# v0.18 liao2021 Reliability-Conditioned Per-Cell AUC Form ## Result (2026-06-03) **Verdict: `reliability_drives_per_cell_auc_supported`** -- the top branch. On a fresh, wider 8x8 grid (18 cells, 2880 rows, quadruple holdout) the pooled transfer replicates a THIRD time, label-blind frame-reliability predicts per-cell AUC, and the reversal guard finds no frame-stable competing signal. ```text pooled (3rd replication): AUC_cond 0.620208 (J 71448 / D 115200), p_perm 1.0e-5, attrition 0.0000, 18/18 primary cells, 2880 rows reliability: Spearman rho(-log10 frame_p90, AUC_cell) = 0.597523, MC p 0.00523 (522/100k >= observed) -> >= 0.45 floor, <= 0.05 reversal guard: stable_decisive_negative_count = 0 -> passes frame_p90 across 18 cells: median 0.006, p75 0.048, p90 0.362, max 0.400 (real fragile tail) ``` **The reproducible heterogeneity IS an instrument-reliability map -- now confirmed, not hypothesized.** The v0.17 anatomy suggested it post-hoc; v0.18 promoted it to a pre-registered, label-blind test on fresh wider-grid rows and it passed: where the four-frame ensemble vf is frame-stable, the v0.11 direction holds (top cells qA2_qB1 0.882, qA1_qB0 0.827 at frame_p90 ~0.003-0.006); where it is fragile, discrimination degrades and reverses (bottom cells qA4_qB2 0.265, qA5_qB2 0.362 at frame_p90 0.36-0.40). **The reversal guard's falsification test passed honestly.** The two strongest negatives (qA4_qB2 0.265, qA5_qB2 0.362) are exactly the two most frame-fragile cells -- explained by unreliability, not a counter-law. The only frame-STABLE sub-0.5 cell (qA6_qB1 AUC 0.440, frame_p90 0.041) is NOT statistically decisive (p_reverse 0.097 > 0.05), so it does not constitute a stable competing signal. A frame-stable decisive-negative cell *could* have falsified the reliability story; none exists. **Independent verification.** A standalone brute-force pair-count pooled AUC + a hand-rolled rank/Pearson Spearman over recomputed per-cell frame_p90 (independent of the runner) reproduced AUC_cond 0.620208 and reliability rho 0.597523 BIT-FOR-BIT. Receipt + verifier: `results/isotrophy/k-facet-v18-liao2021-reliability-auc/` (`manifest.json`, `per_cell_auc.csv`, `frame_reliability_map.csv`, `reliability_auc_test.json`, `reversal_guard.json`, `_independent_check.{py,json}`). **Honest bounds.** The confirmed driver is FRAME-reliability specifically (the only non-circular, label-blind predictor); rho 0.60 is moderate-strong with real scatter, not a deterministic law. The pooled AUC 0.620 is below v0.16/v0.17's 4x4 0.647 because the 8x8 conditioning is finer (expected; it still clears 0.55 at p 1e-5). Bounded as before: Tier-2 / Li-Liao lineage / stable-support / within-cell rank / tail-resolved continuous score / not coarse-zone / not full-catalog prevalence / not Tier-3 / not theorem-facing. This is an EXPLANATION of the reproducible v0.16/v0.17 heterogeneity, and it does not alter those receipts -- it accounts for them. **Arc capstone.** v0.11 internal conditional positive -> v0.16 first external PASS -> v0.17 replication + reproducible heterogeneity -> v0.18 the heterogeneity mechanism (a frame-reliability map) confirmed on a wider fresh grid with a passing reversal guard. --- Status: **OPERATOR LOCK 2026-06-03; VERDICT LANDED `reliability_drives_per_cell_auc_supported` 2026-06-03.** At lock time no v0.18 runner had been written, no v0.18 sample had been drawn, no v0.18 D5 rows had been integrated, and no v0.18 AUC or reliability statistic had been computed. After lock, the runner was implemented, prepared, sharded, merged, analyzed, and independently verified under the locked form. Execution receipts: ```text prepare: npm run isotrophy:v18:prepare measurement: 16 staged shards, then merge + analyze out: results/isotrophy/k-facet-v18-liao2021-reliability-auc/ grid scan: 4x4=7, 5x5=10, 6x6=12, 7x7=16, 8x8=18, 10x10=24, 12x12=34, 16x16=46 (all matched lock) holdout: v14+v15+v16+v17 = 4640 rows, disjoint sample: 2880 rows (80 S + 80 U per cell), 0 attrition verdict: reliability_drives_per_cell_auc_supported ``` ## Frame v0.16 established the first clean Tier-2 external transfer of the tail-resolved velocity-fraction score. v0.17 replicated that transfer and showed that the seven-cell heterogeneity pattern is reproducible, not one-sample texture: ```text v0.16 AUC_cond = 0.6469866, p_perm = 1.0e-5 v0.17 AUC_cond = 0.6468750, p_perm = 1.0e-5 v0.17 heterogeneity Spearman vs v0.16 = 1.0, exact p = 1/5040 ``` The v0.17 anatomy sidecar then suggested a post-hoc explanation: per-cell AUC looks like an instrument-reliability map. The strongest low cell (`qA2_qB1`) is the known frame-fragile pocket; the other low cell (`qA3_qB0`) is close to a near-null rather than a strong competing direction. Everywhere the four-frame read is stable and the score has usable separation, the v0.11 direction holds. v0.18 turns that explanation into a fresh, wider-cell test: > Across a wider liao2021 mass-cell grid, do frame-reliable cells carry higher > per-cell AUC, and are low/reversed cells concentrated in instrument-fragile or > near-null regions rather than stable counter-law regions? This is a **mechanism/anatomy chapter**, not a new feature search and not a promotion of the theorem claim. Expectation calibration: `wider_transfer_replicates_reliability_unresolved` is a live, informative outcome. The primary statistic tests the **frame-fragility** half of the reliability story only. v0.17 had one low cell that was clearly frame-fragile (`qA2_qB1`) and one low cell that was frame-stable but near-null (`qA3_qB0`). If the wider 8 x 8 low cells are dominated by near-null structure rather than frame fragility, the label-blind reliability statistic can honestly miss while the report-only anatomy still explains the pattern. ## Integrity Caveat ```text post-hoc hypothesis disclosed: The reliability-map hypothesis was motivated by the v0.17 anatomy sidecar. v0.18 tests it only on fresh rows and a wider source-defined grid. feature frozen: The v0.16/v0.17 score is reused exactly: score = median(vf_0, vf_37, vf_90, vf_211). domain changed only to widen the cell map: v0.18 uses a nested sorted-mass 8 x 8 grid instead of the v0.14-v0.17 4 x 4 grid. This is a registered domain change for the reliability question, not a rescue of any prior verdict. fresh quadruple holdout: Exclude every liao2021 orbit used in v0.14, v0.15, v0.16, or v0.17 before drawing v0.18 rows. non-circularity boundary: The primary reliability predictor is label-blind frame spread. Label-aware score-split anatomy is reported separately and cannot rescue the primary frame-reliability statistic. ``` Forbidden: ```text changing the score, frame set, D5 gates, stability labels, or permutation seed after seeing v0.18 rows selecting cells or rows by vf, score, zone, frame spread, D5 output, or AUC dropping frame-fragile rows from the primary statistic lowering the pooled transfer floor or the reliability bars after execution using label-aware anatomy to claim a non-circular reliability pass promoting to Tier-3, full-catalog prevalence, or theorem-facing status ``` ## Frozen Inputs Carried forward unchanged unless explicitly listed as v0.18-specific: ```text target: liao2021 non-hierarchical catalog target tier: Tier 2, Li/Liao lineage target SHA-256: 9c06eedc41b537b2ed926217cdf149d9f808a21866148ea3d89b9eb3c6069fd4 D5 measurement: v0.7/v0.13a DOP853 pipeline rtol/atol: 1e-12 / 1e-12 max_step: 0.02*T D5 gates: symplecticity <= 1e-4; reciprocal-pair residual <= 1e-4 frames: {0, 37, 90, 211} degrees score: median(vf_0, vf_37, vf_90, vf_211) success rule: all four frames integrate and pass D5 gates stability label: source-provided linear S/U label primary row sampling: uniform without replacement within (mass_cell, source_label) seed: 20260523 ``` ## v0.18 Domain v0.18 widens the mass-cell grid but keeps the sampling discipline: ```text mass-cell construction: `build_mass_cells` generalized to 8 parts: sort by normalized mass a, split_evenly(..., 8); within each a-slice sort by normalized mass b, split_evenly(..., 8) holdout: v0.14 sample_frame.csv + v0.15 sample_frame.csv + v0.16 sample_frame.csv + v0.17 sample_frame.csv supported cell: eligible stable >= 80 AND eligible unstable >= 80 rows per cell: 160 = 80 stable + 80 unstable expected supported: 18 cells expected rows: 2880 source-support gate: exactly 18 supported cells; otherwise blocked_for_lock_review ``` Source-only feasibility scan (no vf, score, D5, or AUC computed) after excluding the v0.14-v0.17 sample frames: ```text grid parts supported cells with >=80 S and >=80 U rows at 80/80 4 x 4 7 1120 5 x 5 10 1600 6 x 6 12 1920 7 x 7 16 2560 8 x 8 18 2880 <-- proposed v0.18 default 10 x 10 24 3840 12 x 12 34 5440 16 x 16 46 7360 ``` The 8 x 8 grid is the proposed lock default: wide enough for a cell-level reliability test, but still a staged sharded run rather than a full-catalog