From 325601ad64b58f10c6fda659851e3acd43bb10b7 Mon Sep 17 00:00:00 2001 From: Sagar Thakrar Date: Thu, 15 Oct 2026 09:01:05 +0530 Subject: [PATCH] Audit side-condition coverage of the pending T74 outer at #2044 Adversarial audit; no counterexample, no new kappa. Inventory of all 554 asymptotic side conditions written in the 28 notes of research/capped-fusion-t74-k554 at PR #2044 head 322949a5, mapped to 133 exact condition keys and the 62 ledger strict checks, and evaluated exactly at the final point (eps = 1-2e-30010, beta = 1-6e-30010) and at the PR1786/PR1673 points. No load-bearing condition is false there: 262 covered, 53 elementary, 113 explicitly superseded, 64 stale text, 58 non-exponent, 3 false but non-load-bearing statements, 1 uncovered but true constant. Flags double-checked; a seeded 28-item sample of non-flagged classifications re-checked (one mistranslation corrected). Also resolves the #1876/#1897 `or True` reconciliation and the GAUGEFREE sec. 7 g^2-per-record request with exact checks; independently corroborates philippeVV's concurrent reconciliation and HALO finding. Co-Authored-By: Claude Opus 5.5 --- .../INVENTORY.json | 741 ++++++++++++++++ .../POINTS.json | 465 ++++++++++ .../README.md | 259 ++++++ .../REVIEW-ITEMS.md | 124 +++ .../SOURCES-T74.json | 202 +++++ .../SOURCES.json | 18 + .../TASK.json | 72 ++ .../VERIFY.json | 29 + .../review_items.py | 798 ++++++++++++++++++ .../verify.py | 649 ++++++++++++++ 10 files changed, 3357 insertions(+) create mode 100644 research/t74-side-condition-coverage-audit/INVENTORY.json create mode 100644 research/t74-side-condition-coverage-audit/POINTS.json create mode 100644 research/t74-side-condition-coverage-audit/README.md create mode 100644 research/t74-side-condition-coverage-audit/REVIEW-ITEMS.md create mode 100644 research/t74-side-condition-coverage-audit/SOURCES-T74.json create mode 100644 research/t74-side-condition-coverage-audit/SOURCES.json create mode 100644 research/t74-side-condition-coverage-audit/TASK.json create mode 100644 research/t74-side-condition-coverage-audit/VERIFY.json create mode 100644 research/t74-side-condition-coverage-audit/review_items.py create mode 100644 research/t74-side-condition-coverage-audit/verify.py diff --git a/research/t74-side-condition-coverage-audit/INVENTORY.json b/research/t74-side-condition-coverage-audit/INVENTORY.json new file mode 100644 index 0000000000..0848442e8b --- /dev/null +++ b/research/t74-side-condition-coverage-audit/INVENTORY.json @@ -0,0 +1,741 @@ +{ +"audited":{"head": "322949a53488d64023fedb89a6774927707e57ba", "ledger_row": "struct_boundary_radix_union", "package": "research/capped-fusion-t74-k554", "pr": 2044}, +"classes":{"AMBIGUOUS": "translation uncertain", "AUTO_TRUE": "true for an elementary reason (constant inequality / polylog / structural), evaluated exactly where reducible", "COVERED": "equivalent to a named LEDGER strict check (exact equality asserted), implied by named checks via a recorded identity, or asserted inside check_ledger", "FALSE_AT_POINT": "the condition, correctly translated, fails at the final point and is presented as current (not explicitly superseded)", "NON_EXPONENT": "not reducible to an exponent inequality", "OBSOLETE": "explicitly superseded/removed by a later or the same note (citation in reasoning); may be false at the point", "STALE_TEXT_ONLY": "text quotes an old numeric/formula, the generic condition is covered/true", "UNCOVERED_TRUE": "true at the final point but not encoded by any LEDGER strict check nor implied by one"}, +"conditions":[ +{"classification": "AUTO_TRUE", "file": "README.md", "id": "outer-130", "keys": ["slacks_le_r0"], "line": 3, "quote": "Every free slack of the ledger sits at 1e-30010 or below", "reason": ""}, +{"classification": "STALE_TEXT_ONLY", "file": "README.md", "id": "outer-131", "keys": ["xi_gt_half"], "line": 3, "quote": "the cap xi > 1/2 holds with margin 0.00084", "reason": "structured-era margin; now 0.408"}, +{"classification": "OBSOLETE", "file": "README.md", "id": "outer-132", "keys": ["old_theta_guard"], "line": 3, "operative_keys": ["chirp_guard", "beta_lt_1"], "quote": "the precision guard becomes beta + 2 xi - eps <= 1 - r - zeta, and the union tag check becomes 1 - beta > 0 (tag work is paid per visit). beta = 0.9966, xi = 0.5017, eps = 0.9999944.", "reason": "README l.3 history item (3); superseded by later items and GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "STALE_TEXT_ONLY", "file": "README.md", "id": "outer-133", "keys": ["boundary_row"], "line": 3, "quote": "**tau_eff = 2 + 1e-30010** (tau_eff = 2 itself is not claimed; the polylog factors are absorbed by the strict slack)", "reason": "README history item (2); structured boundary unused"}, +{"classification": "STALE_TEXT_ONLY", "file": "README.md", "id": "outer-134", "keys": ["beta_lt_1", "membership", "eps_lt_1", "xi_gt_half", "router_row"], "line": 12, "quote": "1 - beta = 3.35e-3 (record header g log L, tag work per visit, support g polylog p = o(p)), membership 1 - beta - 2(1-eps) = 3.34e-3, 1 - eps = 5.6e-6, cap xi - 1/2 = 1.67e-3, and the global router margin is only 9.4e-9", "reason": "explicitly marked superseded in the README"}, +{"classification": "COVERED", "file": "README.md", "id": "outer-135", "keys": ["eps_lt_1", "beta_lt_1", "membership", "kappa_lt_q"], "line": 14, "quote": "every 'eventually' of the proofs needs p beyond an astronomically large cutoff; no practical cutoff is claimed. Epsilon < 1 strictly and kappa < q always.", "reason": "acknowledged astronomical cutoff"}, +{"classification": "NON_EXPONENT", "file": "README.md", "id": "outer-136", "keys": [], "line": 38, "quote": "stage j needs L_j*gap_j^2 >= 36 and L_j*gap_j >= 2(4+ell_j)", "reason": "supplier bootstrap finite checks (verify.py)"}, +{"classification": "NON_EXPONENT", "file": "README.md", "id": "outer-137", "keys": [], "line": 54, "quote": "0 < a_0 < s < 1 gives a finite increasing chain below s", "reason": "supplier bootstrap recurrence"}, +{"classification": "COVERED", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-116", "keys": ["strassen"], "line": 4, "quote": "its stability lemma only requires omega_C < tau", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "OBSOLETE", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-117", "keys": [], "line": 8, "quote": "saving is 3/10 + xi - epsilon, and the ledger constant is c = (3 - tau)/2 = 3/10", "reason": "c = 3/10 superseded in-file (CLASSICAL l.24-30)", "superseded_by": [{"file": "outer/CLASSICAL-BOUNDARY.md", "line": 24}, {"file": "outer/CLASSICAL-BOUNDARY.md", "line": 8}]}, +{"classification": "OBSOLETE", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-118", "keys": ["tau_gt_legall", "tau_lt_5_2"], "line": 9, "operative_keys": ["strassen"], "quote": "(12/5 > 2.3728639) and `matrix_exponent_below_five_halves` are in the ledger", "reason": "superseded in-file (CLASSICAL l.24-30) and by FINE-PADDING-COMPOSITION l.13; neither row exists in the current check_ledger.py; tau < 5/2 would be false at 45/16", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}, {"file": "outer/CLASSICAL-BOUNDARY.md", "line": 24}, {"file": "outer/CLASSICAL-BOUNDARY.md", "line": 9}]}, +{"classification": "COVERED", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-119", "keys": ["r_pos", "slack_pos", "q_lt_b", "stop_pos", "main_row", "zeta_pos"], "line": 13, "quote": "every strict slack (r0, zeta, layout slack,", "reason": "zeta > 0 is not checked (zeta is used by no ledger formula: dead parameter)"}, +{"classification": "NON_EXPONENT", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-120", "keys": [], "line": 16, "quote": "moment(b) < 1 and moment(endpoint + 1e-30000) > 1 are both proven by exact rational enclosures", "reason": "finite exact moment enclosure (asserted in check_ledger.py)"}, +{"classification": "OBSOLETE", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-121", "keys": ["old_eps_balance"], "line": 22, "operative_keys": ["xi_def"], "quote": "epsilon = (1 + q + q(c - s - r - zeta))/(1 + q)^2, xi = epsilon (1 + q) - c + s", "reason": "eps balance superseded (FINE-PADDING-COMPOSITION sec 2)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/CLASSICAL-BOUNDARY.md", "id": "outer-122", "keys": ["boundary_row"], "line": 30, "quote": "The boundary exponent is now tau_eff = 2 + 1e-30010 from structured solves", "reason": "history line; current boundary is Strassen 45/16"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-01", "keys": ["TH_pos", "xi_lt_TH"], "line": 9, "quote": "fine primes, theta in (1/(4p^2), 1/(2p^2-1)]", "reason": "fine theta ~ p^-2; existence of the primes is PR1786/Trudgian (non-exponent)"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-02", "keys": ["chirp_guard", "chirp_guard_zeta"], "line": 9, "quote": "chirp range a theta B^2 = O(a B^2/p^2): guard beta + 2 xi - 2 < 1", "reason": "ledger row omits zeta; the zeta form also holds (margin 0.184 >> 1e-30012)"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-03", "keys": ["halo_radius", "halo_volume", "face_row"], "line": 10, "quote": "halo 48 / core 128; online precision stays O(p)", "reason": "'online precision stays O(p)' is the non-exponent PR1786 sec 3 setup/online separation"}, +{"classification": "OBSOLETE", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-04", "keys": ["linear_guard_noR"], "line": 11, "operative_keys": ["chirp_guard"], "quote": "the old linear guard beta + xi <= 1 is violated at beta ~ 1, xi = 0.908 (ledger control `old_linear_guard`)", "reason": "line records that the old linear guard fails; linear gauge superseded by GAUGEFREE R1/R3 (PR1758); LEDGER rejecting control old_linear_guard", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-05", "keys": ["old_union_row", "tag_2beta"], "line": 12, "operative_keys": ["union_row", "beta_lt_1"], "quote": "the old g-factor union row 1 - eps - beta - 1/2 + xi is negative (control `old_g_factor_union_row`) and 2 beta < 1 fails (control `old_union_tag_2beta`)", "reason": "superseded by outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125) and per-visit tag accounting (GAUGEFREE sec 7); controls old_g_factor_union_row, old_union_tag_2beta fire", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 108}, {"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-06", "keys": ["strassen", "c_pos", "tau_gt_2"], "line": 