Exp 14 — Operational Re-read: A Positive Small-Family Precursor

With exp13's calibration frozen and fresh held-out seeds, the primary reversible PT kernel finally cuts the calibrated operational time by the compute-normalized criterion — a positive small-family precursor, not the at-scale validation.

This is the complete technical record for experiments/exp14-operational-reread/. It is the corrected operational read on experiments/exp13/'s calibration, and the third beat of an arc that began with the reversible-kernel timescale work in the $\tau$-probe entry. Ran 2026-06-15, CPU, float64, 37.8 s wall; gates frozen at pre-commitment ff865ab (gate-1) and runner 6c53ac6 (gate-2), reusing the frozen exp13 calibration (44a05a9) and the exp12 pt_kernel (a976d80). Reproduce with P0_MODE=full HOST_RAM_GB=8 python3 op_reread.py → op_reread.json (MEASURE-ONLY).

The question

exp12 showed parallel tempering (PT) cut $\tau_{max}$ by $14$–$22\times$ but the operational time $T_O^{PT}$ never stabilized in the registered windows — Outcome F, measurement-limited. exp13 then established that $T_O$ is calibratable (Cal-STABLE under exact-$\pi_r$ init), so the frozen S-ADQ failure was a gate-specification artifact, not a real one. exp14 asks the operational question that exp12 could not answer: with the corrected gates and the calibrated swap schedule $S_a^*$, does the primary reversible PT kernel actually cut the calibrated $T_O$ by the frozen compute-normalized $\ge 2.0$ criterion on the registered small RBM family?

The setup

The verdict metric is a compute-normalized speedup,

$\text{speedup} = \frac{T_O(P_{sym},\ \text{exact})}{T_O^*(\text{PT})\cdot \text{work}_{PT}},$

where $T_O^*(\text{PT})$ is the exp13-calibrated, frozen value — it is not re-estimated here. exp14's fresh held-out seeds (OP_SEEDS=200..204) independently confirm two things against that frozen $T_O^*$: window adequacy (F1 in band at both $20\hat\tau^*$ and $50\hat\tau^*$) and P4. So the precursor is a conjunction: (frozen-$T_O^*$ compute-normalized speedup $\ge 2.0$) and (fresh-seed confirmation that the operational windows are asymptotic against that $T_O^*$, with P4 in band). The family is $m=5$; cells span the primary kernel $K=\tfrac12(LS+SL)$ at $R\in\{4,6,8\}$, the convex kernel $K_{PT}$, a unimodal control C-uni, and C-deep2.

The result

Outcome S-A on C-deep R4 (primary) and R6 (corroborating). The full cell table:

| cell | window-adeq (F1@$20,50\hat\tau^*$) | speedup vs 2.0 | P2 | P4 | $\gamma_{bulk}$ (proj.) | outcome | |---|---|---|---|---|---|---| | C-deep R4 primary | pass | 2.42 (+21%) | pass | pass | 0.22 ($\Omega(1)$) | S-A | | C-deep R6 primary | pass | 2.12 (+6%) | pass | pass | 0.42 ($\Omega(1)$) | S-A | | C-deep R8 primary | pass | 1.86 | fail | pass | 0.48 | S-D | | C-deep R4 / R6 convex | pass | 1.60 / 0.96 | fail | pass | 0.07 / 0.12 | S-D | | C-deep R8 convex | fail (F1@20 out) | 0.59 | fail | — | 0.08 | W-INADQ | | C-uni R4 (diagnostic) | pass | 0.73 | fail | pass | 0.21 | S-D | | C-deep2 R4 | fail (F1@20 out) | 0.48 | — | pass | 0.27 | W-INADQ |

R4 is the robust pass; R6 corroborates but is not co-equal. R4 clears the $2.0$ bar by $21\%$ — beyond the calibration's own $\pm15\%$ $T_O$-stabilization tolerance, so it survives the calibration uncertainty. R6 clears by only $6\%$ — within that $15\%$ tolerance, so R6's pass could flip under calibration noise. Treat R6 as corroborating, not co-equal evidence.

The projected $\gamma_{bulk}^{PT}$ is the lifted-observable VAC $\gamma$ corrected by the multimodal calibration ratio $0.997$; it is $\Omega(1)$ for both S-A cells ($0.22, 0.42 > 0.1$ floor) — a diagnostic, not a full spectral certificate. S-A is read regardless of the §8 tuning-adequacy gate: a positive P2 is not blocked by §8 (high swap-accept is ladder redundancy already charged inside $\text{work}_{PT}$); §8 only splits P2-failures into S-C versus S-D.

The non-S-A cells confirm the design choices. R8 primary erodes the net benefit ($\text{work}_{PT}=12$ at $R=8$ drops speedup to $1.86$) → S-D. The convex kernel mixes far slower (raw $T_O^*$ $294$–$400$, $\gamma_{bulk}$ $0.07$–$0.12$) → S-D / W-INADQ, confirming the primary $K=\tfrac12(LS+SL)$. C-uni shows the expected PT overhead on a unimodal target (speedup $0.73$). C-deep2 and R8-convex are W-INADQ because F1@$50\hat\tau^*$ is in band but F1@$20\hat\tau^*$ is not — $20\hat\tau^*$ is still pre-asymptotic there.

Scope and caveats

Scoped to the registered small RBM family ($m=5$); at-scale G2 untouched. This is a small-family precursor, not the at-scale G2 validation. The speedup rests on a frozen $T_O^*$ — the fresh seeds re-confirm window adequacy and P4, but they do not re-measure $T_O^*$ or the speedup. R6 sits inside the calibration tolerance. $\gamma_{bulk}^{PT}$ is a projected diagnostic, not a spectral certificate. No fundamentality claim. No tag moves: the operational tier stays [conjectured] and the conditional factorization stays [solid]. The central-spine A2$\leftrightarrow$A6 sharpening — reversible-kernel acceleration now operationally demonstrated on the controlled family — is researcher-conferred prose, not a status flip.

The arc lands here: exp12 cut $\tau_{max}$ but could not stabilize $T_O$ (Outcome F); exp13 showed $T_O$ is calibratable and the failure was a gate artifact; exp14 demonstrates that, with corrected gates and the calibrated $S_a^*$, the primary PT kernel at R4 (robust) and R6 (corroborating) cuts the calibrated $T_O$ at least $2\times$ compute-normalized — acceleration operationally demonstrated, not merely $\tau_{max}$-suggested.

What this feeds

Per the outcome map, exp14's S-A confers authorization (researcher-conferred, 2026-06-15; see p0_decision.md) for a GPU DTM-MNIST PT P0 doubling probe — the exp4-style non-circular $\hat\tau$ probe with the reversible PT kernel on the real DTM, where 4-block Gibbs gave $\tau \propto L$. This is authorization, not PROCEED: the separate p0_decision.md must still declare PROCEED/HALT plus GPU-hour limits. Primary arm is R4 primary (strongest margin, lowest replica cost); R6 is a budget-dependent robustness arm. No GPU is committed here; no tag moves.

What this feeds: the GPU DTM PT P0 authorization gate and the A2$\leftrightarrow$A6 spine annotation — recording the first operational demonstration of reversible-kernel acceleration on the controlled family, while leaving the operational factorization tier exactly where it was.