# v0.12 External Frozen Transfer Form Lock Status: **OPERATOR LOCK 2026-05-30.** No v0.12 runner has been written, no v0.12 command has been run, and no supplementary-A row has been scored for this chapter at lock time. This document locks the frozen transfer domain, overlap quarantine, attrition policy, statistic, verdict tree, diagnostics, and claim boundary before any v0.12 scoring. Reviewed for self-consistency, non-circularity, and integrity: - **Strongest non-circularity in the program — breaks the DOMAIN.** The v0.11 rule (cutpoints {0.25,0.50}, zone order, S-up-zone direction) is frozen and pinned by asserting the v0.11 receipt before any scoring; supp-A is genuine out-of-sample. The disallowed-feature list is comprehensive (no cutpoint tuning, no classifier, no raw vf, no period/energy/|L|/branch/z0/eigenvalue features). - **Convention check (done at lock):** supp-A and supp-B use the byte-identical mirrored-velocity ansatz and both canonicalize `z0 > 0`, so a shared orbit lands at identical ICs and the exact 1e-9 quarantine is the correct identity key. The feature (Floquet vf) is well-defined on supp-A (same orbit family, same v0.7 D5 monodromy/gauge conventions) — this is a true transfer, not a domain mismatch. - **Effect floor (AUC_cond >= 0.55) defeats the large-N significance trap:** on a 10,059-row table a tiny AUC could clear a permutation p with no real effect; the 0.55 floor + the `directional_weak` branch (0.50 < AUC < 0.55, p <= 0.01) keep that from masquerading as a transfer while preserving the information. - **Null is appropriate:** stratified within-`m3` label permutation (preserve S_m/U_m), n=100000, seed 20260523 — the same null v0.11 used as its sanity sidecar, made binding here to avoid depending on a novel large-support exact kernel; exact enumeration kept as an optional cheap sidecar (support <= 250000), never binding. - **Attrition is evidence, not housekeeping:** <=5% clean / <=20% warning (PASS reworded to "analyzable-domain transfer") / >20% blocked, plus floor blocks (primary < 500 rows or < 5 both-class strata). Inherits the v0.7 D5 integration lessons; smoke/projection is required before any long run and the agent may not run the full pass inline. - **Claim boundary is the most carefully bounded in the program:** a PASS is a same-paper external-supplement transfer only — not universe-wide, not independent-catalog, no v0.10b overturn, no global predictor, no K_facet revision, no theorem-facing promotion, nothing about excluded rows. Adjustment made at lock (one): hardened the overlap quarantine with an ansatz-reflection-image check — `(z0,vx,vy,vz) -> (-z0,vx,vy,-vz)` at the same `(m3,T)` — folded into the combined overlap fraction and the same `> 0.05` leakage abort, so the external claim is robust to the two supplements having picked opposite vz-sign representatives of a shared orbit (referee-proof de-duplication; expected near-zero given the shared `z0 > 0` canonicalization). ## Frame v0.11 registered the frozen velocity-fraction zone order as a conditional within-`m3` rank signal on the analyzable supplementary-B piano-trio table: ```text AUC_cond: 0.6782549421 exact p: 2.046197217e-7 verdict: m3_conditional_vf_rank_passes ``` That was still an in-sample conditional result. v0.12 asks the next cleaner evidence-upgrade question: > If the v0.11 rule is frozen exactly, does it transfer to a different > Li-Liao catalog table that was not used to discover, tune, or score v0.11? The proposed target is supplementary-A: ```text docs/isotrophy/supplementary-A_periodic-3d_mirror.txt ``` This is a 10,059-row 3D periodic-orbit catalog with the same compact mirrored ansatz and S/U stability labels. It is external to the supplementary-B v0.11 table, but it is still a same-paper / same-source-family transfer. A PASS would therefore