# v0.11 m3-Conditional vf Rank Form Lock Status: **OPERATOR LOCK 2026-05-30.** No v0.11 runner has been written and no v0.11 command has been run at lock time. This document locks the conditional domain, fixed rank score, exact stratified null, pass/fail tree, diagnostics, and claim boundary before any v0.11 statistic is computed. Reviewed for self-consistency, non-circularity, and integrity: - **Arithmetic reconciles** against the v0.10b receipt: the 9 primary strata sum to 229 rows = 82 S / 147 U; +21 report-only (5 one-class + 16 tiny) = 250 analyzable; +23 v0.7a integration-blocked = 273 supp-B catalog. The 9 strata are exactly v0.10b's both-class folds. - **The m3=1.7 exclusion is mathematically inert, not performance-motivated:** a one-class stratum contributes `D_m = S_m*U_m = 0` pairs to `AUC_cond` and nothing to the exact null, so including or excluding it yields identical `J_cond` and `p_exact`. No "drop a stratum to pass" risk. - **Non-circularity breaks the statistic (the allowed one):** v0.10b was a global, trained, leave-one-bin-out AUC with a permutation null; v0.11 is an in-sample, frozen-rule, within-stratum rank AUC with an exact stratified null. The within-stratum construction removes the `m3` base-rate confound by construction. The test is not rigged to pass — v0.10b already showed m3=0.6/0.7 anti-rank within-bin, so the pooled conditional statistic genuinely aggregates working strata (0.8/0.9/1.0/1.1) against failing ones. - **Honest claim boundary:** a PASS registers in-sample within-`m3` conditional rank information (post-hoc direction disclosed — the same footing that licensed v0.10a), NOT a global predictor, NOT a v0.10b overturn, NOT theorem-facing. - **Exact null is sound and cheap:** stratified Mann-Whitney with tied zone-groups; `D_cond = sum S_m*U_m = 1467`, observed convolution support = 1486 doubled-J bins inside the 0..2934 possible score range, seconds. Adjustment made at lock (one): added a non-binding within-stratum permutation sanity cross-check (seed 20260523, n=10000) guarding the hand-rolled enumeration + convolution kernel, with an ABORT-on-gross-divergence branch. The binding p-value remains `p_exact`; the sanity sidecar mirrors v0.10a's exact+permutation discipline. Execution receipt (2026-05-30): ```text command: npm run isotrophy:m3-conditional-vf-rank out: results/isotrophy/k-facet-v11-m3-conditional-vf-rank/ verdict: m3_conditional_vf_rank_passes ``` Primary result: ```text primary domain: 229 rows (82 S / 147 U), D_cond = 1467 AUC_cond: 0.6782549421 J_cond: 995.0 exact p: 2.046197217e-7 exact mass: 1.0000000000 permutation sanity: p = 9.999e-5, consistent_with_exact = true ``` Readback: v0.11 registers the frozen vf zone order as a within-`m3` conditional rank signal on the locked 229-row primary domain. It does not overturn v0.10b's global held-out null and does not promote the program to a theorem-facing claim. ## Frame v0.10a registered a monotone in-sample trend: ```text positional-dominant -> mixed -> velocity-heavy S_fraction 0.1053 0.3394 0.4394 J-T exact p = 0.007304 ``` v0.10b then tested whether that trend becomes a **globally calibrated held-out risk score across mass bins**. It failed cleanly: ```text pooled leave-one-m3-bin-out held-out AUC = 0.4125 <= 0.5 verdict = monotone_vf_predictor_fails_heldout ``` The mandated v0.10b diagnostics showed the failure mode: several held-out `m3` folds had within-bin AUC above 0.5, but the pooled cross-bin score collapsed because `m3` base rates dominate global ordering. v0.11 is therefore a **fresh conditional chapter**, not a v0.10b refinement: > Given a fixed mass-ratio bin, does the frozen vf zone order rank stable rows > above unstable rows? This is a fixed-rule conditional rank test. It is not a calibrated global predictor and not a hard classifier. ## Integrity Caveat The v0.11 hypothesis is diagnostic-driven: v0.10b exposed the within-bin signal after its global gate failed. A v0.11 pass would register a **conditional within-`m3` rank signal** on the frozen analyzable supplementary-B domain. It would not overturn v0.10b, would not rescue the global predictor, and would not be an independent external-catalog validation. The key non-p-hack