weeklong sweep. Lock verification: the privileged-truth source scan reproduced the table above exactly, including the 4 x 4 anchor (`7` supported cells) and the 8 x 8 default (`18` supported cells) with a disjoint quadruple holdout of 4640 rows. The 4 x 4 anchor confirms the generalized grid builder matches the v0.14-v0.17 construction before widening. ## Required Prior Receipts The runner must assert before drawing rows: ```text v0.13 target inventory includes liao2021 as Tier 2 v0.13a leakage bounded 0.0 and adapter parity passed v0.13b verdict = coarse_zone_rule_frame_stable_enough_to_test v0.14 verdict = sample_transfer_undecidable_coverage v0.15 verdict = stable_support_transfer_directional_weak v0.16 verdict = tail_resolved_transfer_passes_clean v0.17 verdict = heterogeneous_transfer_replicates_clean all v0.14-v0.17 target SHA values match this form's target SHA all v0.14-v0.17 sample_frame.csv files exist for the quadruple holdout ``` Any mismatch aborts. ## Primary Measurement For every successful orbit: ```text vf_frames: [vf_0, vf_37, vf_90, vf_211] score: median(vf_frames) frame_spread: max(vf_frames) - min(vf_frames) zone: report-only coarse zone under {0.25, 0.50}; non-gating ``` Within each primary cell: ```text AUC_cell: Mann-Whitney AUC, stable ranked above unstable D_cell: S_success * U_success frame_p50/p75/p90/p95/max over successful rows score quantiles by source label S_p50_minus_U_p50 report-only zone-2 fraction report-only ``` Primary cell coverage: ```text cell enters primary iff S_success >= 50 AND U_success >= 50 coverage pass iff primary_cells >= 16 AND primary_success_rows >= 2400 ``` Attrition policy: ```text clean: attrition <= 0.05 warning: attrition <= 0.10 AND Wilson95_high <= 0.20 blocked: attrition > 0.10 OR Wilson95_high > 0.20 ``` Frame-spread is **not** used to drop rows or cells. It is the object under test. Only a catastrophic global failure blocks: ```text blocked_by_global_frame_instability iff median(frame_spread) > 0.20 OR p90(frame_spread) > 0.75 ``` ## Baseline Transfer Check Before the reliability question is interpreted, v0.18 repeats the pooled within-cell transfer statistic on the wider grid: ```text AUC_cond = sum(J_cell) / sum(D_cell) permutation: 100000 within-cell S/U label shuffles, seed 20260523 pass: AUC_cond >= 0.55 AND p_perm <= 0.01 directional weak: 0.50 < AUC_cond < 0.55 AND p_perm <= 0.01 fail: AUC_cond <= 0.50 OR p_perm > 0.01 ``` This check does not need to pass for the reliability map to be reported, but a pooled fail limits the chapter to "why the wider grid failed," not confirmation. Because v0.18 uses a finer 8 x 8 conditioning grid, its pooled AUC is not numerically interchangeable with the v0.16/v0.17 4 x 4 AUC of ~0.647, even though it keeps the same `>=0.55` floor. ## Primary Reliability Statistic The non-circular reliability predictor is cell-level frame stability: ```text cell_reliability = -log10(frame_p90 + 1e-9) outcome = AUC_cell statistic = Spearman rho(cell_reliability, AUC_cell) null = 100000 random pairings of reliability values to AUC values over the primary cells, seed 20260523 (Monte Carlo; 18! is too large for the exact v0.17-style enumeration) direction = higher reliability -> higher AUC pass bar = rho >= 0.45 AND one-sided p_reliability <= 0.05 ``` This is the only verdict-bearing "reliability drives AUC" statistic. It is label-blind on the predictor side: frame spread is computed without using S/U labels or score splits. ## Reversal Guard The reliability interpretation must not hide a strong, frame-stable competing signal. Define: ```text frame_fragile_cell = frame_p90 >= 0.10 decisive_negative_cell = AUC_cell <= 0.45 AND reverse-direction cell permutation p_reverse <= 0.05 stable_decisive_negative = decisive_negative_cell AND NOT frame_fragile_cell ``` Reversal guard passes iff `stable_decisive_negative_count == 0`. `p_reverse` is a per-cell within-cell S/U-label permutation, one-sided for `AUC_cell < 0.5`, preserving the cell's score multiset and S/U counts. It uses 100000 Monte Carlo shuffles with seed 20260523 offset deterministically by cell order. Cells with AUC below 0.5 but not decisive by this rule are reported as near-null or weak-reversal anatomy, not as a competing law. ## Label-Aware Anatomy (Report-Only) For interpretation, but not for the primary reliability pass, report: ```text per-cell S/U score quantiles S_p50_minus_U_p50 score IQR by label and pooled zone