upgrade the evidence from "supp-B in-sample conditional signal" to "same-paper external supplement transfer." It would not be a universe-wide validation and would not license a claim over unrelated astronomical catalogs. ## Integrity Caveat The rule is frozen because v0.11 has already looked at supplementary-B: ```text zone_index: positional-dominant = 0 if velocity_fraction < 0.25 mixed = 1 if 0.25 <= velocity_fraction < 0.50 velocity-heavy = 2 if velocity_fraction >= 0.50 ``` v0.12 may not tune those cutpoints, fit mass-specific thresholds, train a classifier, use raw `velocity_fraction` as a continuous score, add period, energy, angular momentum, branch labels, `z0`, eigenvalue magnitudes, spectral radius, unit-circle counts, or any other orbital feature to the primary score. `m3` is allowed only as a conditioning stratum, exactly as in v0.11. The question is not "can we build the best predictor?" It is: ```text Within fixed m3 strata in a new table, does the frozen v0.11 zone order rank stable rows above unstable rows? ``` ## Frozen Inputs Discovery / rule source: ```text docs/isotrophy/supplementary-B_piano-init-condit-3d.txt results/isotrophy/k-facet-v11-m3-conditional-vf-rank/manifest.json ``` Primary transfer target: ```text docs/isotrophy/supplementary-A_periodic-3d_mirror.txt ``` The runner must assert the v0.11 receipt before doing any v0.12 scoring: ```text v0.11 verdict: m3_conditional_vf_rank_passes v0.11 AUC_cond: 0.6782549421 v0.11 exact p: 2.046197217e-7 v0.11 zone rule: {0.25, 0.50} ``` Any mismatch aborts. No v0.12 branch may reinterpret v0.11. ## Source Profile Gate Before integration or scoring, parse the target and write a source profile: ```text expected data rows: 10059 required numeric columns: m3, z0, vx, vy, vz, T required label column: stability in {S, U} fixed ansatz: m1=m2=1, m3 variable, mirrored velocities ``` Abort if the target does not parse, if the data row count is not 10,059, if any required numeric column is missing, or if any stability label is outside `{S,U}`. The source profile must report: ```text row count m3 strata S/U counts by m3 period min/median/max by m3 candidate primary strata before overlap and attrition gates ``` ## Overlap Quarantine v0.12 is a transfer test, so rows already consumed by prior isotrophy evidence must not enter the primary statistic. Quarantine sources: ```text docs/isotrophy/supplementary-B_piano-init-condit-3d.txt results/isotrophy/m3eq1-sigma3-precondition-fixed-inverse-orientation-25/ results/isotrophy/k-facet-v03-freeze-supplementary-b-comparison/ results/isotrophy/k-facet-v11-m3-conditional-vf-rank/ ``` Row identity is numeric, not by orbit label. A target row is marked overlap if: ```text same m3 and max_abs_delta(z0, vx, vy, vz, T) <= 1e-9 ``` Labels, row order, and `O_index` are not used for matching. ### Ansatz reflection image (added at lock) Both supplements share the **identical** mirrored-velocity ansatz — `r1=(-1,0,0), r2=(1,0,0), r3=(0,0,z0)`; `v1=(vx,vy,vz), v2=(vx,vy,-vz), v3=(-(m1+m2)vx/m3, -(m1+m2)vy/m3, 0)`; `m1=m2=1` — and both canonicalize to `z0 > 0`. A shared physical orbit therefore lands at identical numeric ICs and the exact rule above catches it. The one residual leakage channel is the ansatz's own z-reflection symmetry, under which the same physical orbit maps to ```text (z0, vx, vy, vz) -> (-z0, vx, vy, -vz) at the same (m3, T) ``` If the two supplements ever picked opposite vz-sign representatives for the same orbit, the exact match would miss it. To make the external claim robust to that, a target row is ALSO marked overlap if a discovery/quarantine row matches its reflection image within `1e-9` (same `m3`, same `T`). Exact and reflection-image matches are tallied separately in `overlap_audit.csv`; the **combined** overlap fraction feeds the same `> 0.05 -> external_transfer_blocked_by_leakage` gate. A near-zero reflection-image count (expected, since both supplements canonicalize `z0 > 0`) is itself a clean-separation receipt rather than noise. Overlap policy: ```text overlap rows are excluded from the primary statistic overlap rows are written to report_only_rows.csv if overlap_fraction_of_candidate_primary > 0.05, abort as leakage-prone ``` The strict `m3=1` sigma3 rows from supplementary-A are also excluded from the primary transfer statistic and reported separately. They have already carried K_facet structural-null work and should not quietly double-count as new transfer evidence. ## Velocity-Fraction Receipt The v0.12 feature is the v0.7a D5 velocity-fraction receipt, with the same operational meaning: ```text velocity_fraction = fraction of the selected Floquet direction's physical displacement norm carried by velocity coordinates ``` Selection rule: ```text use the largest-real-part nontrivial Floquet direction under the existing v0.7 monodromy / gauge conventions ``` Numerical controls inherit v0.7a/v0.7a-prime: ```text integrator: DOP853 rtol: 1e-12 atol: 1e-12 max_step_fraction: 0.02 symplecticity gate: 1e-4 reciprocal-pair gate: 1e-4 ``` Rows that fail integration or sanity gates are not silently dropped. They are counted in attrition and written with a machine-readable failure reason. ## Probe Before Full Run The full supplementary-A velocity-fraction pass is expected to exceed the agent inline-run budget. v0.12 therefore has a required probe stage. Probe command shape, after implementation: ```powershell python scripts/v12_external_frozen_transfer.py profile ` --target docs/isotrophy/supplementary-A_periodic-3d_mirror.txt ` --discovery docs/isotrophy/supplementary-B_piano-init-condit-3d.txt ` --out results/isotrophy/k-facet-v12-external-frozen-transfer python scripts/v12_external_frozen_transfer.py smoke ` --target docs/isotrophy/supplementary-A_periodic-3d_mirror.txt ` --discovery docs/isotrophy/supplementary-B_piano-init-condit-3d.txt ` --out results/isotrophy/k-facet-v12-external-frozen-transfer ` --smoke-rows 30 ` --rtol 1e-12 ` --atol 1e-12 ``` The smoke selection is deterministic: ```text choose up to 5 rows from each of 6 m3 bins spanning the target's m3 range within each selected m3 bin, choose period quantiles {min, q25, median, q75, max} after overlap quarantine cap total smoke rows at 30 ``` The smoke writes: ```text seconds_per_row integration_success_fraction sanity_fail_fraction projected_full_wall_clock projected_analyzable_rows ``` If projected full wall-clock exceeds about 10 minutes, the full transfer command must be staged for the operator or a long-budget runner. The agent must not run the full pass inline. ## Probe Results (steps 1-4, executed 2026-05-30) Receipt: `results/isotrophy/k-facet-v12-external-frozen-transfer/` (`manifest.json`, `source_profile.csv`, `overlap_audit.csv`, `integration_smoke.csv`). Runner `scripts/v12_external_frozen_transfer.py` reuses the v0.7a D5 `per_row_pipeline` verbatim -- identical monodromy / gauge / gate conventions, no reimplementation. **Profile (integration-free):** ```text rows: 10,059 (source gate PASS; all labels in {S,U}) m3 strata: 20 over [0.1, 2.0] S = 1,996 U = 8,063 overlap vs supp-B: exact 235 / reflection 0 = 2.75% (< 5% leakage abort) -> reflection 0 = clean-separation receipt (both supplements canonicalize z0>0) strict m3=1 excluded: 1,504 (conservative "all m3=1"; see decision A) nonoverlap candidate rows: 8,320 (>> 500 floor) candidate primary strata: 17 pre-vf (N>=30 / S>=5 / U>=5) (>> 5 floor) ``` **Smoke (30 rows, reused D5 pipeline, 34.9 min wall):** ```text seconds_per_row: 69.77 (median 67, max 214 -- long-period dominated) integration success: 22/30 = 73.3% (6 blocked + 2 sanity-fail) projected full wall-clock: 161 h ~= 6.7 days single-threaded (8,320 rows) projected analyzable rows: ~6,101 ``` **Two findings that gate the full run:** 1. **Cost: 6.7 days single-threaded.