13, "quote": "explicit Strassen, tau = 45/16 (7^16 < 2^45), c = 3/32", "reason": "tau=45/16 > 5/2: old below-five-halves rows would fail but are not needed for an explicit Strassen formula"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-07", "keys": ["xi_lt_eps", "boundary_row", "boundary_eq"], "line": 13, "quote": "at xi = 0.908 < eps the boundary row is not binding", "reason": "wording: 'boundary row not binding' vs l.37 / UNION 5b 'boundary = main + s binds' (exact equality); no condition affected"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-08", "keys": ["main_row", "kappa_def"], "line": 19, "quote": "main = epsilon q is the binding saving, kappa = floor(epsilon q) - 1e-30022", "reason": "coverage: main_row = ledger main_transform_above_kappa; kappa_def asserted (check_ledger definition)"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-09", "keys": ["gauss_row", "gauss_window", "gauss_minus_main_id"], "line": 20, "quote": "Gaussian row: 1 - epsilon + q beta >= epsilon q iff **beta >= 1 - delta(1 + 1/q)** (a window of width ~ 594 delta below 1)", "reason": "window [1-delta(1+1/q), 1-2delta) has width delta(1/q-1) = 594.32 delta"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-10", "keys": ["membership"], "line": 21, "quote": "membership: 1 - beta - 2(1-epsilon) > 0 iff **beta < 1 - 2 delta**", "reason": "eventual: margin 2e-30010"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-11", "keys": ["beta_lt_1", "beta_lt_eps"], "line": 21, "quote": "header / tag per visit: 1 - beta > 0; group below dimension: epsilon - beta > 0", "reason": "eventual: margins 6e-30010, 4e-30010"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-12", "keys": ["gamma_slack"], "line": 22, "quote": "**1 - epsilon - r0 > 0** (`global_gamma_power_slack`, r0 = 1e-30010: the spare power for u <= p^r0)", "reason": "row is the theta~1/d form of the global range; the fine-theta offline term a/(4theta)=O(p^2 log p) is NOT this row (PR1786 sec 3 P_setup, non-exponent)"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-13", "keys": ["eps_lt_1"], "line": 22, "quote": "`source_axis_superpolynomial` 1 - epsilon > 0", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-14", "keys": ["xi_lt_eps", "xi_gt_half", "chirp_guard"], "line": 23, "quote": "boundary / union rows: xi = 0.9079 < epsilon (cap_below_cell), xi - 1/2 > 0, guard 1 - (2 xi - 2) - r0 - beta = 0.184 > 0: independent of delta", "reason": "coverage: xi_lt_eps = ledger cap_below_cell; xi_gt_half = ledger cap_above_band; chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-15", "keys": ["face_row", "face_lt_0"], "line": 24, "quote": "core-face corrections epsilon + beta + 48 - 128 + 2 < 0: independent of delta", "reason": "literal '< 0' is stronger than the ledger row (< 1-kappa) and also true"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-16", "keys": ["gamma_slack", "beta_def"], "line": 26, "quote": "The only lower bound on delta is **delta > r0 = 1e-30010**, a free strict slack of the proof.", "reason": "all delta-dependent rows (membership delta, Gaussian delta(1-2q), header 3delta, group 2delta) positive for every delta>0"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-17", "keys": ["xi_def"], "line": 28, "quote": "epsilon = 1 - 2e-30010, beta = 1 - 6e-30010, xi = 0.90792965478815...,", "reason": "quoted xi = 0.90792965478815... is PR1786's delta=1e-7 value; exact final xi = 0.9079297549561255...; no xi-condition has a margin below 0.09 except the boundary row, which uses the exact xi"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-18", "keys": ["eps_lt_1", "kappa_lt_q"], "line": 33, "quote": "Within this construction epsilon < 1 strictly", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard; kappa_lt_q implied by main_transform_above_kappa+epsilon_below_one+q_positive (kappa < eps q and eps q < q; also asserted in independent_check.py (gap_to_q))"}, +{"classification": "FALSE_AT_POINT", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-19", "keys": ["all_nonmain_margins_ge_r0"], "line": 37, "load_bearing": false, "operative_keys": ["all_checks_pos"], "quote": "all other rows have positive margins >= 1e-30010", "reason": "literal claim false: global_coordinate_router_above_kappa = 5.0336e-30011 < 1e-30010 (also several supplier strict checks are 2.5e-30011..5e-30011 and stop_positive = 1e-30016); descriptive only, every row is strictly positive, not load-bearing"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-20", "keys": ["union_eq", "union_row"], "line": 37, "quote": "union = main + s + 13/32", "reason": "coverage: union_eq asserted (check_ledger.py l.196 assert); union_row = ledger sparse_union_movement_above_kappa"}, +{"classification": "FALSE_AT_POINT", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-21", "keys": ["xi_free_c_half", "boundary_at_xi_half"], "line": 38, "load_bearing": false, "operative_keys": ["boundary_row", "xi_gt_half", "xi_def"], "quote": "no effect on kappa (only on xi, which is free in (1/2, epsilon)). Using c = 1/2 would give xi = 0.5 and the same kappa", "reason": "hypothetical aside: with Strassen c=3/32 xi is pinned at eps(1+q)-c+s (not free in (1/2,eps)); with c=1/2 xi would be eps(1+q)-1/2+s = 0.5016798, and xi=0.5 itself violates the boundary row (saving 1-eps = 2e-30010 < kappa) and the strict cap xi>1/2; not load-bearing"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-22", "keys": ["router_row"], "line": 39, "quote": "The router row a_eff = (q+b)/2 > epsilon q by 5e-65 + q delta", "reason": "'5e-65 + q delta' is exact at the PR1786 point (gap 1e-64); at the final point a - eps q = 5e-30011 + q delta = 5.0336e-30011"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-23", "keys": ["eps_lt_1"], "line": 44, "quote": "log x = Theta(p^(1-epsilon)) = p^(2e-30010) must dominate log p in the prime-count estimate", "reason": "Trudgian error needs roughly sqrt(log x) >> log p, i.e. p^((1-eps)/2) >> log p: implied by 1-eps>0 (astronomical cutoff)"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-24", "keys": ["eps_lt_1"], "line": 44, "quote": "source axes 2^(p^delta) must exceed every fixed polynomial of p", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-25", "keys": ["all_checks_pos"], "line": 44, "quote": "the polylog factors of every row are absorbed by p^delta-type slack", "reason": "eventual: smallest exponent slack is the 1e-30022 backoff of the main row"}, +{"classification": "COVERED", "file": "outer/FINE-PADDING-COMPOSITION.md", "id": "outer-26", "keys": ["TH_pos", "chirp_guard"], "line": 46, "quote": "uses theta^-1 = O(p^2) in the symbol bound (PR1786 sec. 3); the Gauge-free note's guard is superseded by `beta + 2 xi - 2 < 1` at fine theta.", "reason": "coverage: TH_pos = ledger theta_positive_polynomial_power; chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-27", "keys": ["chirp_guard"], "line": 1, "quote": "theta >= 1/(4p^2) replaces theta >= 1/(4d) in every bound below, the chirp range becomes O(a B^2/p^2) and the guard of Section 5 becomes beta + 2 xi - 2 < 1", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-28", "keys": ["TH_pos"], "line": 1, "quote": "the symbol bound mu >= (1 - e^{-gamma theta/2}) e^{-pi^2/(3 gamma)} is polynomial for theta^-1 = O(p^2)", "reason": "polynomial symbol bound for any fixed THETA_POWER; ledger only encodes THETA_POWER=2>0 (weak)"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-29", "keys": ["chirp_axis_o1"], "line": 15, "quote": "only the quadratic chirp remains, range O(a theta B^2) = O(a B^2/d)", "reason": "body formula O(aB^2/d) uses theta~1/d; overridden by GAUGEFREE l.1 (O(aB^2/p^2)); per-axis range p^(2xi-2) polylog = o(1)"}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-30", "keys": ["old_theta_guard"], "line": 17, "operative_keys": ["chirp_guard", "beta_lt_1"], "quote": "guard beta + 2 xi - eps <= 1-r-zeta; tag check 1-beta > 0", "reason": "old-theta guard false at the final point; superseded by GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46; LEDGER control old_theta_chirp_guard; tag check 1-beta>0 covered", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-31", "keys": ["linear_guard_zeta", "tag_2beta"], "line": 17, "operative_keys": ["chirp_guard", "beta_lt_1"], "quote": "ledger guard beta + xi <= 1-r-zeta; union tag check 1-2 beta > 0", "reason": "replaced in this note (R3); controls old_linear_guard, old_union_tag_2beta", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-32", "keys": ["theta_ge_1_over_d"], "line": 21, "operative_keys": ["TH_pos"], "quote": "1/(4d) <= theta <= 1/(2d-1)", "reason": "superseded by GAUGEFREE l.1 and PR1786 FINE-PRIME-PADDING.md l.62-67 (1/(4p^2) < theta <= 1/(2p^2-1); old theta>=1/(4d) not reused)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 62}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "NON_EXPONENT", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-33", "keys": [], "line": 21, "quote": "length n <= B (dyadic)", "reason": "definitional (n = interior length <= B)"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-34", "keys": ["xi_lt_eps", "xi_lt_TH"], "line": 21, "quote": "B = p^xi, d = p^eps, xi < eps", "reason": "coverage: xi_lt_eps = ledger cap_below_cell; xi_lt_TH = ledger cap_below_phase_cell_power"}, +{"classification": "NON_EXPONENT", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-35", "keys": [], "line": 23, "quote": "|delta| <= 1/2, b0 = pi/alpha^2", "reason": "phase offset |delta|<=1/2, b0 = pi/alpha^2 (geometry)"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-36", "keys": ["xi_lt_1", "chirp_axis_o1"], "line": 31, "quote": "the linear leftover has logarithmic range <= 2 b0 theta B (total), and the quadratic parts b0 (1-lambda) x^2, b0 lambda (1-lambda) y^2 have range <= b0 theta B^2/4 each", "reason": "per axis both exponents negative; group total is the chirp guard"}, +{"classification": "NON_EXPONENT", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-37", "keys": [], "line": 31, "quote": "Also |s| <= (1-theta)/2, i.e. 1 - 2|s| >= theta.", "reason": "exact algebra (s = Toeplitz shift)"}, +{"classification": "NON_EXPONENT", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-38", "keys": [], "line": 37, "quote": "1 - 2|s| >= 1 - 1/rho = theta/rho >= theta/2", "reason": "exact