# v0.17 liao2021 Tail-Resolved Heterogeneity Replication Form ## Result (2026-06-02) **Verdict: `heterogeneous_transfer_replicates_clean`** -- the top of the tree. On fresh triple-held-out rows the Tier-2 tail-resolved transfer replicates AND its mass-cell heterogeneity reproduces. ```text pooled replication: AUC_cond 0.646875 (J 28980 / D 44800) vs v0.16 0.6469866 -> clears 0.55 p_perm 1.0e-5 attrition 0.0000 frame-spread median 0.00037 p90 0.0256 (clean) heterogeneity: Spearman rho 1.0 exact-perm p_rho 1/5040 = 0.000198 (only the correct pairing of 5040 reaches rho=1) -> heterogeneity replicates ``` **The pooled transfer is not a v0.16 fluke.** A pre-registered replication on fresh rows (excluding all v0.14/v0.15/v0.16 orbits, 0/0/0 overlap) lands AUC_cond 0.646875 -- within 0.0001 of v0.16's 0.6469866 -- at the permutation floor. The held-out external Tier-2 transfer is confirmed twice. **The mass-cell heterogeneity is reproducible structure, not one-sample texture.** All seven fresh per-cell AUCs preserve v0.16's exact rank order (rho=1.0), and all seven preserve their direction relative to 0.5 -- including both sub-0.5 cells staying sub-0.5 (`qA2_qB1` 0.432->0.453, `qA3_qB0` 0.470->0.474). The local pattern is real and reproducible. The fresh AUCs are genuinely different from v0.16 (max abs diff 0.031), so rho=1.0 is a true rank replication, not a re-read. **Honest bound (n=7):** rho=1.0 is a seven-point rank concordance; the exact-perm p=1/5040 is genuinely significant (a perfect ordering is unlikely by chance), but the claim is "reproducible seven-cell heterogeneity," not a mechanism. WHY `qA2_qB1` and `qA3_qB0` sit below 0.5 is the open question the non-gating anatomy sidecar opens. **Post-hoc anatomy (interpretation, not a registered mechanism).** Ordered by fresh v0.17 AUC, the sidecar reads the replicated pattern as an instrument-reliability map: ```text cell AUC masses(a,b,c) zone2 S_p50 U_p50 S-U frame_p90 qA2_qB1 0.453 .311 .327 .362 158 .9366 .9687 -0.0322 0.321 qA3_qB0 0.474 .320 .325 .355 154 .9461 .9540 -0.0079 0.025 qA1_qB0 0.563 .302 .325 .376 157 .9937 .9938 -0.0000 0.022 qA3_qB2 0.653 .326 .333 .341 158 .9548 .9198 +0.0351 0.004 qA3_qB1 0.700 .324 .330 .346 156 .9558 .9286 +0.0272 0.009 qA3_qB3 0.744 .324 .336 .339 159 .9517 .8472 +0.1044 0.005 qA0_qB0 0.941 .289 .327 .383 157 .9966 .9905 +0.0061 0.001 ``` `qA2_qB1` is the frame-fragile cell: its frame-spread p90 is 0.321, over an order of magnitude above the well-calibrated cells and exactly the localized fragility already flagged by the v0.13b frame audit. `qA3_qB0` is closer to a near-null than to a competing physics: fresh AUC 0.474 with a median score gap of only -0.008. Everywhere the ensemble is frame-stable and the cell has score resolution, the v0.11 direction holds. Zone saturation is uniform (154-159/160 rows in zone 2), so the coarse zone is not the discriminator. This anatomy is coherent with the receipts, but it remains descriptive: confirming "reliability drives per-cell AUC" would require its own wider-cell chapter. **Independent verification.** A standalone brute-force pair-count pooled AUC + a hand-rolled rank/Pearson exact-permutation Spearman (independent of the runner's midrank path) reproduced AUC_cond 0.646875, J 28980, D 44800, rho 1.0, p_rho 1/5040 BIT-FOR-BIT, and confirmed the v0.17 vector differs from v0.16 (not a re-read). Receipt + verifier: `results/isotrophy/k-facet-v17-liao2021-heterogeneity/` (`manifest.json`, `per_cell_rank.csv`, `heterogeneity_replication.json`, `anatomy_sidecar.csv`, `_independent_check.