** The vf pass is row-independent, so the full run must be SHARDED (Phase-15 pattern; the v0.7a runner already carries R2.C append-per-row resume). 8x concurrent -> ~20 h; 16x -> ~10 h. 2. **Attrition risk vs the locked >0.20 BLOCK gate.** Smoke attrition = 26.7%, and it is period-biased: 7 of 8 failures are long-period (T = 38-201) hitting the integrator step-size wall (6 blocked) or the symplecticity gate (2 sanity). The smoke is period-STRATIFIED by design ({min,q25,median,q75,max} per m3 bin), so it over-weights the hard long-period tail and OVER-ESTIMATES the uniform-catalog `attrition_fraction` the Attrition Policy actually scores. The true full-run rate is uncertain and could land in either the 0.05-0.20 "analyzable-domain transfer" band or the >0.20 "external_transfer_blocked_by_attrition" band. An UNBIASED uniform-random attrition probe (not period-stratified) is the cheap de-risk before committing 6.7 days: if it reads >0.20, the locked policy pre-blocks the full run and the compute is saved. **Staging (step 6) -- the full transfer pass is NOT run inline.** Three operator decisions precede authorizing the full run (step 7): ```text A. m3=1 exclusion: conservative all-m3=1 (drops 1,504; safe over-exclusion) vs strict-sigma3-only (recovers ~1,479 rows; needs a sigma3 pass on supp-A m3=1). B. Attrition de-risk: a uniform-random ~150-row attrition probe for an unbiased attrition_fraction before the full run (recommended). C. Shard count for the full vf pass (8x ~20 h / 16x ~10 h), then build step 7 (stratified-permutation transfer statistic + verdict) on the analyzable output. ``` ### Attrition de-risk probe result (decision B, executed 2026-05-30) A sharded uniform-random SRS (NOT period-stratified) of 300 candidate rows -- 6 shards x 50, seed 20260523, reusing `per_row_pipeline`; the merge reconciles the shards to the exact deterministic sample (`reconcile_abort = None`). ```text uniform attrition_fraction = 0.3433 (103/300: 66 blocked + 37 sanity-fail) Wilson 95% CI = [0.2919, 0.3987] -- entire interval ABOVE 0.20 vs locked 0.20 BLOCK gate = decisive_above (CI low 0.292 >> 0.20; no straddle) verdict implication = external_transfer_blocked_by_attrition ``` Per-m3 the loss is SYSTEMIC, not localized (so no domain restriction rescues it, and restriction would be a disallowed post-hoc move regardless): m3=0.4 is 0% but m3 = 0.5-1.8 run 23-67%, rising with m3 (0.7 -> 35%, 0.8 -> 41%, 1.2 -> 44%, 1.3 -> 53%, 1.6 -> 67%). **Honest correction to the step-5 readback.** It predicted the period-stratified smoke (26.7%) would OVER-estimate the uniform rate. It UNDER-estimated: uniform is 34.3%, higher. The smoke forces each bin's {min,q25} short-period rows (which succeed) into the sample, so it under-represents the catalog's long-period bulk. The directional guess was wrong; the probe was decisive regardless -- which is the whole reason we measured the unbiased rate instead of assuming it. **Verdict: the full transfer run is policy-BLOCKED and is NOT run.** The locked D5 measurement (DOP853, rtol/atol 1e-12, max_step 0.02 T) cannot integrate ~1/3 of supp-A's candidate orbits at the frozen precision (long-period / high-m3 step-size wall + symplecticity failures). Per the Attrition Policy this is `external_transfer_blocked_by_attrition`: NOT a failure of the velocity-fraction hypothesis, but a statement that the frozen measurement cannot support the external transfer question on this target. Both rescue paths are closed by the form --- relaxing precision breaks the "identical frozen v0.7 measurement" requirement (it would no longer be the same feature), and restricting to the short-period analyzable subset is a disallowed