# v0.13a liao2021 Adapter + Leakage Preflight Form Lock Status: **OPERATOR LOCK 2026-05-31; AMENDED R1 2026-05-31** (P2 re-registered from monodromy-eigenvalue-multiset invariance to vf-invariance after the original invariant was found numerically unachievable -- see Amendment R1). This document locks the two contracts that must pass BEFORE v0.13 may profile or rate-probe the Li/Liao 2021 non-hierarchical table: (1) an **expansion-only D5 adapter** and (2) a **cross-ansatz leakage bound**. Reviewed for self-consistency, non-circularity, and integrity: - **Expansion-only boundary is locked.** The only new source-specific code is the row parser, the row-to-state expansion, and a thin explicit-state integration wrapper whose sole job is to feed that state to the inherited Newtonian RHS and variational machinery. No equation, solver, monodromy, gamma, vf definition, or gate logic may be reimplemented. - **Parity check is vf-free.** The frame-invariance check compares only monodromy eigenvalue multisets and gate residuals. It must not call `velocity_fraction_and_z_fraction`, and no `velocity_fraction` / `zone_index` field may appear in the preflight receipt. - **Canonical leakage comparison is implementable.** The scale normalization now gives explicit formulas for mass-normalized length, time, energy, angular momentum, and period. Near-zero comparisons use a symmetric relative tolerance denominator, so `|L| ~= 0` cannot make the leakage test numerically undefined. - **All proposed tolerances are locked as written.** `tol_parity = 1e-8`, `tol_mass = 1e-6`, and `tol_E = tol_L = tol_T = 1e-4`; the inherited leakage gate remains `0.05`. ## Frame v0.13's signal-blind discovery returned an **independent-target landscape negative**: every genuinely independent (Tier 3) external catalog fails a hard gate (equal-mass -> conditioning-strata; restricted substrate; or too small), and the only schema-viable path is **Tier 2 — Li/Liao 2021 non-hierarchical unequal-mass** (135,445 rows, source S/U linear-stability labels, full Newtonian planar). Snapshot: `docs/isotrophy/kfacet/kfacet_v13_target_inventory_snapshot.md`. That table is attractive but carries two integrity hazards a naive run would miss: ```text H1 it is NOT the supp-A/B mirrored ansatz, so the frozen D5 expand_initial_state does not apply -- a new source-row -> 18D-state map is required. H2 cross-ansatz physical duplicates between liao2021 and supp-A/B would NOT match by raw IC delta (different coordinates), so the v0.13 IC-overlap quarantine could silently miss real leakage. ``` v0.13a is a **preflight**: it does not test the velocity-fraction signal and does not lock a target. It only decides whether liao2021 is admissible for v0.13 profile + rate-probe at all. Cheapest gate first (the v0.12 lesson): no integration sweep until the adapter is proven measurement-frozen and the leakage is proven bounded. ## Integrity Caveat v0.13a stays inside the v0.13 firewall: ```text forbidden in v0.13a: recording velocity_fraction or zone_index in any receipt, or any S/U-vs-feature stat tabulating adapter / leakage results by stability label relaxing any inherited D5 numerical control changing the v0.11 cutpoints allowed in v0.13a: a new source-row -> 18D-state expansion (the adapter; H1) E, |L|, T, and mass-tuple computation used ONLY as overlap/identity invariants (H2) -- these are catalog-coordinate invariants, not the vf stability feature (same allowance v0.6 used for (E,|L|) and the v0.13 form used for the weaker invariant identity key); they never enter a stability statistic computing velocity_fraction SOLELY as a discarded frame-invariance assertion inside the P2 parity check (Amendment R1) -- the value is never recorded in a receipt and never associated with a stability label; only the invariance residual |dvf| is kept ``` Under Amendment R1 the preflight computes `velocity_fraction` ONLY