{py,json}`). **Claim (locked):** the tail-resolved velocity-fraction projection transfers on fresh held-out liao2021 samples AND its mass-cell heterogeneity is reproducible enough to report as structure. Bounded: Tier-2 / Li-Liao lineage / stable-support region / within-cell rank signal / not coarse-zone / not full-catalog prevalence / not Tier-3 independent / not theorem-facing. The v0.16 pass stands; v0.17 strengthens it from a single external pass to a replicated one with reproducible per-cell structure. --- Status: **OPERATOR LOCK 2026-06-02; VERDICT LANDED `heterogeneous_transfer_replicates_clean` 2026-06-02.** At lock time no v0.17 runner had been written, no v0.17 sample had been drawn, no v0.17 D5 rows had been integrated, and no v0.17 statistic had been computed. The completed run followed the locked form: fresh-row REPLICATION of v0.16, not a new feature search. Prepared receipt: ```text command: npm run isotrophy:v17:prepare out: results/isotrophy/k-facet-v17-liao2021-heterogeneity/ supported: 7/7 locked cells sample: 1120 rows (80 S + 80 U per cell) holdout: excluded 3520 prior sample rows (v0.14 + v0.15 + v0.16) overlap: v17 vs v14/v15/v16 = 0 / 0 / 0 status: tail_resolved_heterogeneity_prepared_not_measured ``` Lock-review adjustments folded in (2026-06-02): ```text heterogeneity stat: recast from a bare Spearman rho>=0.60 threshold to an EXACT permutation Spearman test (7! = 5040 enumeration, p <= 0.05); rho>=0.60 alone is ~p 0.07 at n=7, not significant. sign concordance: demoted to a report-only per-cell panel with per-cell SE; only the ~3-SE-separated cells carry a real directional prediction. verdict gate: the POOLED replication is the sole verdict-bearing gate; the heterogeneity test only chooses between the two pooled-pass labels. open decisions: sample 80/80 (parity); exact-perm rho bar; lock the exact reference vector (rho consumes its rank order); add Option C anatomy sidecar non-gating on existing v0.16 rows. verified pre-lock: pinned v0.16 vector == receipt (0.0 diff); triple-holdout 80/80 feasible in all 7 cells (smallest eligible stable pool 322). ``` ## Frame v0.16 landed the first clean Tier-2 external transfer of the tail-resolved score (`AUC_cond = 0.6470`, `p_perm = 1.0e-5`, 1120 fresh double-holdout rows). It is real at the pooled within-cell level but not a uniform per-cell law: ```text in-direction cells: qA0_qB0, qA1_qB0, qA3_qB1, qA3_qB2, qA3_qB3 reversed cells: qA2_qB1, qA3_qB0 range: AUC_cell 0.432 -> 0.972 ``` v0.17 asks the replication question: > Does the tail-resolved velocity-fraction signal replicate as a pooled external transfer > at the locked v0.16 floor on fresh rows, and does the v0.16 mass-cell heterogeneity > pattern repeat well enough to report as structure rather than one-sample texture? ## Integrity Caveat ```text replication, not discovery: v0.17 may use v0.16 to DEFINE the replication target (the per-cell reference vector) precisely because it replicates a discovered pattern on FRESH rows -- it does not discover a new law. feature: FROZEN. The v0.16 4-frame ensemble-median score is reused exactly. No new feature, kernel, cutpoint, or mass partition. domain: FRESH (triple-holdout). The seven v0.16 supported cells, excluding every v0.14, v0.15, AND v0.16 sampled orbit. firewall: the heterogeneity test MUST NOT rescue a pooled failure; a heterogeneity failure MUST NOT demote the v0.16 pass. ``` Frozen from v0.14 / v0.15 / v0.16 (unchanged): ```text target file SHA-256: 9c06eedc41b537b2ed926217cdf149d9f808a21866148ea3d89b9eb3c6069fd4 