boundary: ```text v0.10b claim failed: one global zone-only risk score transfers across mass bins. v0.11 claim, if passed: within fixed m3 strata, the frozen zone order carries stability ranking information. ``` Those are different claims. v0.11 may not be used to rewrite v0.10b's verdict. ## Frozen Inputs Primary input: ```text results/isotrophy/k-facet-v09a-signed-vf-three-zone/per_row_table.csv ``` Required receipt cross-checks: ```text results/isotrophy/k-facet-v10a-jt-trend/manifest.json results/isotrophy/k-facet-v10b-monotone-vf-heldout/manifest.json ``` The runner must assert: ```text v0.9a/v0.10a frozen row count: 250 stability totals: 87 S / 163 U zone counts: positional-dominant: N=19, S=2, U=17 mixed: N=165, S=56, U=109 velocity-heavy: N=66, S=29, U=37 zone recompute: recompute from velocity_fraction under {0.25,0.50}; require zero mismatches v0.10a verdict: jt_trend_monotone_registered v0.10b verdict: monotone_vf_predictor_fails_heldout v0.10b pooled AUC condition: AUC <= 0.5 ``` Any mismatch aborts. No new orbit integration, variational integration, gauge minimization, or re-derivation of `velocity_fraction` is authorized. ## Primary Conditional Domain The primary domain uses frozen analyzable rows in `m3` strata with: ```text N >= 5 S >= 1 U >= 1 ``` This includes every non-tiny, both-class mass bin and excludes no bin based on the observed v0.10b fold AUC. ```text m3 N S U 0.4 55 35 20 0.5 30 15 15 0.6 22 6 16 0.7 18 4 14 0.8 18 6 12 0.9 21 6 15 1.0 35 7 28 1.1 23 1 22 1.2 7 2 5 ``` Primary rows: `229` (`82 S / 147 U`). Report-only strata: ```text one-class N>=5: m3=1.7 N=5 S=0 U=5 tiny N<5: m3=1.3 N=4 S=2 U=2 m3=1.4 N=4 S=0 U=4 m3=1.5 N=4 S=1 U=3 m3=1.6 N=2 S=2 U=0 m3=1.9 N=2 S=0 U=2 ``` The report-only strata are scored and printed, but do not enter the primary statistic, exact null, p-value, or verdict. ## Fixed Rank Score Feature and score are frozen from v0.9a/v0.10a: ```text zone_index: positional-dominant = 0 mixed = 1 velocity-heavy = 2 ``` No training is performed. No mass-specific threshold, smoothing, calibration, logistic regression, raw `velocity_fraction` threshold, branch label, `z0`, `E`, `|L|`, period, or `m3` value may enter the score. `m3` is used only to define the conditional comparison strata. ## Primary Statistic Within each primary `m3` stratum, compare every stable row to every unstable row in the same stratum: ```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 constant-score conditional baseline. Larger values mean stable rows tend to occupy higher vf zones than unstable rows **within the same mass-ratio bin**. ## Exact Stratified Null Binding p-value: deterministic exact fixed-stratum enumeration. For each primary `m3` stratum: 1. Preserve the zone counts in that stratum. 2. Preserve the total `S_m` and `U_m` in that stratum. 3. Enumerate every feasible allocation of `S` counts across the occupied zones. 4. Weight each allocation by the stratum's multivariate-hypergeometric probability. 5. Compute the stratum `J_m` for that allocation. The runner combines the per-stratum exact distributions by convolution over `2 * J_m` integer scores, yielding the exact null distribution of `J_cond` under within-stratum exchangeability of S/U labels. Binding one-sided p-value: ```text p_exact = P_null(J_cond >= J_cond_observed) ``` Sanity gates: ```text per-stratum probability mass within 1e-10 of 1 combined probability mass within 1e-9 of 1 ``` If either mass check fails, abort rather than fall back to Monte Carlo. ### Permutation sanity cross-check (non-binding) The per-stratum enumeration and the cross-stratum convolution are the novel kernel of this chapter; the mass-sanity gates prove the enumeration is *complete* but not that `J_m` and the convolution score-axis are aligned correctly. As an independent guard (mirroring v0.10a's exact+permutation discipline), the runner also estimates the same one-sided p-value by within-stratum label permutation: shuffle the S/U labels within each primary `m3` stratum (preserving `S_m`, `U_m`, and the zone counts), recompute `J_cond`, repeat with the program-locked seed `20260523` for `n = 10000` draws, and report ```text p_perm_sanity = (1 + #{J_cond_perm >= J_cond_observed}) / (1 + 10000) ``` This is a SANITY sidecar; the binding p-value remains `p_exact`. The two must agree within Monte-Carlo error (`p_exact` inside `p_perm_sanity +/- 5` standard errors, accounting for the `1/n` resolution floor in the deep tail). A gross divergence indicates an enumeration/convolution kernel bug and INVALIDATES the run (ABORT, fix, re-run) — it never silently changes the verdict. ## Verdict Tree ```text if frozen-input cross-check fails: ABORT (not the frozen v0.9a/v0.10a/v0.10b receipt chain) elif primary conditional domain != the 9 strata / 229 rows listed above: ABORT (domain mismatch) elif exact-null probability-mass sanity fails: ABORT (exact enumeration invalid) elif exact-vs-permutation-sanity divergence beyond ~5 Monte-Carlo SE: ABORT (enumeration/convolution kernel bug) elif AUC_cond <= 0.5: verdict = m3_conditional_vf_rank_fails elif p_exact <= 0.01: verdict = m3_conditional_vf_rank_passes else: verdict = m3_conditional_vf_rank_fails ``` No partial branch exists. Results with `0.01 < p <= 0.05` are reported as descriptive hints and formal failures. ## Required Diagnostics The receipt must report: - per-stratum `N`, `S`, `U`, zone counts, `J_m`, `D_m`, and `AUC_m`; - `m3 = 0.4` diagnostic block, because prior chapters identified it as load-bearing; - pair-weight contribution by stratum (`D_m / D_cond`); - exact-null support size per stratum and after convolution; - comparison against v0.10b pooled AUC: - v0.10b global pooled held-out AUC = `0.4125` (failed); - v0.11 conditional AUC (this run); - report-only stratum table for one-class and tiny bins; - alignment diagnostic against v0.5a branch labels, report-only. Branch labels are never features. ## Disallowed Moves v0.11 may NOT use: - raw continuous `velocity_fraction`; - v0.7a-prime quartile labels or quartile cutpoints; - `m3` as a score feature or calibration input; - mass-specific thresholds; - branch labels, `z0`, `E`, `|L|`, period, or catalog-coordinate features; - eigenvalue magnitudes, spectral radius, unit-circle status, unstable-pair count, or any threshold that defines the published S/U label; - post-run domain changes to drop weak strata or rescue a fail. ## Claim Boundary A PASS: - says the frozen vf zone order carries **within-`m3` conditional rank information** about stability on the 229-row primary analyzable supp-B domain; - does NOT claim a globally calibrated predictor across mass bins; - does NOT overturn v0.10b's held-out global null; - does NOT cover the 21 report-only rows or the 23 v0.7a integration-blocked rows; - does NOT make isotrophy theorem-facing or revise the v0.3h K_facet structural-null. A FAIL: - says the encouraging v0.10b per-fold diagnostics do not survive the registered exact conditional rank gate; - should close the conditional-predictor rung unless a fresh external catalog or genuinely different physical mechanism is registered. ## Receipt Schema ```text results/isotrophy/k-facet-v11-m3-conditional-vf-rank/ manifest.json - schema = "sundog.isotrophy.v0.11-m3-conditional-vf-rank.v1" - mode = "v0.11-m3-conditional-vf-rank" - form_lock = "docs/isotrophy/kfacet/kfacet_v11_m3_conditional_vf_rank_form.md" - input_v09a_per_row_table - input_v10a_manifest - input_v10b_manifest - frozen_input_crosscheck - primary_strata - report_only_strata - score = { feature: zone_index, values: {positional:0, mixed:1, velocity_heavy:2} } - observed = { J_cond, D_cond, AUC_cond } - exact_null = { per_stratum_support, combined_support, per_stratum_probability_mass, combined_probability_mass, p_value_one_sided } - permutation_sanity = { seed: 20260523, n: 10000, p_perm_sanity, standard_error, consistent_with_exact } - verdict per_stratum_table.csv report_only_strata.csv exact_null_summary.csv ``` ## Lock-In Statement This form is committed before any v0.11 conditional statistic, exact null, stratum AUC, or report-only score is computed. Any change to the primary domain, fixed rank score, exact-null construction, significance floor, verdict tree, or claim boundary after runner execution is a re-registration, not a refinement. Implementation may proceed against the frozen v0.9a per-row table plus v0.10a and v0.10b manifests only. Expected runtime: seconds.