algebra"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-39", "keys": ["chirp_guard"], "line": 37, "quote": "the gauge is the chirp D' = exp(a theta t^2) of logarithmic range a theta B^2/4 (centred)", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-40", "keys": ["chirp_guard", "beta_lt_1"], "line": 41, "quote": "differs from it by <= poly(p) 2^{-Cp} times the diagonal range e^{O(g (a theta B^2 + polylog))}, which is covered by the same precision guard", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-41", "keys": ["setup_Cp"], "line": 41, "quote": "Entrywise |H^ - K| <= 4 * 2^{-P} e^{a/(4 theta)} relative to the weights (audit sec. 2)", "reason": "with P = Cp the factor e^(a/(4theta)) = e^(Theta(p^2 log p)) is not covered at fine theta; superseded by PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10; no ledger row (offline, non-exponent)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}]}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-42", "keys": ["old_theta_guard_noR"], "line": 41, "operative_keys": ["chirp_guard"], "quote": "and the exponent is o(p) bits by the precision guard beta + 2 xi - eps < 1 of Section 5", "reason": "literal guard false (beta+2xi-eps = 1.816); superseded by GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-43", "keys": ["chirp_guard", "beta_lt_1"], "line": 41, "quote": "For C > 1 the perturbation is <= 2^{-(C-o(1))p} <= 2^{-p}/poly", "reason": "C>1 fixed (non-exponent)"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-44", "keys": ["halo_radius"], "line": 41, "quote": "every audited uniform bound (row gap, inverse norms, Neumann tail J = Cp^2, halo radius A) holds for K~ with polynomially perturbed constants", "reason": "J = Cp^2 / old halo / row gap 1/(16p) are theta~1/d audit constants; PR1786 sec 5 l.215 forbids reusing them and replaces them (J = p^42, halo p^48); the transfer itself is non-exponent"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-45", "keys": ["TH_pos", "r_pos"], "line": 64, "quote": "Broad: gamma = b0 lambda = pi/(alpha^2 rho) = Theta(1/log p), 1-2|s| >= theta >= 1/(4d): mu >= (gamma theta/2) e^{-pi alpha^2 rho /3} = p^{-O(1)}", "reason": "hypothesis theta >= 1/(4d) stale (overridden by GAUGEFREE l.1); mu still p^-O(1) at theta >= 1/(4p^2)"}, +{"classification": "AUTO_TRUE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-46", "keys": ["TH_pos"], "line": 64, "quote": "Narrow: gamma = a rho >= 4 log(16 p), 1 - 2|s| >= theta/2: mu >= (1 - e^{-a theta/2}) e^{-pi^2/(3 gamma)} >= a theta/3 = p^{-O(1)}", "reason": "a theta = O(log p / p^2) -> 0, mu ~ a theta/3 polynomial"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-47", "keys": ["beta_lt_1"], "line": 70, "quote": "If Lambda/mu = p^{O(1)} the guard is O(log N log p) bits per axis.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-48", "keys": ["xi_gt_half"], "line": 82, "quote": "For the broad kernel the truncation tail is <= 2^{-p}, and mu >= p^{-O(1)}.", "reason": "W ~ p^(1/2) relies on truncation at online O(p) precision (PR1786 sec 3; non-exponent)"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-49", "keys": ["xi_gt_half"], "line": 84, "quote": "boundary segments of physical length B' <= B + 2W", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-50", "keys": ["old_theta_guard", "setup_Cp"], "line": 94, "operative_keys": ["chirp_guard", "beta_lt_1", "eps_lt_1"], "quote": "P >= p + O(a d) + O(g a theta B^2) + O(g log N log p) + ... , i.e. g B^2/d * polylog <= p^{1-r-zeta}:", "reason": "old-theta budget superseded by GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46; its O(ad) term becomes O(a/theta) = O(p^2 log p) and is moved to setup precision by PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-51", "keys": ["old_theta_guard"], "line": 95, "operative_keys": ["chirp_guard"], "quote": "**beta + 2 xi - eps <= 1 - r - zeta**", "reason": "superseded by GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46; control old_theta_chirp_guard", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-52", "keys": ["setup_Cp"], "line": 96, "operative_keys": ["gamma_slack"], "quote": "The offline accuracy term a d = o(p) is unchanged.", "reason": "at fine theta the offline term is a/(4theta) = Theta(p^2 log p), not ad; literal 'ad = o(p)' (1-eps-r0>0, global_gamma_power_slack) remains true but no longer bounds it; superseded by PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10; no ledger row encodes P_setup (non-exponent)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}]}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-53", "keys": ["xi_pos"], "line": 96, "quote": "The leftover linear term (exponent beta + xi - eps) is dominated by the chirp (exponent beta + 2 xi - eps) since xi > 0.", "reason": "named row shift_leftover_linear_dominated_by_chirp is absent from check_ledger.py but implied by cap_above_band"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-54", "keys": ["beta_lt_1"], "line": 96, "quote": "The circuit norms add g * O(log N log p) bits (Theorem 4.1), polylog per axis, as before.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-55", "keys": ["old_theta_guard_noZ"], "line": 101, "operative_keys": ["chirp_guard"], "quote": "`group_gauge_power_slack`: 1 - xi - r - beta -> **1 - (2 xi - eps) - r - beta**", "reason": "stated ledger edit superseded: check_ledger uses 2xi - THETA_POWER (GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-56", "keys": ["xi_pos", "eps_pos", "TH_pos"], "line": 101, "quote": "Add `shift_leftover_linear_dominated_by_chirp`: xi > 0, `shift_gap_theta_polynomial`: eps > 0.", "reason": "named rows absent but implied (cap_above_band, epsilon_positive, theta_positive_polynomial_power)"}, +{"classification": "OBSOLETE", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-57", "keys": ["gauss_eq_main_old", "guard_balance_old"], "line": 102, "operative_keys": ["gauss_row", "chirp_guard", "xi_def"], "quote": "eps = (1 + q beta)/(1 + q) (main = Gaussian), xi = eps(1+q) - c + slack (boundary = main + slack), beta = 1 - 2 xi + eps - r - zeta", "reason": "pkg8 balance superseded by FINE-PADDING-COMPOSITION.md sec 2 (eps free, beta = 1 - 3 delta); xi equation is still the ledger definition", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-58", "keys": ["beta_lt_1", "membership"], "line": 103, "quote": "`union_header_fits_record` (1-beta) and `membership_arithmetic_fits_record` (1 - beta - 2(1-eps)) stay: pkg8 values 3.354e-3 and 3.343e-3.", "reason": "pkg8 values; now 6e-30010 and 2e-30010"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-59", "keys": ["neg_linear_guard_noR", "neg_tag_2beta"], "line": 104, "quote": "Controls added: `old_linear_gauge_guard` (1 - xi - beta < 0), `old_union_tag_2beta` (1 - 2beta < 0) must fire as rejecting controls (they do).", "reason": "controls present (old_linear_guard includes r0) and fire"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-60", "keys": ["eps_def"], "line": 105, "quote": "superseded by outer/FINE-PADDING-COMPOSITION.md for the current epsilon = 1 - 2e-100 point", "reason": "current point is eps = 1 - 2e-30010, not 1 - 2e-100"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-61", "keys": ["beta_lt_1"], "line": 110, "quote": "Total = O(g mu V (p polylog p + g log L)) = O(g mu V p polylog p) as soon as g log L = o(p polylog p), i.e. beta < 1", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-62", "keys": ["chirp_guard"], "line": 115, "quote": "error poly(p) 2^{-Cp} e^{O(g a theta B^2)} = 2^{-(C-o(1))p}, C > 1", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-63", "keys": ["beta_lt_1", "membership"], "line": 117, "quote": "header (g log L bits) and membership (g (log s)^2) rows hold only \"eventually\", with exponent margins 3.3e-3", "reason": "margins now 6e-30010 / 2e-30010"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/GAUGEFREE-INTERIORS.md", "id": "outer-64", "keys": ["xi_gt_half"], "line": 118, "quote": "cap xi > 1/2 (still binding at 1.67e-3)", "reason": "cap no longer binding (0.408)"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-104", "keys": [], "line": 8, "quote": "**omega(1,1,5) = omega(1,5,1) = omega(5) < 6.156708**", "reason": "rectangular fallback not used (CLASSICAL l.28-30; FINE-PADDING-COMPOSITION l.13, l.38)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 38}, {"file": "outer/CLASSICAL-BOUNDARY.md", "line": 28}]}, +{"classification": "COVERED", "file": "outer/RECT-BOUNDARY.md", "id": "outer-105", "keys": ["beta_lt_eps"], "line": 19, "quote": "padding the last incomplete batch costs a polynomial amount per axis substream", "reason": "fallback file (unused)"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-106", "keys": [], "line": 22, "quote": "n^5 W^6 = poly(p) records (about p^3 polylog p)", "reason": "rectangular fallback (unused); W^6 = p^3 polylog consistent with W ~ p^(1/2)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "COVERED", "file": "outer/RECT-BOUNDARY.md", "id": "outer-107", "keys": ["beta_lt_eps"], "line": 24, "quote": "superpolynomial because d - g = p^epsilon - p^beta grows; W^5 = p^2.5 polylog p is far below it", "reason": "fallback file; L = p^8 there"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-108", "keys": [], "line": 28, "quote": "**tau_eff = omega(1,1,5) - 5 + 1 = omega(1,1,5) - 4**", "reason": "rectangular-boundary tau_eff formula; the rectangular fallback is not used: explicit Strassen tau = 45/16 boundary (FINE-PADDING-COMPOSITION l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "COVERED", "file": "outer/RECT-BOUNDARY.md", "id": "outer-109", "keys": ["boundary_row"], "line": 29, "quote": "The boundary row exponent is epsilon - xi + (tau_eff - 1)/2 and its saving is c + xi - epsilon with c = (3 - tau_eff)/2.", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-110", "keys": [], "line": 38, "quote": "`rect_leaf_domination`: sigma - (k+1) = sigma - 6 > 0", "reason": "rect_leaf_domination not in current ledger", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "NON_EXPONENT", "file": "outer/RECT-BOUNDARY.md", "id": "outer-111", "keys": [], "line": 53, "quote": "the total record width is O(P + h + log W) = O(p) at the retained boundary interface (P, h = O(p))", "reason": "fast matrix product record width"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-112", "keys": ["tau_gt_2", "tau_lt_5_2"], "line": 