target tier: Tier 2 only mass-cell construction: v0.14 nested sorted-mass 4 x 4 cells D5 measurement: v0.7/v0.13a DOP853 pipeline (rtol=atol=1e-12, max_step 0.02, symplecticity/reciprocal gates 1e-4) score: median(vf_0, vf_37, vf_90, vf_211) (frames {0,37,90,211} deg) all-four-frames rule: success requires all four frames to integrate AND pass D5 gates; any failing frame counts as attrition (no partial medians) within-cell statistic: pooled conditional rank AUC (Mann-Whitney, ties 0.5) effect floor: AUC_cond >= 0.55 permutation p gate: p_perm <= 0.01 permutation: 100000 within-cell S/U label shuffle, seed 20260523 frame-spread gate: median(frame_spread) <= 0.10 & p90 <= 0.50 clean; <= 0.20 & 0.75 warning; > 0.20 or > 0.75 blocked ``` **The effect floor is HELD at 0.55. It is not lowered to v0.16's 0.647 nor to any other value.** Forbidden: ```text introducing any new feature, kernel, cutpoint, or mass partition lowering the effect floor or the p gate using the heterogeneity test to rescue a pooled failure using a heterogeneity failure to demote or revise the v0.16 pass selecting sampled rows by any vf, score, zone, or D5 output (draw on mass_cell + source stability label only) including any v0.14, v0.15, OR v0.16 sampled orbit in the v0.17 primary sample dropping frame-fragile rows from the primary statistic tuning the reference vector, the rho bar, or the sign panel after seeing v0.17 rows promoting to Tier-3 / independent confirmation or theorem-facing status ``` ## Required Prior Receipts The runner must assert all of the following before drawing a sample: ```text v0.13 target inventory includes liao2021 as Tier 2; v0.13a leakage bounded 0.0; 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 v0.14 + v0.15 + v0.16 target SHA all match this form's target SHA v0.14, v0.15, AND v0.16 sample_frame.csv all exist (for the triple holdout) v0.16 per_cell_rank.csv exists and supplies the reference vector ``` Any mismatch aborts. ## Pinned v0.16 Reference Vector (verified == receipt, 0.0 diff) ```text mass_qA0_qB0 0.97203125 mass_qA3_qB0 0.47046875 mass_qA1_qB0 0.57515625 mass_qA3_qB1 0.69593750 mass_qA2_qB1 0.43156250 mass_qA3_qB2 0.63921875 mass_qA3_qB3 0.74453125 ``` The heterogeneity Spearman test consumes the RANK ORDER of this vector; the exact values are pinned for transparency and the report-only sign panel. ## Source-Support Census (fresh triple-holdout) Signal-blind (source masses + stability labels only). Eligible = source minus the v0.14 ∪ v0.15 ∪ v0.16 holdout (3520 orbits excluded). Independently reproduced with v0.14's `build_mass_cells`: | mass cell | eligible S | eligible U | disposition | |---|---:|---:|---| | `mass_qA0_qB0` | 322 | 7,744 | supported | | `mass_qA1_qB0` | 488 | 7,578 | supported | | `mass_qA2_qB1` | 2,584 | 5,481 | supported | | `mass_qA3_qB0` | 2,434 | 5,632 | supported | | `mass_qA3_qB1` | 2,998 | 5,067 | supported | | `mass_qA3_qB2` | 2,261 | 5,804 | supported | | `mass_qA3_qB3` | 958 | 7,107 | supported | Locked rule: supported iff eligible S >= 80 AND eligible U >= 80 after the triple exclusion. Expected supported cells: 7 (smallest eligible stable pool 322, 4x the draw). ## Sample Design ```text domain: the seven v0.16 supported cells rows per cell: 160 (80 stable + 80 unstable) -- v0.16 parity expected rows: 1120 seed: 20260523 sampling: uniform without replacement within (mass_cell, source_label) holdout rule: exclude every orbit_index in v0.14 AND v0.15 AND v0.16 sample_frame.csv, applied BEFORE the seeded draw ``` If any supported cell has fewer