saturation period / energy / angular momentum summaries if already available in the row receipts band_A / band_B membership from v0.13b, if the orbit index lies in the known fragile bands ``` This panel may explain a low cell as "near-null" or "fragile," but it cannot change the primary reliability statistic or any verdict branch. Readback must explicitly surface the frame-p90 distribution across the 18 primary cells (min, median, p75, p90, max, plus the sorted per-cell table). If only a few cells populate the low-reliability tail, the report must say so; the Spearman power then comes from a small number of detector cells, not a broad continuous spread. ## Verdict Tree ```text blocked_by_receipt required prior receipts / target SHA / sample-frame files missing or inconsistent blocked_for_lock_review 8 x 8 source-support census yields anything other than the locked 18 supported cells blocked_by_attrition attrition_fraction > 0.10 OR attrition_wilson95_high > 0.20 blocked_by_global_frame_instability median(frame_spread) > 0.20 OR p90(frame_spread) > 0.75 blocked_by_coverage primary_cells < 16 OR primary_success_rows < 2400 wider_transfer_fails AUC_cond <= 0.50 OR p_perm > 0.01 wider_transfer_directional_weak 0.50 < AUC_cond < 0.55 AND p_perm <= 0.01 wider_transfer_replicates_reliability_unresolved AUC_cond >= 0.55 AND p_perm <= 0.01 AND (rho < 0.45 OR p_reliability > 0.05) frame_reliability_supported_but_reversal_guard_fails AUC_cond >= 0.55 AND p_perm <= 0.01 AND rho >= 0.45 AND p_reliability <= 0.05 AND stable_decisive_negative_count > 0 reliability_drives_per_cell_auc_supported AUC_cond >= 0.55 AND p_perm <= 0.01 AND rho >= 0.45 AND p_reliability <= 0.05 AND stable_decisive_negative_count == 0 ``` Attrition warning without hard block appends `_with_attrition_warning`. ## Required Outputs ```text results/isotrophy/k-facet-v18-liao2021-reliability-auc/ manifest.json source_support_census.csv sample_frame.csv sample_shard_XX_of_NN.csv per_row_sample.csv per_cell_auc.csv frame_reliability_map.csv reliability_auc_test.json reversal_guard.json anatomy_sidecar.csv permutation_summary.json operator_commands.md ``` `manifest.json` must include verdict, startedAt/completedAt, gitCommit, target_sha256, excluded sample-frame counts, sample_seed, grid parts, supported_cells, sample_rows_requested/success, attrition + Wilson interval, primary_cells, primary_success_rows, AUC_cond, J_cond, D_cond, p_perm, reliability_rho, reliability_p, stable_decisive_negative_count, frame-spread global median/p90, target_tier=2, and the claim boundary. ## Implementation Commands (to add after lock) The run is above the inline agent budget. Implementation should stage the exact operator commands and shard the D5 measurement: ```powershell npm run isotrophy:v18:prepare npm run isotrophy:v18:shard -- --shard 0 --shards 16 npm run isotrophy:v18:shard -- --shard 1 --shards 16 # ... npm run isotrophy:v18:shard -- --shard 15 --shards 16 npm run isotrophy:v18:merge npm run isotrophy:v18:analyze ``` Expected cost is roughly 2.5-3x the 1120-row v0.16/v0.17 measurement, because the proposed sample is 2880 rows and uses the same four-frame D5 score. The operator command file must record measured per-row rate after the first shard finishes and revise the wall-clock estimate. ## Claim Boundary Allowed if `reliability_drives_per_cell_auc_supported`: ```text Across a fresh wider liao2021 mass-cell map, per-cell transfer strength tracks the frame reliability of the tail-resolved velocity-fraction read. Low or reversed cells are not evidence of a stable competing law unless they survive the reversal guard; the supported claim is an instrument-reliability explanation of the reproducible v0.16/v0.17 heterogeneity. ``` Bounded exactly as before: Tier-2 / Li-Liao lineage / liao2021 stable-support sampling / within-cell rank signal / tail-resolved continuous score / not coarse-zone / not full-catalog prevalence / not Tier-3 independent / not theorem-facing. If reliability fails, the allowed claim is only that the v0.17 reliability-map interpretation did not survive a wider fresh-cell test. That does **not** erase the v0.16/v0.17 external transfer receipts. ## Lock-In Statement Committed as a draft before any v0.18 runner or v0.18 sample exists. Any change to the grid, holdout, sample size, score, D5 path, reliability statistic, bars, reversal guard, verdict tree, or claim boundary after execution is a re-registration.