inside the P2 frame-invariance assertion (the original eigenvalue-multiset invariant was found numerically unachievable -- see Amendment R1). The vf values are discarded; only the invariance residual is kept. No `velocity_fraction` field appears in any receipt, and nothing in v0.13a is conditioned on a stability label. ## Locked Contract 1 -- Expansion-Only Adapter **What is new (the only new physics-facing code):** ```text parse_liao2021(path) non-mirrored planar parser for the 2021 table expand_liao2021_state(row) source row -> (masses, x[3,3], v[3,3]) for the liao2021 planar ansatz: r1=(x1,0,0) r2=(1,0,0) r3=(0,0,0) v1=(0,v1,0) v2=(0,v2,0) v3=(0,-(m1 v1 + m2 v2)/m3, 0) masses=(m1,m2,m3) CoM-centered identically to expand_initial_state (center_com=True), z=vz=0 (planar). ``` **What is FROZEN, inherited byte-for-byte (imported, never redefined) from `scripts.v07a_velocity_fraction_audit` / v0.12:** ```text compute_monodromy_vectorized (324-dim variational monodromy) select_gamma_1 (largest-real-part + tie-break cascade) velocity_fraction_and_z_fraction (vf definition; CoM + mass-weighted norm) symplecticity_residual, reciprocal_pair_residual RTOL = ATOL = 1e-12, MAX_STEP_FRACTION = 0.02 SYMPLECTICITY_GATE = RECIPROCAL_PAIR_GATE = 1e-4 ``` The adapter changes ONLY the IC expansion. Because the v0.7 `integrate_orbit(row)` function calls the mirrored-ansatz `expand_initial_state(row)`, liao2021 may use a thin explicit-state wrapper. That wrapper may only: ```text accept (masses, x0, v0, period) from expand_liao2021_state CoM-center exactly as registered call the same Newtonian rhs_factory / DOP853 solve_ivp path emit an IntegratedOrbit-compatible object for compute_monodromy_vectorized ``` It may not modify the equations, method, tolerances, max-step convention, variational monodromy, gamma selection, vf definition, or gates. **Parity verification (pre-registered; no vf recorded; P2 = vf-invariance per R1):** ```text P1 code-inheritance identity assert: the adapter module's references to the frozen D5 symbols above are `is`-identical to the v07a objects (no shadowing, no re-implementation). The explicit-state wrapper is separately audited by P2. Fails -> ABORT. P2 frame-invariance via vf-invariance (Amendment R1): for K_PARITY = 6 liao2021 probe rows (deterministic uniform, seed 20260523), apply each pre-registered isometry to the initial configuration, run the full integration + monodromy + gamma-selection + vf path, and assert velocity_fraction is invariant: rotations SO(2) by {0, 37, 90, 211} degrees in the orbit plane translation by a fixed offset (absorbed by CoM-centering) tolerance tol_parity = 1e-8 relative (symmetric near-zero comparator) The vf values are a DISCARDED code-correctness assertion -- never recorded, never stability-associated; only max|dvf| over the isometries is kept. vf is the correct invariant: it IS the measurement (so its frame-invariance directly proves expansion-only), and it is well-conditioned -- a bounded ratio of norms of the DOMINANT (best-conditioned) Floquet eigenvector -- unlike the monodromy eigenvalue multiset, whose tiny reciprocal eigenvalues are numerical garbage for unstable orbits (see Amendment R1). Integration-feasibility failure of an isometry on an extremely unstable orbit is REPORTED but does not by itself fail P2 (it is a feasibility matter the later rate-probe measures); vf-invariance is asserted over the isometries that integrate, requiring at least the base plus one isometry per row. ``` P1 + P2 together certify the adapter is expansion-only: only the coordinates fed into the frozen pipeline changed, and the measurement (vf) is unchanged. ## Amendment R1 (2026-05-31) -- P2 re-registered to vf-invariance The original P2 asserted invariance of the **monodromy eigenvalue multiset** (plus gate residuals) at `tol_parity = 1e-8`. Implementation on the staged table found this