than 80 eligible stable or unstable rows after the triple exclusion, the run aborts for lock review. The draw is outcome-balanced by source label and blind to vf / score / zone (case-control; AUC is prevalence-invariant; no prevalence estimate is licensed). ## D5 Measurement + Score Per orbit, the frozen four-frame ensemble (identical to v0.16): integrate the {0,37,90,211}-degree rotations of the CoM-centered state through the frozen D5 path, compute vf at each, `score = median(vf_0, vf_37, vf_90, vf_211)`. An orbit is a success only if all four frames integrate and pass both D5 gates; otherwise it is attrited. Attrition policy (frozen): `<=0.05` clean; `0.05-0.10` with Wilson95_high `<=0.20` warning; `>0.10` or Wilson95_high `>0.20` -> `blocked_by_attrition`. ## Primary Domain A supported cell enters the primary statistic iff `N_success >= 120`, `S_success >= 50`, `U_success >= 50`. Coverage gate: `primary_supported_cells >= 6` AND `primary_success_rows >= 900`; else `blocked_by_coverage`. ## Primary Statistic -- Pooled Replication (the sole verdict gate) Within each primary cell, Mann-Whitney `J_cell = #[score(S)>score(U)] + 0.5*ties`, `D_cell = S*U`; pool `AUC_cond = sum J_cell / sum D_cell`. Direction pre-registered: stable ranks above unstable. Binding null: 100000 within-cell S/U label shuffle preserving each cell's score multiset and S/U counts, seed 20260523, one-sided, `p_perm = (1 + #perm >= observed) / (1 + 100000)`. Pooled replication passes iff `AUC_cond >= 0.55 AND p_perm <= 0.01` (the exact v0.16 floor, unchanged). ## Heterogeneity Replication Check (secondary; chooses between pooled-pass labels only) Computed ONLY if the pooled replication passes. Compares the fresh v0.17 per-cell AUC vector to the pinned v0.16 reference vector over the matched primary cells. ```text statistic: Spearman rho( v0.16 reference AUC_cell , v0.17 AUC_cell ) over matched cells null: EXACT permutation -- enumerate all k! pairings of the k matched cells (k=7 -> 5040), p_rho = #{rho_perm >= rho_obs} / k! bar: heterogeneity replicates iff p_rho <= 0.05 ``` At n=7, `p_rho <= 0.05` corresponds to `rho >= ~0.64` (Sigma d^2 <= 20); a bare `rho >= 0.60` is only ~`p 0.07` and is NOT used as the bar. The n=7 power limit is disclosed: this is a low-power rank check, not a high-resolution map test. Report-only per-cell sign panel (NON-gating): for each cell, report `v0.17 AUC_cell`, `v0.16 reference`, direction-vs-0.5 match, `|AUC-0.5|`, and an approximate per-cell AUC SE (`~0.032` near 0.5 at 80/80). Only the cells with `|reference - 0.5| > ~0.10` (`qA0_qB0`, `qA3_qB3`, `qA3_qB1`, `qA3_qB2`) carry a real directional prediction; `qA1_qB0` (+0.075), `qA2_qB1` (-0.068) sit ~2 SE out (lean-but-uncertain) and `qA3_qB0` (-0.030, ~1 SE) is sampling-indeterminate. A sign flip in a sub-2-SE cell is expected and is NOT a heterogeneity failure on its own. ## Frame-Stability Gate Carried forward from v0.16: `frame_spread = max(vf)-min(vf)` over the four frames; report median/p75/p90/p95/max overall + by cell + by fragile band; gate `median<=0.10 & p90<=0.50` clean / `<=0.20 & <=0.75` warning / else `blocked_by_frame_instability`. ## Verdict Tree ```text blocked_by_receipt required prior receipts / SHA / triple-holdout exclusion missing or inconsistent OR supported-cell census deviates from the locked rule and cannot draw 80/80 blocked_by_attrition attrition_fraction > 0.10 OR attrition_wilson95_high > 0.20 blocked_by_frame_instability median(frame_spread) > 0.20 OR p90(frame_spread) > 0.75 blocked_by_coverage primary_supported_cells < 6 OR primary_success_rows < 900 tail_resolved_transfer_not_replicated AUC_cond <= 0.50 OR p_perm > 0.01 (clear null on fresh rows) tail_resolved_transfer_replication_directional_weak 0.50 < AUC_cond < 0.55 AND p_perm <= 0.01 (directional but below the v0.16 floor) pooled_transfer_replicates_heterogeneity_unresolved AUC_cond >= 0.55 AND p_perm <= 0.01 AND attrition/frame not hard-blocked AND heterogeneity p_rho > 0.05 heterogeneous_transfer_replicates_clean AUC_cond >= 0.55 AND p_perm <= 0.01 AND attrition clean AND frame clean AND heterogeneity p_rho <= 0.05 ``` A pooled pass under an attrition/frame WARNING band (not a hard block) appends a `_with_warning` note to the pooled-pass label; it does not change the pass/fail. ## Required Outputs ```text results/isotrophy/k-facet-v17-liao2021-heterogeneity/ manifest.json source_support_census.csv sample_frame.csv sample_shard_XX_of_NN.csv per_row_sample.csv per_cell_rank.csv frame_dispersion.csv heterogeneity_replication.json (rho, p_rho, matched cells, v0.16 vs v0.17 per-cell AUC, sign panel + SE) anatomy_sidecar.csv (Option C, non-gating) permutation_summary.json operator_commands.md ``` `manifest.json` must include: verdict, startedAt/completedAt, gitCommit, target_sha256, v14/v15/v16 excluded counts, sample_seed, supported_cells, sample_rows_requested/success, attrition (+Wilson), primary_supported_cells, primary_success_rows, frame_spread median/p90, AUC_cond, J_cond, D_cond, p_perm, heterogeneity_rho, heterogeneity_p_rho, target_tier=2. ## Anatomy Sidecar (Option C -- non-gating, existing v0.16 rows) On the ALREADY-MEASURED v0.16 rows only (no new D5), report per cell -- especially the two reversed cells `qA2_qB1`, `qA3_qB0`: mass coordinates, score quantiles, frame spread, zone saturation, and any already-present period / energy / angular-momentum summaries. Pure interpretation; it cannot set or change any v0.17 verdict. ## Claim Boundary Even a clean v0.17 pass remains: Tier-2 / Li-Liao-lineage external; liao2021 stable-support region only; within-cell rank signal only; tail-resolved continuous score only; not coarse-zone transfer; not full-catalog prevalence; not Tier-3 independent; not theorem-facing. ```text heterogeneous_transfer_replicates_clean -> allowed claim: "The tail-resolved velocity-fraction projection transfers on fresh held-out liao2021 samples and its mass-cell heterogeneity is reproducible enough to report as structure, not merely v0.16 texture." (Tier-2, bounded as above.) pooled_transfer_replicates_heterogeneity_unresolved -> allowed claim: "The pooled within-cell transfer replicates on fresh rows; local per-cell signs remain descriptive only (heterogeneous in the discovery sample, n=7 rank check inconclusive)." tail_resolved_transfer_not_replicated / _directional_weak -> allowed claim: limited to the non-replication; does NOT retroactively demote v0.16 (a single fresh-sample miss bounds the claim's robustness, it does not erase the v0.16 receipt). blocked_* -> claim limited to the blocking condition. ``` ## Lock-In Statement Committed before the v0.17 runner is written. Any change to the feature, frame set, sample, triple-holdout rule, reference vector, decision bars, effect floor, permutation, heterogeneity statistic, firewall, or claim boundary after runner execution is a re-registration. The runner imports the frozen v0.14/v0.15/v0.16 D5 + frame + ensemble + AUC + permutation symbols unchanged and adds only the triple holdout, the exact-permutation Spearman heterogeneity check, and the non-gating anatomy sidecar.