59, "operative_keys": ["strassen"], "quote": "`rect_effective_exponent_above_two` (tau_eff > 2, the trivial output-size bound) and `rect_effective_exponent_below_five_halves`", "reason": "rows absent from the current ledger; tau < 5/2 false at 45/16 but only the explicit-formula gap log2 7 < tau is needed (FINE-PADDING-COMPOSITION l.13; PR1786 sec 6)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 246}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/RECT-BOUNDARY.md", "id": "outer-113", "keys": ["xi_gt_half", "union_row"], "line": 65, "quote": "cap xi > 1/2 holds with margin 0.0791; union saving xi + 1/2 - epsilon = 0.080 (the old g-factor union row would be -0.341)", "reason": "pkg6 numbers"}, +{"classification": "OBSOLETE", "file": "outer/RECT-BOUNDARY.md", "id": "outer-114", "keys": ["tag_2beta"], "line": 66, "operative_keys": ["beta_lt_1"], "quote": "union tag work 1 - 2 beta = 0.158", "reason": "per-visit accounting (GAUGEFREE sec 7)", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 108}]}, +{"classification": "COVERED", "file": "outer/RECT-BOUNDARY.md", "id": "outer-115", "keys": ["beta_lt_eps", "eps_lt_1"], "line": 71, "quote": "the number of right-hand sides in an axis substream is superpolynomial in the regime used", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-123", "keys": ["b_lt_cert"], "line": 9, "quote": "must lie strictly inside the certified supplier endpoint", "reason": "coverage: b_lt_cert asserted (check_ledger asserts b < certified complex < bit; ledger_eval identity b = pinned - r0)"}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-124", "keys": ["q_lt_a", "a_lt_b"], "line": 10, "quote": "q < a_eff < b strictly", "reason": "coverage: q_lt_a = ledger q_below_effective/q_below_internal; a_lt_b = ledger complex_above_effective"}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-125", "keys": ["main_row"], "line": 11, "quote": "strict gap absorbs polylog factors", "reason": "coverage: main_row = ledger main_transform_above_kappa"}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-126", "keys": ["r_pos"], "line": 13, "quote": "only eventual u = alpha^2 <= p^r0", "reason": "coverage: r_pos = ledger alpha_logarithm_absorption"}, +{"classification": "OBSOLETE", "file": "outer/RETUNED-SLACKS.md", "id": "outer-127", "keys": ["linear_guard_zeta"], "line": 14, "operative_keys": ["chirp_guard"], "quote": "r + zeta > 0 gives g a B = o(p)", "reason": "stale rationale: linear gauge removed (GAUGEFREE R1/R3; FINE-PADDING-COMPOSITION l.11); zeta now has no role in any ledger check", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 11}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-128", "keys": ["stop_pos", "leaf_gt_a", "q_lt_leaf"], "line": 15, "quote": "any t_stop > 0 with (1-t)b > a_eff, q < (1-t)b", "reason": "coverage: stop_pos = ledger stop_positive; leaf_gt_a = ledger leaf_saving_above_effective; q_lt_leaf = ledger q_below_leaf/lambda_prime_above_leaf"}, +{"classification": "COVERED", "file": "outer/RETUNED-SLACKS.md", "id": "outer-129", "keys": ["gamma_slack", "beta_def"], "line": 23, "quote": "any DELTA_E > r0 = 1e-30010 is admissible", "reason": "coverage: gamma_slack = ledger global_gamma_power_slack; beta_def asserted (check_ledger beta = 1 - 3 DELTA_E)"}, +{"classification": "COVERED", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-89", "keys": ["xi_lt_eps"], "line": 3, "quote": "with fine source-prime padding the boundary row is not binding (xi = 0.908 < epsilon), and the explicit Strassen boundary of PR1786 is used", "reason": "file is an unused alternative"}, +{"classification": "OBSOLETE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-90", "keys": [], "line": 9, "quote": "The boundary row then has exponent epsilon - xi + 1/2 + o(1) (tau_eff = 2 + delta for every fixed delta > 0; tau_eff = 2 itself is not claimed)", "reason": "structured boundary not used (FINE-PADDING-COMPOSITION.md l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "NON_EXPONENT", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-91", "keys": [], "line": 19, "quote": "The truncation to bandwidth W (rows farther than W are below 2^-P and are zero in the retained rounded matrix) keeps T banded Toeplitz.", "reason": "W = Theta(sqrt(P) polylog) with online P = O(p) (inherited)"}, +{"classification": "OBSOLETE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-92", "keys": ["old_theta_guard_noR"], "line": 24, "operative_keys": ["chirp_guard"], "quote": "O(a theta B'^2) = O(a B^2/d) (B' <= B + 2W) in the fractional-shift representation of GAUGEFREE-INTERIORS.md (chirp only), inside the group guard g a B^2/d = o(p) used by this package (beta + 2 xi - eps < 1)", "reason": "STRUCTURED-BOUNDARY unused (FINE-PADDING-COMPOSITION l.13); guard superseded (GAUGEFREE-INTERIORS.md l.1 package note + FINE-PADDING-COMPOSITION.md l.46)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}]}, +{"classification": "COVERED", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-93", "keys": ["xi_gt_half"], "line": 38, "quote": "because the band is W and the separators have length >= W", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "OBSOLETE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-94", "keys": [], "line": 58, "quote": "the boundary arithmetic is **O(V (d/B) W polylog p)**, so the boundary exponent is epsilon - xi + 1/2 + o(1), i.e. tau_eff = 2 + delta (any fixed delta > 0 absorbs the polylog factors since W = p^(1/2) polylog p)", "reason": "structured boundary cost (unused, FINE-PADDING-COMPOSITION l.13); W exponent 1/2 premise consistent", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-95", "keys": ["TH_pos"], "line": 61, "quote": "(the regime: row gap about 1/(16p), poly(p) conditioning)", "reason": "row gap 1/(16p) is the theta~1/d value; fine theta gives ~1/(8p^2), still polynomial; file unused"}, +{"classification": "AUTO_TRUE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-96", "keys": ["TH_pos"], "line": 64, "quote": "||N^-1||_inf < 16 theta^-2", "reason": "16 theta^-2 <= 256 p^4"}, +{"classification": "COVERED", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-97", "keys": ["xi_lt_1"], "line": 68, "quote": "which cost O(aB) = o(p) extra bits", "reason": "per page only; if charged over g axes it would be the false linear guard; file unused"}, +{"classification": "COVERED", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-98", "keys": ["chirp_guard"], "line": 70, "quote": "Hence P' = P + O(log p) + o(p) (the guard), i.e. O(p) bits suffice", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "AUTO_TRUE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-99", "keys": [], "line": 77, "quote": "= O(e^(a/4)) = O(p)", "reason": "e^(a/4) = (16p)^(1+o(1)) (a = 4 log 16p + O(sqrt log p)): polynomial; literal O(p) slightly overstated; file unused"}, +{"classification": "COVERED", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-100", "keys": ["xi_lt_1"], "line": 82, "quote": "about e^{O(aB)}) are stored inside the coupling pages and cost O(aB) = o(p) guard bits per page", "reason": "coverage: xi_lt_1 implied by cap_below_cell+epsilon_below_one"}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-101", "keys": ["TH_pos"], "line": 92, "quote": "theta >= 1/(4d), and BILATERAL-LDU.md bounds the periodic inverse by ||N^-1||_inf < 16 theta^-2", "reason": "theta >= 1/(4d) stale; ||N^-1|| < 16 theta^-2 still polynomial"}, +{"classification": "OBSOLETE", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-102", "keys": [], "line": 96, "quote": "tau_eff = 2 + delta (delta = 1e-30010): c = (3 - tau_eff)/2 = 1/2 - delta/2.", "reason": "c = 1/2 - delta/2 superseded by Strassen c = 3/32 (FINE-PADDING-COMPOSITION l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/STRUCTURED-BOUNDARY.md", "id": "outer-103", "keys": ["xi_gt_half", "beta_lt_1"], "line": 97, "quote": "xi = 0.50167, xi - 1/2 = 0.00167 > 0 (cap holds), beta = 0.99665, union tag work per visit 1 - beta = 0.00335 > 0", "reason": "earlier-package numbers (file says so)"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-65", "keys": ["beta_lt_1"], "line": 11, "quote": "a header of O(g log L) bits (g=p^beta, L=poly(p) the microbox side, beta<1, so the header is o(p)", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-66", "keys": ["xi_gt_half"], "line": 13, "quote": "mu = max_i |E_i|/L = O((W/B) polylog p)", "reason": "carving (|E_i|, mu) is an inherited PR1673 assumption (non-exponent)"}, +{"classification": "OBSOLETE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-67", "keys": ["old_union_row"], "line": 18, "operative_keys": ["union_row"], "quote": "`O(V [g^2 mu + g mu polylog p])` per window and the union row `eps + beta + 1/2 - xi`", "reason": "replaced by outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125); control old_g_factor_union_row", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-68", "keys": ["beta_lt_1"], "line": 47, "quote": "g log L = o(p) since beta < 1 (ledger check `union_tag_work_per_visit_fits_record`)", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "AUTO_TRUE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-69", "keys": ["beta_lt_1"], "line": 53, "quote": "Total O(N log g) = O(N log p).", "reason": "log g = beta log p <= log p"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-70", "keys": ["beta_lt_1"], "line": 58, "quote": "(O(g log L) bits per comparison, o(p))", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-71", "keys": ["membership", "eps_lt_1"], "line": 59, "quote": "the rank of x_f in E_f costs O(polylog p) with the carving description", "reason": "ordinal of x_f in E_f is computed once per record in the U-forming scan; every cost reading needs beta+2(1-eps)<1 = membership_arithmetic_fits_record (two independent verifiers; was AMBIGUOUS in the matcher)"}, +{"classification": "AUTO_TRUE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-72", "keys": [], "line": 60, "quote": "Let `a = |E_f| <= L = poly(p)`.", "reason": "a = |E_f| <= L = poly(p): transpose depth O(log p)"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-73", "keys": ["beta_lt_eps", "eps_lt_1"], "line": 66, "quote": "factor pages (regenerated once per microbox and axis from its coarse origins, polynomial in p, amortised by the superpolynomial payload)", "reason": "amortization inequality itself non-exponent (inherited)"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-74", "keys": ["scan_row"], "line": 75, "quote": "O(V polylog p) per window, in the group-scan row", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-75", "keys": ["union_row"], "line": 85, "quote": "the total is O(p (log g + log L + 1) * sum_r |S_r|)", "reason": "polylog factor absorbed by the union row margin"}, +{"classification": "NON_EXPONENT", "file": "outer/UNION-SCHEDULE.md", "id": "outer-76", "keys": [], "line": 90, "quote": "`sum_r |S_r| = sum_x |F(x)| = sum_i |U_i| = sum_i |E_i| L^(g-1) * (spectators) <= g mu V.