invariant **physically unachievable** for three-body monodromy: the residual scales with the eigenvalue condition number (cond 1.0 stable orbit -> 5.8e-3; cond 7600 -> ~1.0), because an unstable orbit's reciprocal Floquet eigenvalue (1/lambda, |lambda| large) is computed as numerical noise by `np.linalg.eigvals`, and even the degenerate unit-eigenvalue block of a stable orbit cannot be multiset-matched to 1e-8. This is a property of the FROZEN `compute_monodromy_vectorized`, not of the adapter (P1 passes; the residual-vs-conditioning correlation proves the rotation is a genuine symmetry defeated only by float precision). P2 is therefore re-registered to assert invariance of `velocity_fraction` -- the measurement itself, which is well-conditioned (it depends only on the dominant Floquet eigenvector) and whose invariance IS the expansion-only claim. `tol_parity = 1e-8` is retained; vf is computed only as a discarded assertion. P1, Contract 2 (leakage), all tolerances, the verdict tree, and the claim boundary are unchanged. Evidence: `results/isotrophy/k-facet-v13a-liao2021-preflight/parity_rows.csv` (pre-amendment eigenvalue-multiset residuals + |lambda| condition numbers). ## Locked Contract 2 -- Cross-Ansatz Leakage Bound Raw IC matching is insufficient (H2). Leakage is bounded by a **canonical-invariant** overlap against supp-A/B, dominated by a mass-tuple disjointness argument. **Canonical normalization (fixes all three scaling freedoms so invariants are comparable across catalogs):** rescale every orbit (liao2021 and supp-A/B) to ```text G = 1, total mass sum(m_i) = 1, moment of inertia I0 = sum m_i |r_i - R_com|^2 = 1 ``` (G=1 + sum m = 1 fixes the mass scale; I0 = 1 fixes the length scale; both together fix the time scale.) In these canonical units E, |L|, and T are pure numbers. Implementation formulas: ```text M = sum_i m_i mu_i = m_i / M R_com = sum_i mu_i r_i I_mu = sum_i mu_i |r_i - R_com|^2 ell = sqrt(I_mu) tau = sqrt(ell^3 / M) # original time units per canonical time mass* = sort(mu_i) E* = E * ell / M^2 |L|* = |L| / (M^(3/2) * sqrt(ell)) T* = T / tau = T * sqrt(M / ell^3) ``` If `M <= 0`, `I_mu <= 0`, a period is missing, or any invariant is non-finite, the canonical reconciliation fails and leakage is declared unbounded. **Identity key (canonical units):** ```text (sorted mass-ratio triple, E*, |L|*, T*) ``` **Dominant bound -- mass-tuple disjointness.** supp-A/B occupy ONLY the two-equal-mass family (1,1,m3). A liao2021 row can be a supp-A/B duplicate only if its canonical mass-ratio triple has two equal entries whose third matches a supp-A/B m3 within `tol_mass`. The 2021 table is non-hierarchical UNEQUAL-mass, so this equal-pair slice is expected to be near-empty; the leakage bound is dominated by its size. **Backstop -- invariant match on the slice.** For each liao2021 row in the equal-pair slice, match against supp-A/B rows of the same mass-tuple on (E*, |L|*, T*) within tolerances. A liao2021 row is a leak iff mass-tuple AND all three invariants match. ```text tol_mass = 1e-6 (relative, mass-equality + m3-grid match) tol_E = 1e-4 (relative, canonical energy) tol_L = 1e-4 (relative, canonical |L|) tol_T = 1e-4 (relative, canonical period) relative comparator: abs(a - b) <= tol * max(1, abs(a), abs(b)) leakage_fraction = (#liao2021 rows that leak) / (#liao2021 rows after eligibility) leakage gate = leakage_fraction <= 0.05 (inherited v0.13 overlap gate) ``` Reflection-image leakage `(z0,vx,vy,vz)->(-z0,vx,vy,-vz)` is moot here (liao2021 is planar, z0=vz=0) but is still reported as `reflection_leak = 0` for the receipt. **Bound-quality guard (the honest escape hatch).