post-hoc fail-rescue that would bias the transfer. The ~2.5 h probe saved the projected 6.7-day full run. The supp-B conditional-positive (v0.10a in-sample trend + v0.11 within-m3 rank, exact p = 2.05e-7) stands unchanged; it simply does not receive an external-catalog confirmation from supp-A, because supp-A is numerically intractable for the frozen D5 integrator. A genuinely external confirmation would need either a different target catalog whose orbits integrate cleanly at 1e-12, or a separately-registered measurement chapter -- not a v0.12 refinement. Steps 1-4 plus the decision-B de-risk probe are complete; the unbiased probe decisively blocks the full run under the locked attrition policy, so step 7 (the full 8,320-row pass + transfer statistic) is NOT run. ## Primary Transfer Domain Start from target rows that pass all of: ```text not overlap-quarantined not strict m3=1 sigma3 prior-evidence row velocity_fraction computed symplecticity gate passed reciprocal-pair gate passed ``` Primary `m3` strata must satisfy: ```text N >= 30 S >= 5 U >= 5 ``` Rows in one-class or tiny strata are report-only. They are scored when possible, but they do not enter the primary statistic or p-value. ## Attrition Policy Attrition is evidence, not housekeeping. ```text attrition_fraction = blocked_or_sanity_failed_rows / nonoverlap_candidate_rows ``` Branches: ```text attrition_fraction <= 0.05: clean domain 0.05 < attrition_fraction <= 0.20: attrition warning; scoring may proceed, but any PASS is explicitly "analyzable-domain transfer" rather than clean catalog transfer attrition_fraction > 0.20: verdict = external_transfer_blocked_by_attrition ``` Also block if, after attrition and primary-stratum gates: ```text primary rows < 500 primary both-class m3 strata < 5 ``` These blocks are not failures of the velocity-fraction hypothesis. They mean the locked D5 measurement could not support the external transfer question on this target. ## Fixed Score For every analyzable row: ```text zone_index = 0 if velocity_fraction < 0.25 zone_index = 1 if 0.25 <= velocity_fraction < 0.50 zone_index = 2 if velocity_fraction >= 0.50 ``` No training, smoothing, calibration, fold fitting, or mass-specific adjustment is allowed. ## Primary Statistic Within each primary `m3` stratum, compare every stable row to every unstable row: ```text J_m = #{(S_i, U_j): zone_index(S_i) > zone_index(U_j)} + 0.5 * #{(S_i, U_j): zone_index(S_i) = zone_index(U_j)} D_m = S_m * U_m ``` Pool across primary strata: ```text J_cond = sum_m J_m D_cond = sum_m D_m AUC_cond = J_cond / D_cond ``` `AUC_cond = 0.5` is the frozen conditional baseline. Larger values mean stable rows tend to occupy higher velocity-fraction zones than unstable rows within the same `m3` stratum. ## Binding Null Binding p-value: stratified label permutation. Permutation rule: ```text within each primary m3 stratum, shuffle S/U labels while preserving S_m and U_m recompute J_cond and AUC_cond seed = 20260523 permutations = 100000 p_perm = (1 + count(AUC_perm >= AUC_observed)) / (1 + permutations) ``` The exact v0.11 enumeration kernel may be reported as a sidecar only if the combined support is small enough to compute comfortably: ```text exact sidecar allowed if total doubled-J support <= 250000 exact sidecar never replaces the binding permutation p in v0.12 ``` This avoids making v0.12 depend on a novel large-support exact kernel while still permitting the exact receipt when it is cheap. ## Verdict Tree Run source, overlap, smoke, attrition, and primary-domain gates first. ```text external_transfer_blocked_by_source source profile fails external_transfer_blocked_by_leakage overlap_fraction_of_candidate_primary > 0.05 external_transfer_blocked_by_attrition attrition_fraction > 0.20 OR primary rows < 500 OR primary both-class m3 strata < 5 