`", "reason": "exact identity (sched_test.py)"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-77", "keys": ["beta_lt_eps", "union_row"], "line": 96, "quote": "`O(V (d/g) g mu polylog p) = O(V d W polylog p / B)`,", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record; union_row = ledger sparse_union_movement_above_kappa"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-78", "keys": ["union_row"], "line": 98, "quote": "i.e. union-movement exponent `eps + 1/2 - xi` (saving `xi + 1/2 - eps`).", "reason": "coverage: union_row = ledger sparse_union_movement_above_kappa"}, +{"classification": "AUTO_TRUE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-79", "keys": ["dense_union"], "line": 101, "quote": "the expected number of flags g*mu = p^(beta+1/2-xi) is larger than 1 (xi - beta - 1/2 < 0)", "reason": "descriptive; negation of the deleted sparsity row"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-80", "keys": ["beta_lt_1"], "line": 103, "quote": "O(g mu V (p polylog p + g log L)) = O(g mu V p polylog p) as soon as g log L = o(p), i.e. beta < 1", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-81", "keys": ["tag_2beta"], "line": 103, "operative_keys": ["beta_lt_1"], "quote": "An earlier version of this note charged O(g^2) per record against o(p) and required 2 beta < 1", "reason": "superseded by GAUGEFREE sec 7 per-visit accounting; control old_union_tag_2beta", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 108}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/UNION-SCHEDULE.md", "id": "outer-82", "keys": ["boundary_row"], "line": 107, "quote": "`tau_eff = 2 + 1e-30010` (structured boundary solves, outer/STRUCTURED-BOUNDARY.md;", "reason": "sec 4 quotes the structured tau_eff = 2+1e-30010; sec 5b of the same file uses Strassen c = 3/32"}, +{"classification": "OBSOLETE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-83", "keys": ["linear_g_param", "guard_balance_old"], "line": 108, "operative_keys": ["xi_gt_half", "chirp_guard"], "quote": "guard `beta = 1 - xi - r - zeta` (linear gauge; in this package the guard is the chirp-only `beta = 1 - (2 xi - eps) - r - zeta`, see Section 5b); `xi > 1/2`", "reason": "guard-as-balance superseded (sec 5b; FINE-PADDING-COMPOSITION sec 2: beta = 1 - 3 delta)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-84", "keys": ["old_eps_balance"], "line": 109, "operative_keys": ["xi_def", "union_row"], "quote": "`eps = (1 + q + q (c - s - r - zeta))/(1 + q)^2`, `xi = eps (1 + q) - c + s`. The union row is far above kappa at this point (saving about 0.080 here).", "reason": "eps balance superseded (eps free); xi formula current; union saving now 0.408", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "STALE_TEXT_ONLY", "file": "outer/UNION-SCHEDULE.md", "id": "outer-85", "keys": ["neg_old_union_row"], "line": 110, "quote": "reinstating the old row `1 - eps - beta - 1/2 + xi` at the new point fails (it is about -0.125)", "reason": "control fires; number now -0.592 (5b states it correctly)"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-86", "keys": ["beta_lt_1"], "line": 123, "quote": "support router span 1-beta = 6e-30010 > 0 (the supplier's total moved support O(g polylog p) = o(p) holds eventually, with exponent margin 6e-30010)", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "outer/UNION-SCHEDULE.md", "id": "outer-87", "keys": ["beta_lt_eps"], "line": 124, "quote": "group key fits the record (eps-beta = 4e-30010)", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "OBSOLETE", "file": "outer/UNION-SCHEDULE.md", "id": "outer-88", "keys": ["union_density"], "line": 125, "quote": "The ledger row `sparse_union_fraction_decays` (xi-beta-1/2 > 0) stays deleted: it is false", "reason": "row deleted here (UNION-SCHEDULE l.101-102, l.125); the statement 'it is false' is correct", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 101}, {"file": "outer/UNION-SCHEDULE.md", "line": 125}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-01", "keys": ["strassen", "tau_gt_2"], "line": 13, "quote": "where `tau > 2` is a fixed rational number.", "reason": "coverage: strassen = ledger strassen_integer_power_gap; tau_gt_2: rejecting control fires"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-05", "keys": [], "line": 22, "quote": "`M(t)` is a regular integer multiplication bound: `M(t) >= t`, `M(Ct)=O_C(M(t))` for fixed `C`, and precision doubling sums to `O(M(t))`", "reason": "conversion of O(p+h+log W)-bit scalar work into O(M(p)) cost"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-06", "keys": [], "line": 23, "quote": "If the input encoding has `h = O(p)`, this is", "reason": "h = O(log p) at final (p^10 norms, dyadic normalizers)"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-07", "keys": [], "line": 29, "quote": "If also `log W = O(p)`, it is exactly `O(W^tau M(p))`, without a suppressed logarithmic factor. In particular this holds for `W = Theta(sqrt(p))`.", "reason": "log W = O(log p)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-02", "keys": ["strassen"], "line": 31, "quote": "The strict exponent slack is essential to this statement", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-03", "keys": ["strassen"], "line": 87, "quote": "For rational `tau=a/d`, the first comparison is the integer comparison `r^d < b^a`.", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-04", "keys": ["strassen"], "line": 115, "quote": "Every case is `O(N^tau)` because `rho2`.", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-10", "keys": [], "line": 158, "quote": "For `epsilon <= 1`, all these terms have the stated recurrence after enlarging `K`.", "reason": "error recurrence E_d <= K E_{d-1} + K b^{d-1}"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-08", "keys": [], "line": 169, "quote": "q=p+2\\max(h,0)+\\lceil L\\log_2K\\rceil+O(1).", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-09", "keys": [], "line": 180, "quote": "Only `O(h+log N)` integer bits are needed. The total working bit width is therefore `O(p+h+log N)`.", "reason": ""}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/ALGEBRAIC-STABILITY-INDEPENDENT.md", "id": "pr1673c-11", "keys": [], "line": 190, "quote": "It does not justify using the exact infimum exponent without slack, treating a varying family of coefficients as fixed", "reason": "scope: formula must be one fixed finite formula independent of p"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-12", "keys": ["TH_pos"], "line": 7, "quote": "Let `1=1`, define on Z", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-14", "keys": ["TH_pos"], "line": 17, "quote": "`||N^-1||_infinity <= c^-4 exp(a/2)/(1-exp(-a rho theta))^2`.", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-15", "keys": ["TH_pos"], "line": 21, "quote": "`||N^-1||_infinity < 16 theta^-2`.", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-16", "keys": [], "line": 23, "quote": "No lower bound proportional to log(1/theta) on a is needed for this norm theorem.", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-17", "keys": ["TH_pos"], "line": 57, "quote": "Because each q-gap is at least 1,", "reason": ""}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-18", "keys": [], "line": 79, "quote": "Both use only `-1/2<=beta_k<1/2`.", "reason": "phase offsets used in the inverse-factor bounds"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/BILATERAL-LDU.md", "id": "pr1673c-19", "keys": ["TH_pos"], "line": 121, "quote": "Also `1-exp(-rho theta)>=theta/2` for 0=p+O(ad+g*a*Bcap+log g+polylog p), rather than p+O(g*a*d). Both added power terms are o(p) in the proposed parameter family.", "reason": "g*a*Bcap term superseded by the chirp guard; the offline a*d accuracy term is superseded at fine theta by PR1786 P_setup = Cp + 64 p^2 L_p", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 1}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 46}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-123", "keys": ["linear_guard_noR"], "line": 89, "operative_keys": ["chirp_guard"], "quote": "Both diagonal logarithmic ranges on the capped block are at most `b0 Bcap`.", "reason": "broad gauge superseded by GAUGEFREE R1 (broad chirp b0 theta B^2)", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-124", "keys": ["beta_lt_1", "TH_pos"], "line": 97, "quote": "Shallow Toeplitz circuit amplification contributes polylog(p) per axis.