** If the canonical normalization cannot be computed for either catalog (missing field, parser ambiguity, or the unit conventions cannot be reconciled to the registered canonical frame), leakage is declared **unbounded**, and liao2021 is report-only regardless of how attractive the schema is. A wide leakage estimate is not a pass. ## Preflight Verdict Tree ```text if adapter parity P1 or P2 fails: verdict = adapter_not_expansion_only -> ABORT (not the frozen measurement) elif leakage is unbounded (canonical reconciliation fails): verdict = leakage_unbounded_report_only -> liao2021 report-only elif leakage_fraction > 0.05: verdict = leakage_blocked_report_only -> liao2021 report-only else: verdict = preflight_passed_probe_authorized -> v0.13 may profile + run a 12-row rate probe on liao2021 (full 100-row probe still gated by --authorize-full-probe) ``` A report-only outcome closes v0.13 as **`no_viable_external_target_found`** with the field result preserved: an independent D5-tractable external target does not exist in the surveyed landscape, and the sole schema-viable Tier-2 candidate is leakage-blocked. That is a legitimate, publishable negative, not a failure of the velocity-fraction hypothesis. ## Frozen Inputs ```text liao2021 table docs/isotrophy/external_targets/_staging/liao2021_nonhierarchical.txt fetched from the snapshot's raw URL; download SHA-256 recorded; promoted from _staging only after parse + this preflight overlap sources docs/isotrophy/supplementary-A_periodic-3d_mirror.txt docs/isotrophy/supplementary-B_piano-init-condit-3d.txt inherited D5 scripts/v07a_velocity_fraction_audit.py (the seven frozen symbols) inventory results/isotrophy/k-facet-v13-external-target-search/target_inventory.csv (snapshot: kfacet_v13_target_inventory_snapshot.md) ``` No relaxation of the inherited D5 controls is authorized. The preflight does not run the full 135,445-row sweep; parity uses 6 rows, leakage uses invariants only (no integration beyond the 6 parity rows). ## Output Contract ```text results/isotrophy/k-facet-v13a-liao2021-preflight/ manifest.json - schema = "sundog.isotrophy.v0.13a-liao2021-preflight.v1" - download_sha256, row_count, mass_variation_summary - adapter_parity = { code_inheritance_ok, frame_invariance_max_residual, passed } - leakage = { canonical_norm_ok, equal_pair_slice_count, leaked_rows, leakage_fraction, reflection_leak, bounded, tolerances } - verdict parity_rows.csv (6 rows: monodromy eigenvalue stats + gate residuals per isometry; NO vf) leakage_audit.csv (equal-pair-slice rows + invariant match results) ``` No receipt in this chapter contains `velocity_fraction`, `zone_index`, or a per-row stability-conditioned feasibility field. `parity_rows.csv` may identify row indices, mass keys, periods, isometry names, eigenvalue summary residuals, and gate residuals; it may not include source stability labels. ## Claim Boundary ```text preflight pass = permission for v0.13 to profile + rate-probe liao2021. It does NOT test, confirm, or estimate the velocity-fraction signal; it does NOT lock a transfer; it does NOT upgrade independence beyond Tier 2. preflight fail = liao2021 report-only; v0.13 closes no_viable_external_target_found, preserving the independent-target landscape negative. in all cases = no v0.10b / v0.11 revision, no v0.3h K_facet revision, not theorem-facing, and the supp-B conditional positive is unchanged. ``` Even a fully successful downstream liao2021 transfer would be a **Tier-2, same-Li/Liao-lineage** external result (different paper / orbit construction, same author family) -- "near-the-source external," to be stated honestly, not an arm's-length independent confirmation. ## Lock-In Statement This form is committed before any adapter, parser, or preflight code is written. After lock, implementation may add only `parse_liao2021` + `expand_liao2021_state` + the preflight runner, importing the seven frozen D5 symbols unchanged. Any change to the adapter's frozen-symbol set, the canonical normalization, the identity key, the tolerances, the leakage gate, or the verdict tree after runner execution is a re-registration, not a refinement.