAILED, decisively: the break rung is d=1 — deleting ONE compute-matched step costs 25.8 points (easy 83->62, hard 64->36, drop 45->17); the recurrence cannot absorb even one step's computation at this budget/recipe. (b) monotone through d=2, then a plateau (d=2 18.4 -> d=3 19.1, within n=256 noise): the decay bottoms out ABOVE the floor rather than collapsing to it. (c) CONFIRMED: d=3 (pause-only for ~87% of items) = 19.1 vs base 10.9 — paired McNemar 33-12 discordants, p=0.0025 — and vs cold answer-only carry 9.4: the curriculum-reached latent loop DOUBLES the cold-trained equivalent. Composition of the d=3 edge: easy is DAMAGED (58.6 vs 93.1 base) while hard (18.9 vs 0.8) and drop (8.0 vs 0.0) are lifted — the latent loop trades easy-bucket reliability for reach, echoing item 21's drop-bucket signature in latent form. Deliverable: measured capacity of this recurrence budget = a plateau at ~19% overall / ~2x the cold floor; the visible scratchpad carried the other ~38 points. Val-loss note: hard val rose with d (0.36 -> 0.56 -> 0.59) while easy fell (d=3 0.13, mostly answer-line targets) — CE fit does not track eval accuracy at deep rungs. Interpretation for the plan: rung C' (no pauses) is moot as a capability claim — C already plateaued at 19; the E2-L line's value is now the 2x-over-cold curriculum effect + the reach trade, not scratchpad-free parity. Next knobs if the line continues: longer per-rung retraining, finer deletion schedule (fractional rungs), or E2-N noise-hardening stacked on the rungs.

23. E2-L d=1 capacity-ceiling controls (pre-registered 2026-07-16 ~15:55, before running; Nils: "run that one control"). Item 22's break-at-d=1 has two untested confounds; one arm each, single-knob changes from item 22's d=1 (both warm-start rung-A e400, seed 0): arm A "x600" = 600 steps instead of 200 (3x training; tests the brief-retrain objection — note d=1 val had plateaued at 0.36, so prediction is NO recovery); arm B "pp30" = 30 pauses per deleted step instead of 10 (3x latent bandwidth, same 200 steps; tests whether inert-pause capacity, not training, binds). Eval n=256: arm A cells 0:0, 2:12, 2:16 (e600); arm B cells 0:0, 2:32, 2:36 (e200). Decision rule, stated in advance: item 22 d=1 best = 31.6; a control within +-5 points confirms the ceiling on that axis;

    =+5 (>36.6) reopens the ladder on that knob (longer schedules or wider pause-chains); if BOTH land within +-5, the d=1 ceiling is confirmed structural and the ladder chapter closes as scored. Job: scripts/jobs/zzz_n_rungb_ctrl.sh. AMENDMENT (2026-07-16 ~19:05, mid-run, Nils's call): arm A's eval skipped to save ~50min GPU — the verdict was already decided by training evidence (train loss memorized to 0.02-0.10 by step 200; val easy 0.386->0.397->0.426, hard 0.357->0.376->0.421 across e200/e400/e600 — monotone UP, textbook overfit, no recovery; k=0 sanity row reproduced base before the kill). Arm A scored from the val trajectory: training time is NOT the binding constraint. Arm B (pp30) runs in full as registered.

--- Outcome, item 23 (scored 2026-07-16 ~23:55; rc=0). k=0 sanity rows reproduced base in both arms' evals (arm A's before its eval was skipped). Arm A (x600): scored from val trajectory per amendment — no recovery, mild overfit; training-time axis CONFIRMS the ceiling. Arm B (pp30): best cell 29.3 (2:36; 28.5 at 2:32) vs item-22 d=1's 31.6 — WITHIN the +-5 band, slightly below: 3x latent positions bought nothing (hard 33.9/36.2 vs 36.2; drop 14 vs 17; easy 51.7-55.2 vs 62.1). Decision rule: BOTH axes confirm -> the d=1 break is STRUCTURAL. Neither longer training nor a longer pause-chain lets this carry absorb one scratchpad step; the binding constraint is the carried state itself (its per-position expressivity/fidelity, not its compute budget). Converging evidence from the same evening's microscopy (probe_discount*/probe_gsm*): the board natively carries plans ("Multiply", "subtract"), coarse magnitudes ("sixty/eighty"), and completion-state ("plus" kept alive at the 430 divergence — carry defers where FF commits a wrong digit at 99.3%), while exact digits appear only just-in-time, 1-2 positions pre-emission. The ladder chapter closes as scored in item 22; the loop program's live paths are state-side (rung-2 band-LoRA / wider merge, E2-N hardening, coarse-target auxiliary supervision matched to the medium) or the hybrid (A2), not longer/denser pause-chains.

24. E2-L d=1 with a trainable band: loop-only band-LoRA (pre-registered 2026-07-17 ~00:30, before running; Nils: "can we unfreeze the entire band and try this again?"). Item 23 located the constraint in the carried state's per-position transformation; this is the state-side attack. Full unfreeze rejected in design (642M params vs 427 examples, and it would break the frozen-model guarantee); instead LoopLoRA (lora_band.py, built for the rung-2 design): rank-16 deltas on q/v/down of EVERY band layer (L14-30, uniform scale 1.0, 4.8M params), active ONLY during band re-runs — initial forward and k=0 stay bit-exact by construction. Otherwise identical to item-22 d=1: front-first deletion, 10 pauses/step, warm-start rung-A e400 (adapter lr 3e-4; fresh LoRA lr 1e-3, B zero-init so step-0 matches item 22 exactly), 200 steps, seed 0. Eval n=256: 0:0 (sanity, must equal base), 2:12, 2:16; e200. Decision rule (same bands as item 23, vs d=1's 31.6): >=+5 (>36.6) = band expressivity was binding -> escalate (rank 64, all projections, or full-band rung ladder); within +-5 = the medium verdict stands even with a trainable band -> internalization line CLOSED, program pivots (A2 / E2-N / coarse-aux / divergence batch). Prediction, honest: mild gain but under threshold (~33-36) — the microscopy says the board's failure mode is WHAT it carries, not how flexibly it transforms it; but this is the experiment the 'wider state' hypothesis deserves before the line closes. Job: scripts/jobs/zzz_p_rungb_blr.sh.

--- Outcome, item 24 (closed 2026-07-17 ~02:10, STOPPED by Nils mid-eval: "stop that idea. does not seem to work either"). Training completed; evidence at stop: val easy 0.346 / hard 0.405 vs adapter-only 0.356/0.361 — the trainable band did not improve fit (hard slightly worse), consistent with the registered prediction that capacity/expressivity is not what binds. k=0 sanity row with trained LoRA loaded reproduced base EXACTLY (10.9/93.1/0.8) — the loop-only LoopLoRA guarantee holds in practice; the mechanism is validated even though the hypothesis died (useful for any future band-side work). Accuracy cells not measured (eval killed at Nils's call to save ~50min GPU); adapter+lora e200 checkpoints in the bucket if anyone ever wants the number. Verdict: with items 22+23 this closes the E2-L internalization line entirely — adapter capacity, training time, pause bandwidth, and band expressivity have all now failed to move the d=1 break. The carried state's native cargo (plans, magnitudes, completion-state — see the probe series) is the program's remaining asset; next candidates: divergence batch replay, coarse-target auxiliary supervision, A2, E2-N.