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record; TH_pos = ledger theta_positive_polynomial_power"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-125", "keys": ["linear_guard"], "line": 101, "operative_keys": ["chirp_guard"], "quote": "`O(g a Bcap + g polylog p)`", "reason": "control old_linear_guard", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-126", "keys": ["linear_guard_zeta"], "line": 105, "operative_keys": ["chirp_guard"], "quote": "`g a Bcap=O(p^(1-r-zeta) log p)=o(p)`.", "reason": "linear-gauge budget g a Bcap = o(p) (beta + xi + r0 + zeta <= 1) is false at final; superseded by gauge-free interiors (GAUGEFREE R1/R3); LEDGER control old_linear_guard", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-127", "keys": ["full_cell_gauge_TH"], "line": 107, "operative_keys": ["chirp_guard"], "quote": "In particular no remaining full-cell term g*a*d may be charged after exact recentering.", "reason": "prohibition holds; control full_cell_gauge", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "line": 107}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-128", "keys": ["setup_Cp"], "line": 107, "quote": "Offline accuracy still needs to dominate ad=o(p), as above.", "reason": "offline accuracy must dominate a/(4theta) = O(p^2 log p) at final; PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}]}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-129", "keys": [], "line": 111, "quote": "so all completed Schur and inverse norms remain polynomial under the cap.", "reason": "narrow Schur norms"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "id": "pr1673a-130", "keys": [], "line": 117, "quote": "Block Schur entries are bounded by `H+H H_EE^-1 H`, hence polynomial.", "reason": "whole-group elimination norms"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-82", "keys": ["xi_gt_half", "xi_lt_eps"], "line": 5, "quote": "where `1/20.", "reason": "control old_linear_guard; superseded by GAUGEFREE R1/R3", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-89", "keys": ["eps_lt_1", "beta_lt_1"], "line": 29, "quote": "The supplier support proof needs each individual K-neighborhood to fit its original axis and total moved support o(p)", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-90", "keys": ["beta_lt_1_minus_eps"], "line": 29, "operative_keys": ["beta_lt_1"], "quote": "The sufficient auxiliary inequality `beta<1-epsilon` in the uncapped ledger must therefore be removed in this follow-up.", "reason": "removed here (load-bearing removal)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "line": 29}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-91", "keys": ["main_row"], "line": 35, "quote": "| main transform | `1-epsilon*q` |", "reason": "coverage: main_row = ledger main_transform_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-92", "keys": ["gauss_row"], "line": 36, "quote": "| fused Gaussian circuits | `epsilon-q*beta` |", "reason": "coverage: gauss_row = ledger fused_gaussian_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-93", "keys": ["boundary_row"], "line": 37, "quote": "| boundary algebra | `epsilon-b+(omega-1)/2` |", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-94", "keys": ["old_union_row"], "line": 38, "operative_keys": ["union_row"], "quote": "| sparse union movement | `epsilon+beta+1/2-b` |", "reason": "control old_g_factor_union_row; outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-95", "keys": ["scan_row"], "line": 39, "quote": "| grouped scans | `epsilon-beta` |", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-96", "keys": ["full_key_union"], "line": 43, "operative_keys": ["union_row"], "quote": "Even a conservative full active-group key surcharge adds only `beta+1-epsilon` to the union exponent.", "reason": "control full_key_sort", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-97", "keys": ["face_row"], "line": 43, "quote": "Sparse core-face corrections have exponent at most `epsilon+beta-3`", "reason": "stale numeric: halo_minus_core_m5 (final -80, at pr1673: -5 matches)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-98", "keys": ["slack_pos", "c_pos"], "line": 45, "quote": "put c=(3-omega_upper)/2=3/32 and take a positive boundary slack s_boundary=10^-5", "reason": "eventual only (exponent margin slack_pos=1E-30010)"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-99", "keys": ["old_eps_balance"], "line": 48, "operative_keys": ["xi_def"], "quote": "epsilon=(1+q+q*(c-s_boundary-r-zeta))/(1+q)^2,", "reason": "eps formula superseded (FINE-PADDING-COMPOSITION sec 2); xi formula retained", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-100", "keys": ["eps_def"], "line": 57, "quote": "epsilon = 0.9984838711085557536432677624420451614...", "reason": "PR1673 pinned point"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-101", "keys": ["boundary_eq"], "line": 64, "quote": "The boundary saving equals `kappa_limit+10^-5`.", "reason": "slack 1e-5 -> 1e-30010"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-102", "keys": ["old_union_row", "full_key_union"], "line": 64, "operative_keys": ["union_row"], "quote": "The union movement exponent is below 0.686, and even its optional full-key surcharge leaves it below 0.781.", "reason": "both claims true at PR1673's point, false at final; old union row and full-key sort superseded (outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125))", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-103", "keys": ["membership"], "line": 64, "quote": "The per-record phase metadata exponent `beta+2(1-epsilon)` is below 0.097", "reason": "exponent now 1 - 2e-30010 (not below 0.097); condition < 1 holds"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-104", "keys": ["face_row"], "line": 64, "quote": "Core-face repair costs remain negligible at L=p^8.", "reason": "stale numeric: core_power_8 (final 128, at pr1673: 8 matches)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-105", "keys": ["eps_lt_1"], "line": 66, "quote": "Since `1-epsilon>0`, this holds eventually even though gK is larger than one axis width.", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-106", "keys": ["beta_lt_1"], "line": 66, "quote": "The total support is O(g polylog p)=o(p), because beta<1.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-107", "keys": ["xi_gt_half", "xi_lt_eps", "beta_pos", "beta_lt_eps"], "line": 68, "quote": "At the displayed parameters, `b>1/2`, `epsilon>b`, `beta>0`, `epsilon>beta`", "reason": "coverage: xi_gt_half = ledger cap_above_band; xi_lt_eps = ledger cap_below_cell; beta_pos = ledger group_positive; beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-108", "keys": ["linear_guard"], "line": 68, "operative_keys": ["chirp_guard"], "quote": "`1-b-r-beta=zeta>0`", "reason": "control old_linear_guard", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-109", "keys": ["gamma_slack"], "line": 68, "quote": "and `1-epsilon-r>0`", "reason": "at fine theta the rounding range is O(p^2 log p) and is paid by P_setup, not by this row"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-110", "keys": [], "line": 68, "quote": "The raw global rounded weights may still have O(ad) logarithmic range during offline generation.", "reason": "raw range now O(p^2 log p) (PR1786 l.114); offline only, PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 114}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "id": "pr1673a-111", "keys": ["chirp_guard"], "line": 68, "quote": "approximating those ratios to the retained precision introduces `exp(o(p))` error amplification, already paid by the strict group guard.", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-SIGNOFF.md", "id": "pr1673a-66", "keys": ["xi_lt_eps", "xi_lt_TH"], "line": 4, "quote": "`B=p^b infinity`", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-SIGNOFF.md", "id": "pr1673a-79", "keys": ["halo_volume"], "line": 63, "quote": "With L=p^8 and halo A=p^3, the additional output fraction is", "reason": "now p^(beta-80)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-SIGNOFF.md", "id": "pr1673a-80", "keys": ["face_row"], "line": 65, "quote": "old sequential local solvers are still negligible.", "reason": "coverage: face_row = ledger microbox_face_corrections_above_kappa"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/CAPPED-SIGNOFF.md", "id": "pr1673a-81", "keys": ["eps_def"], "line": 71, "quote": "epsilon = .9984838711085558", "reason": "PR1673 pinned point"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-21", "keys": ["r_pos"], "line": 5, "quote": "Let the narrow parameter be `a=pi alpha^2=Theta(log p)`", "reason": "coverage: r_pos = ledger alpha_logarithm_absorption"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-22", "keys": [], "line": 19, "quote": "for every finite contiguous principal block with q-gaps at least 1 and |beta_i|<=1/2,", "reason": "hypotheses of the small-parameter (b>0) LDU inverse bound for broad blocks"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-23", "keys": [], "line": 33, "quote": "Since b*rho*theta=pi*theta/(alpha^2 rho)<1 for alpha>=2 and theta<=1", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-24", "keys": ["TH_pos", "r_pos"], "line": 33, "quote": "Thus every such normalized block inverse has norm polynomial in p when alpha^2=O(log p) and theta^-1 is polynomial in p.", "reason": "weak encoding: polynomial for any finite THETA_POWER"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-25", "keys": [], "line": 53, "quote": "` =O(alpha^5 rho^2 theta^-2 exp(pi alpha^2 rho/3))=poly(p)`.", "reason": "K^-1|| = O(p^(2TH+5/3+o(1))) at final, polynomial (see umbrella pr1673c-84)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-26", "keys": ["xi_lt_TH"], "line": 55, "quote": "Target holes should be retained as boundary vertices, so every interior coordinate has the asserted original beta bound.", "reason": "hole retention itself is a non-exponent layout obligation"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-27", "keys": [], "line": 63, "quote": "A Gaussian lattice-sum bound gives `||R||=O(1)` after the alpha^-1 factor.", "reason": "hole-row coupling block of the augmented forward map"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-28", "keys": [], "line": 67, "quote": "Gaussian truncation and sufficiently accurate structure-preserving coefficient rounding perturb both it and all required interior blocks by exponentially small amounts", "reason": ""}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-29", "keys": [], "line": 73, "quote": "To justify a particular sequential block-LU implementation, its prefix factor norms still need to be checked.", "reason": "prefix factor norms of the block-LU boundary elimination"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-30", "keys": [], "line": 79, "quote": "`delta=(1-lambda)m-c`, with |delta|<=1/2.", "reason": "anchor recentring offset for the exact local Toeplitz split"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-31", "keys": ["full_cell_gauge_d", "full_cell_gauge_TH"], "line": 91, "operative_keys": ["chirp_guard"], "quote": "On a phase cell of O(d) coordinates, the two diagonal logarithmic ranges are O(d/alpha^2). These are smaller than the O(alpha^2 d) narrow inverse gauges already paid by the proposed group size.", "reason": "superseded by CAPPED-INTERIORS, GAUGEFREE R1 and PR1786 l.149; control full_cell_gauge", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 149}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}, {"file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "line": 107}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-32", "keys": [], "line": 101, "quote": "`sqrt(pi/gamma) exp[-pi^2/(4gamma)] <= f(omega) <= 