# v0.13b Frame-Zone Stability Audit Form Lock Status: **OPERATOR LOCK 2026-05-31; VERDICT LANDED `coarse_zone_rule_frame_stable_enough_to_test`.** A tiny, locked diagnostic -- not a transfer step. It measures the EXACT frame-zone-change fraction so the v0.13a frame-sensitivity finding can be priced precisely, rather than proxied by the |dvf| severity buckets. ## Result (2026-05-31) **Verdict: `coarse_zone_rule_frame_stable_enough_to_test`.** Both locked bars cleared. ```text supp-B exact zone-change fraction = 4.35% (2/46, Wilson95 [1.2%, 14.5%]) <= 0.15 bar -> v0.11 remains VALID with a MODEST frame caveat. liao2021 pooled exact zone-change fraction ~= 1.3% (10/789 across the n=200 + the pre-registered n=600 expansion; n=600 alone 3/599 = 0.5%, Wilson95 [0.17%, 1.46%]; n=200 7/190 = 3.7%) <= 0.05 bar -> cross-ansatz testing is NOT blocked by frame fragility. ``` Receipts: `results/isotrophy/k-facet-v13b-frame-zone-stability/` (supp-B + liao2021 n=50) and `.../liao2021_n600/` (the n=600 expansion). **Fragility is localized, not uniform.** All 10 liao2021 zone-changers across both samples fall in two narrow mass-ordered catalog bands (orbit index ~74.7k-84.7k and ~109.8k-116.6k); zero zone-changes anywhere else in 135,445 rows. The n=200/n=600 disagreement (3.7% vs 0.5%) is this heterogeneity showing through small samples, not a bug -- some mass-tuple regions have near-degenerate dominant Floquet directions (frame-fragile vf) while the rest are frame-robust. **This argues for stratified frame-stability diagnostics in the eventual transfer readback** -- the catalog-wide ~1.3% does not guarantee every `m3` stratum is frame-robust; a stratum overlapping the fragile bands must be checked per-stratum. **Honest object (restated):** not "dominant-direction velocity-fraction is a frame- invariant geometric quantity" (v0.13a refuted that), but "a coarse, frame-dependent projection (the v0.11 zone) whose registered bins are empirically frame-stable under the tested frame changes -- on average and on the v0.11 domain, with frame-fragility localized to identifiable mass regions." v0.11's within-supp-B statistics are unchanged; only the feature's geometric interpretation is downgraded from invariant to coarse-frame-stable. ## Frame v0.13a's parity found the raw `velocity_fraction` is frame-relative for most orbits (`select_gamma_1`'s largest-real-part direction selection flips under coordinate rotation when Floquet real-parts cluster). The |dvf| severity proxy then suggested the v0.11 ZONES are mostly frame-robust (liao2021 0% / supp-B ~11% severe), but a |dvf| threshold both under- and over-counts zone changes near a cutpoint. v0.13b records the EXACT zone change, `zone(base) != zone(rotated)`, under the already-locked frame perturbations. The proxy is good enough to save the idea; it is not good enough to spend the claim. ## Primary Question > Under the exact v0.13a frame perturbations, does the frozen v0.11 `zone_index(vf)` > change? `zone_index` is frozen from v0.11: `0` if vf < 0.25, `1` if 0.25 <= vf < 0.50, `2` if vf >= 0.50. The cutpoints {0.25, 0.50} are not changed. ## Locked Records (per row, per frame) ```text base_zone zone_index of the base (unperturbed) orbit rotated_zone zone_index under the perturbed frame zone_changed base_zone != rotated_zone distance_to_nearest_cutpoint min(|vf_base - 0.25|, |vf_base - 0.50|) -- robustness margin ``` Per orbit, `orbit_zone_changed = any(zone_changed over the frames)`. ## Locked Frame Perturbations The exact v0.13a isometry set (excluding the identity): ```text rotations SO(2) by {37, 90, 211} degrees in the orbit plane translation by the v0.13a fixed offset (absorbed by CoM-centering) ``` Applied to the CoM-centered initial state, integrated through the frozen D5 path (`integrate_liao2021_state` explicit-state wrapper + `compute_monodromy_vectorized` + `select_gamma_1` + `velocity_fraction_and_z_fraction`), all imported byte-for-byte. ## Locked Domain + Sample ```text catalogs supp-B (the v0.11 domain; frozen mirrored expand_initial_state) liao2021 (the v0.13a adapter; expand_liao2021_state) sample n = 50 uniform rows per catalog, seed 20260523 (program seed) integration-failed rows are reported and excluded from the fraction ``` ## Decision Bars ```text supp-B exact zone-change fraction <= 0.15 -> v0.11 frame caveat is MODEST liao2021 exact zone-change fraction <= 0.05 -> cross-ansatz zone transfer remains VIABLE ``` Verdict tree: ```text supp-B <= 0.15 AND liao2021 <= 0.05 -> coarse_zone_rule_frame_stable_enough_to_test supp-B > 0.15 -> v0.11_language_downgrade (zone rule is too frame-sensitive on its own domain) liao2021 > 0.05 -> cross_ansatz_zone_transfer_shaky ``` A Wilson 95% CI on each fraction is reported; if a fraction straddles its bar, the diagnostic is INCONCLUSIVE on that axis and the sample is expanded before any claim. ## Firewall ```text forbidden: any S/U conditioning, any vf-vs-stability statistic, any AUC/J_cond/chi-sq, any target selection, recording the raw velocity_fraction value allowed: recording base_zone / rotated_zone / zone_changed / distance_to_cutpoint SOLELY as a frame-stability measurement, never associated with a stability label, never used to select or score a transfer ``` This is a frame-stability audit of a frozen projection, not a test of the signal. ## Claim Reframing (the honest object) If both bars pass, the theorem-facing object is restated, humbler but usable: > NOT "dominant-direction velocity-fraction is a frame-invariant geometric quantity" > (v0.13a shows it is not), BUT "a coarse, frame-dependent projection (the v0.11 zone) > whose registered bins are empirically frame-stable under the tested frame changes." v0.11's within-supp-B statistics are unchanged; only the geometric interpretation of the feature is downgraded from invariant to coarse-frame-stable. ## Output Contract ```text results/isotrophy/k-facet-v13b-frame-zone-stability/ frame_zone_{catalog}.json summary: sampled, checked, integration_failed, orbit_zone_changed_count, zone_change_fraction, wilson95, per_frame_change_rate, distance_quantiles, decision_bar, axis_verdict frame_zone_{catalog}.csv per row: orbit_index, base_zone, zone_changed, distance_to_nearest_cutpoint, per-frame rotated_zone ``` No receipt records raw `velocity_fraction` or any stability label. ## Lock-In Statement Committed before the v0.13b runner is written. Any change to the records, the frame set, the sample, the decision bars, the firewall, or the claim reframing after runner execution is a re-registration. The runner imports the frozen D5 + v0.13a symbols unchanged and adds only the zone-derivation + zone-change accounting.