external_transfer_passes_clean attrition_fraction <= 0.05 AND AUC_cond >= 0.55 AND p_perm <= 0.01 external_transfer_passes_attrition_warning 0.05 < attrition_fraction <= 0.20 AND AUC_cond >= 0.55 AND p_perm <= 0.01 external_transfer_directional_weak AUC_cond > 0.50 AND p_perm <= 0.01 AND AUC_cond < 0.55 external_transfer_fails AUC_cond <= 0.50 OR p_perm > 0.01 ``` The `0.55` effect floor is deliberately above a barely-positive rank signal. This chapter is meant to upgrade evidence, not merely re-detect a tiny directional trace in a much larger table. ## Required Diagnostics The results readback must include: ```text source row count and S/U totals overlap count and overlap fraction strict m3=1 prior-evidence exclusion count smoke seconds/row and projected full wall-clock attrition by failure reason attrition by m3 and period quintile primary rows, S/U totals, and primary m3 strata count per-stratum N/S/U, zone counts, J_m, D_m, AUC_m pooled J_cond, D_cond, AUC_cond p_perm, seed, and permutation count comparison to v0.11 AUC_cond = 0.6782549421 comparison to v0.10b global held-out AUC = 0.4125 m3=0.4 diagnostic if that stratum survives primary gates ``` Report-only tables: ```text overlap rows strict sigma3 prior-evidence rows tiny / one-class strata blocked or sanity-failed rows exact-enumeration sidecar, if computed ``` ## Output Contract Expected output directory: ```text results/isotrophy/k-facet-v12-external-frozen-transfer/ ``` Required files: ```text manifest.json source_profile.csv overlap_audit.csv integration_smoke.csv per_row_transfer_table.csv per_stratum_transfer_table.csv permutation_summary.json report_only_rows.csv ``` `manifest.json` must include: ```text verdict startedAt completedAt gitCommit nodeVersion or pythonVersion target_path discovery_path v0.11_manifest_path zone_cutpoints seed permutations attrition_fraction primary_row_count primary_strata_count AUC_cond p_perm ``` ## Claim Boundary If v0.12 passes, the allowed claim is: > The v0.11 frozen velocity-fraction zone order transfers from the > supplementary-B piano-trio table to the distinct supplementary-A periodic-orbit > table as a conditional within-`m3` stability-ranking signal. If v0.12 passes with attrition warning, append: > on the analyzable domain that passed the locked v0.7 D5 numerical gates. Forbidden upgrades: ```text does not overturn v0.10b's mass-marginal held-out null does not create a globally calibrated predictor does not revise the v0.3h K_facet structural null does not promote isotrophy to theorem-facing status by itself does not claim anything about rows excluded by overlap, prior-evidence, attrition, or tiny/one-class strata does not claim independent-catalog validation beyond the same-paper supplement ``` If v0.12 fails, the allowed claim is: > The v0.11 conditional velocity-fraction signal is not shown to transfer under > the frozen same-paper external supplement test. If v0.12 blocks, the allowed claim is: > The locked D5 velocity-fraction measurement did not support a decisive external > transfer test on supplementary-A under the pre-registered attrition/source gates. ## Implementation Boundary This draft authorizes no code. On lock, the next implementation should be additive: ```text scripts/v12_external_frozen_transfer.py npm script alias, if desired no edits to v0.11 result files no edits to prior manifests ``` The implementation sequence after lock: 1. Write parser/profile/overlap code. 2. Run profile only. 3. Write smoke path and velocity-fraction measurement wrapper. 4. Run the 30-row smoke. 5. Record measured seconds/row and projected full cost in this file or the results readback. 6. Stop if the full run exceeds the inline budget; stage the exact PowerShell command for operator or long-budget runner. 7. Run full transfer only after operator confirmation.