1+sqrt(pi/gamma)`.", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-33", "keys": [], "line": 103, "quote": "At alpha^2=O(log p), its condition number is polynomial in p. Truncation width O(sqrt(p/gamma)) and Cp-bit rounding perturb the matrix far less than its lower eigenvalue", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-34", "keys": ["beta_lt_1"], "line": 105, "quote": "This calls for O(log^2 p) internal circuit guard bits per axis, rather than claiming the near-identity theorem's O(log p) unchanged. It is still below the group budget dominated by the local Gaussian diagonals.", "reason": "comparative claim stale: at final the per-axis chirp is o(1), so the polylog circuit guard dominates the group budget"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/FORWARD-SMALL-A-AUDIT.md", "id": "pr1673c-35", "keys": ["xi_gt_half"], "line": 107, "quote": "using the broader width O(sqrt(p alpha^2)). It keeps target holes and separators as boundary, adds only polylogarithmic boundary volume", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-95", "keys": ["beta_lt_eps"], "line": 13, "quote": "Assume B=Theta(p), `g h=O(p)`, and the active group grows", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-96", "keys": ["beta_pos"], "line": 14, "quote": "superpolynomially.", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-97", "keys": [], "line": 22, "quote": "where `L=poly(p)`.", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-98", "keys": ["halo_volume", "core_gt_halo", "eps_lt_1"], "line": 30, "quote": "with `N>4L` and `gL/N=o(1)`.", "reason": "coverage: halo_volume = ledger microbox_halo_volume; core_gt_halo implied by microbox_halo_volume; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-99", "keys": ["eps_lt_1"], "line": 31, "quote": "`K0=O(g(h+b)+log g)=O(gh)`", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-100", "keys": ["halo_metadata"], "line": 32, "quote": "Require `K0^2=O(B)` or retain the explicit extra metadata term below.", "reason": "hypothesis is a disjunction: branch 1 (K0^2 = O(B)) is false at final; branch 2 (explicit metadata term) holds, dominated by microbox_face_corrections"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-102", "keys": ["halo_copysort"], "line": 40, "quote": "+ (gL/N) (K0 + g polylog p) ])", "reason": "coverage: halo_copysort implied by microbox_face_corrections_above_kappa+epsilon_positive"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-101", "keys": ["halo_metadata"], "line": 44, "quote": "plus `O((gL/N)V K0^2/B)` if metadata arithmetic is not absorbed by records.", "reason": "no explicit row, implied by microbox_face_corrections_above_kappa (+ eps > beta)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-103", "keys": ["bitrouter_row"], "line": 58, "quote": "`O(V (gb)^(1-a) polylog p)`.", "reason": "coverage: bitrouter_row = ledger group_bit_router_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-104", "keys": ["core_gt_halo", "beta_pos"], "line": 71, "quote": "`N/L >= p^eta`, `g -> infinity`", "reason": "coverage: core_gt_halo implied by microbox_halo_volume; beta_pos = ledger group_positive"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-105", "keys": ["halo_volume"], "line": 118, "quote": "= O((gL/N)V).", "reason": "coverage: halo_volume = ledger microbox_halo_volume"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-106", "keys": ["beta_pos"], "line": 158, "quote": "Their setup per coarse tile is absorbed by its N^g payload.", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-107", "keys": ["beta_lt_eps"], "line": 168, "quote": "Since K0=O(B), each pass costs O(M); K0 passes", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-108", "keys": ["halo_passes"], "line": 185, "quote": "`O(g polylog p)` for movement and unconditional polynomial-length arithmetic.", "reason": "coverage: halo_passes implied by microbox_face_corrections_above_kappa"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-109", "keys": [], "line": 188, "quote": "O(p+log N)=O(p) guard bits", "reason": ""}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-110", "keys": ["stale_g_param2"], "line": 200, "operative_keys": ["beta_def"], "quote": "`g=p^(1-epsilon-zeta)` with fixed positive", "reason": "partial-fusion parameterisation; beta re-set by FINE-PADDING-COMPOSITION sec 2", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-111", "keys": ["eps_gt_5_6"], "line": 201, "quote": "zeta and epsilon>5/6.", "reason": "true; derived under the superseded g"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-112", "keys": ["halo_radius"], "line": 201, "quote": "Suppose `L=O(p polylog p)` and take the dyadic side", "reason": "stencil radius is p^48 at final (PR1786 sec 5)"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-113", "keys": ["N_gt_4halo_old"], "line": 202, "operative_keys": ["core_gt_halo"], "quote": "`N=2^ceil((3/2)log2 p)`.", "reason": "N = p^(3/2) would violate N > 4L with the final halo p^48; superseded by core 2^ceil(128 log2 p) (PR1786 l.230)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 230}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-114", "keys": ["eps_lt_1"], "line": 202, "quote": "The actual S_i eventually exceed every polynomial,", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "FALSE_AT_POINT", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-115", "keys": ["K0sq_branch1"], "line": 205, "load_bearing": false, "operative_keys": ["halo_metadata"], "quote": "and `K0^2=o(p)`", "reason": "correctly translated to the actual g = p^beta, K0 = O(gh) = p^(beta+1-eps) and K0^2 = o(p) needs 2(beta+1-eps) < 1: false (-1 + 8e-30010). Not load-bearing provided HALO-THEOREM is used with its explicit metadata term (l.32, l.44), which holds (dominated by microbox_face_corrections, margin ~79); no final note records that branch choice"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-116", "keys": ["halo_K0_mult"], "line": 209, "quote": "(gL/N) K0 = O(p^(5/2-3epsilon-2zeta) polylog p) = o(1),", "reason": "stale formula p^(5/2-3eps-2zeta) (old g); with actual g and halo/core 48/128 the multiplier is p^(2beta-eps+1-80) = o(1)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-117", "keys": ["halo_g_mult"], "line": 210, "quote": "(gL/N) g = O(p^(3/2-2epsilon-2zeta) polylog p) = o(1).", "reason": "stale formula; actual multiplier p^(2beta-80) = o(1)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-118", "keys": ["gauss_row"], "line": 215, "quote": "since log N=Theta(log p)", "reason": "coverage: gauss_row = ledger fused_gaussian_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-119", "keys": ["tile_gauge", "tile_gauge_core"], "line": 221, "operative_keys": ["chirp_guard"], "quote": "g [a0 theta N + a0/theta]", "reason": "false under every reading; the final halo path copies actual windows and applies original coefficients, no translation-invariant tile gauge (PHASE-LAYOUT-AUDIT l.203-211)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "line": 203}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md", "id": "pr1673b-120", "keys": ["eps_gt_5_6"], "line": 227, "quote": "for epsilon>5/6 and fixed zeta>0.", "reason": "true; the gauge conclusion it supports (pr1673b-119) is not used"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-36", "keys": ["theta_ge_1_over_d"], "line": 3, "operative_keys": ["TH_pos"], "quote": "`a=pi alpha^2=Theta(log p)`, `theta=Theta(1/d)`, even though `a theta` tends to zero.", "reason": "regime theta = Theta(1/d) superseded by PR1786 sec 1-2", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 17}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-37", "keys": [], "line": 33, "quote": "so their entire two-sided tail is below `4 exp(-2a)` for a>=1.", "reason": ""}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-38", "keys": ["theta_ge_1_over_4p"], "line": 39, "operative_keys": ["TH_pos"], "quote": "For p>=101, theta>=1/(4p), and `a>=4 log(16p)`,", "reason": "PR1786 sec 2 (l.73-78) re-proves the estimate for every theta>0 with gap 1/(8p^2)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 69}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-39", "keys": ["TH_pos"], "line": 45, "quote": "Hence N has row diagonal-dominance margin at least `1/(8p)`", "reason": "gap is 1/(8p^2) at fine theta, still polynomial"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-40", "keys": ["r_pos"], "line": 49, "quote": "`alpha=ceil(sqrt((4/pi)log(16p)))`.", "reason": "coverage: r_pos = ledger alpha_logarithm_absorption"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-41", "keys": ["u_ge_log2_8p"], "line": 51, "quote": "The old sufficient condition `u>=ceil(log2(8p))` need not be reused", "reason": "'need not be reused' (same line); would be false eventually (4 ln 2 < pi)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "line": 51}]}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-42", "keys": [], "line": 57, "quote": "`w=ceil(sqrt(16p/u))+2`, u=alpha^2=a/pi;", "reason": "defines w ~ sqrt(p/log p) (the W of the ledger), independent of theta"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-43", "keys": ["full_cell_axis"], "line": 72, "quote": "`0<=-log a_j<=a/(4theta)=O(a d)`", "reason": "'O(ad)' corrected to O(p^2 log p) by PR1786 l.114; PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 114}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-44", "keys": ["theta_ge_1_over_d"], "line": 74, "operative_keys": ["TH_pos"], "quote": "under theta between 1/(4d) and 1/(2d-1).", "reason": "PR1786 l.66-67", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 66}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-45", "keys": ["gamma_slack"], "line": 74, "quote": "The old eventual condition u*d<=p holds whenever d=p^epsilon, epsilon<1, and u=O(log p).", "reason": "true; no longer bounds the weight range at fine theta (that is u p^2, P_setup)"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-46", "keys": ["setup_Cp"], "line": 76, "quote": "The retained bound `p*2^(16p+7)*eta+2^(-46p)` at eta=2^(-32768p) is more than sufficient.", "reason": "PR1786 FINE-PRIME-PADDING.md sec 3 (l.110-128, l.159-162: P_setup = Cp + 64 p^2 ceil(log2 p) replaces Cp; online pages stay O(p)); imported by FINE-PADDING-COMPOSITION.md l.10; underflow witness in outer/check_fine_padding.py", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 108}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 10}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-47", "keys": ["TH_pos"], "line": 76, "quote": "Then H has diagonal 1, row gap at least `1/(16p)`, row norm below 2, and inverse norm at most 16p.", "reason": "stale numeric: row_gap_power_m1 (final -2, at pr1673: -0.9984838711085557536432678 matches)"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-48", "keys": ["a_theta_gt_1"], "line": 78, "quote": "## 3. Schur complement bounds without an a*theta>1 assumption", "reason": "hypothesis removed in this section", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "line": 78}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-49", "keys": ["TH_pos"], "line": 94, "quote": "Rounding S by a row perturbation below 1/(32p) preserves gap at least 1/(32p) and inverse norm at most 32p.", "reason": "stale numeric: row_gap_power_m1 (final -2, at pr1673: -0.9984838711085557536432678 matches)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-50", "keys": ["xi_lt_TH"], "line": 96, "quote": "keep first/last w vertices of each physical cell, yielding O(s*w/d) boundary vertices and circular half-bandwidth at most 2w.", "reason": "O(s w/d) with old cells of length d"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-51", "keys": [], "line": 102, "quote": "Because a is eventually larger than 4pi, the symmetric Toeplitz matrix Ghat_cell satisfies", "reason": "log(16p) > pi for p >= 2"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-52", "keys": ["full_cell_gauge_d"], "line": 112, "operative_keys": ["chirp_guard"], "quote": "choosing `g<=p/(d polylog p)` with sufficient logarithmic slack keeps the total data precision O(p).", "reason": "superseded by capped interiors and the chirp-only guard (GAUGEFREE R1; PR1786 l.169)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 169}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-53", "keys": ["beta_lt_1"], "line": 112, "quote": "The shallow circuit contributes polynomial-in-d amplification per axis, hence only O(g log d) additional logarithmic range.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-54", "keys": [], "line": 118, "quote": "Padding every tensor axis to its next power of two would be invalid.", "reason": "layout: no per-axis dyadic padding"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-55", "keys": [], "line": 130, "quote": "There are `O(1+log(L/w))` interiors and the total boundary count in the cell is `O(w(1+log(L/w)))`.", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-56", "keys": ["xi_gt_half"], "line": 134, "quote": "an interior has length greater than w in the loop above.", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-57", "keys": ["boundary_row"], "line": 136, "quote": "`n_boundary=O((s/d) w log d)`.", "reason": "(s/d) w log d is the uncapped formula; capped cost is the boundary row"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/LOG-A-PHASE-SCHUR-AUDIT.md", "id": "pr1673c-58", "keys": ["boundary_row"], "line": 140, "quote": "The boundary solve and coupling work therefore gain only polylogarithmic factors.", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-131", "keys": [], "line": 5, "quote": "theorem gives `omega_C<=9/4`", "reason": "9/4 matrix-corollary premise; the 9/4 branch is not used (explicit Strassen tau = 45/16, FINE-PADDING-COMPOSITION l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-132", "keys": [], "line": 9, "quote": "Fix `tau=19/8>9/4`.", "reason": "9/4 branch tau = 19/8 not used; final tau_eff = 45/16 (FINE-PADDING-COMPOSITION l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-133", "keys": [], "line": 15, "quote": "Here P,h=O(p), so the old boundary interface still has O(p)-bit records.", "reason": "structural premise of the boundary interface (O(p)-bit entries, h=O(p), W=O(sqrt(p) polylog p)); not encoded by eps<1 (corrected after the seeded sampled re-check; previously COVERED via eps_lt_1)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-134", "keys": ["strassen"], "line": 15, "quote": "Any residual logarithmic tape overhead is absorbed by choosing the fixed rank exponent strictly below tau.", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-135", "keys": [], "line": 15, "quote": "it is not simultaneous tensor-axis padding", "reason": "no tensor-axis padding"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-136", "keys": ["boundary_row"], "line": 21, "quote": "the new power is consequently `epsilon-xi+(tau-1)/2`", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-137", "keys": ["mc_xi_balance"], "line": 28, "operative_keys": ["xi_def"], "quote": "xi=(3/2+q-(1+q)*(r0+zeta)+s_union)/(2+q),", "reason": "9/4-branch balance superseded", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}, {"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-138", "keys": ["linear_g_param"], "line": 30, "operative_keys": ["beta_def"], "quote": "beta=1-xi-r0-zeta.", "reason": "PR1673 linear-guard parameterisation beta = 1 - xi - r0 - zeta superseded by beta = 1 - 3 delta (FINE-PADDING-COMPOSITION sec 2)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-139", "keys": ["gauss_eq_main_old"], "line": 36, "operative_keys": ["gauss_row"], "quote": "epsilon*q = 1-epsilon+q*beta,", "reason": "equality superseded; inequality holds (fused_gaussian)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-140", "keys": ["old_union_row"], "line": 37, "operative_keys": ["union_row"], "quote": "1-epsilon-beta-1/2+xi = epsilon*q+s_union.", "reason": "control old_g_factor_union_row", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-141", "keys": [], "line": 42, "quote": "`kappa=0.001673360105405778`.", "reason": "9/4 branch numerics", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-142", "keys": [], "line": 58, "quote": "`5/16+xi-epsilon=.063968602202727648...`,", "reason": "9/4 branch", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-143", "keys": ["xi_gt_half", "xi_lt_eps", "xi_lt_TH"], "line": 64, "quote": "The cap is above the bandwidth and below the physical phase-cell scale: `1/20`.", "reason": "deleted row; outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125) l.101-102, l.125; PR1786 l.268", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 268}, {"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-150", "keys": ["beta_pos"], "line": 66, "quote": "All local coefficient pages remain polynomial in p, while `L^g` remains superpolynomial.", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-151", "keys": ["face_row"], "line": 66, "quote": "Microedge correction has exponent `epsilon+beta-3<-1.75`", "reason": "stale numeric: mc_face_lt_m1_75 (final -1 - 8E-30010, at pr1673mc: -1.751469612202727648 matches)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-152", "keys": ["scan_row"], "line": 68, "quote": "the q-image scans have the already-paid Vd/g cost", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "id": "pr1673a-153", "keys": ["full_key_union"], "line": 70, "operative_keys": ["union_row"], "quote": "The **optional full-group-key sort surcharge on the sparse union is omitted** because it is absent from the actual algorithm.", "reason": "omission statement correct; control full_key_sort", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-154", "keys": ["beta_lt_1_minus_eps", "beta_lt_xi_half"], "line": 6, "operative_keys": ["beta_lt_1"], "quote": "implementation requires g 0 (sparse_union_fraction_decays) is false at final; row deleted, sparsity not used (UNION-SCHEDULE l.101-102, l.125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 101}, {"file": "outer/UNION-SCHEDULE.md", "line": 125}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-156", "keys": ["membership"], "line": 20, "quote": "beta + 2(1-epsilon) < 1, # membership arithmetic fits p-bit record", "reason": "coverage: membership = ledger membership_arithmetic_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-157", "keys": ["old_union_row"], "line": 21, "operative_keys": ["union_row"], "quote": "epsilon + beta + 1/2 - xi < 1-kappa,", "reason": "old g-factor union row eps + beta + 1/2 - xi < 1 - kappa is false at final; replaced by the radix union row (UNION-SCHEDULE l.17-18, l.125); LEDGER control old_g_factor_union_row", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}, {"file": "outer/UNION-SCHEDULE.md", "line": 125}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-158", "keys": ["scan_row"], "line": 22, "quote": "epsilon - beta < 1-kappa. # grouped full scans", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-159", "keys": ["union_density"], "line": 26, "operative_keys": ["union_row"], "quote": "inflation from carving still tends to zero.", "reason": "carving inflation -> 0 relies on the deleted union-density row (false at final); sparsity not used (UNION-SCHEDULE l.101-102, l.125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 101}, {"file": "outer/UNION-SCHEDULE.md", "line": 125}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-160", "keys": ["halo_volume", "face_row"], "line": 37, "quote": "p^-5 slack; increasing beta to .25 does not change their negligible status.", "reason": "stale numeric: halo_minus_core_m5 (final -80, at pr1673: -5 matches)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-161", "keys": ["beta_pos", "eps_lt_1"], "line": 41, "quote": "local generator has polynomial preparation. L^g and the spectator RHS stock", "reason": "coverage: beta_pos = ledger group_positive; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/MATRIX-LAYOUT-SIGNOFF.md", "id": "pr1673a-162", "keys": ["scan_row"], "line": 50, "quote": "tensor remains axis-major. Each is one scan, for O(Vd/g) total work.", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-07", "keys": ["eps_pos"], "line": 11, "quote": "Global one-axis preprocessing is polynomial in the original axis sizes and p, hence `n^o(1)`.", "reason": "coverage: eps_pos = ledger epsilon_positive"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-08", "keys": ["beta_pos"], "line": 11, "quote": "Table construction or page loading repeated per coarse block is charged to its superpolynomial `L^g` payload", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-09", "keys": ["all_checks_pos"], "line": 11, "quote": "Every cost row below is `O(V p^e polylog p)` with `1-e>kappa`. The minimum excess is greater than `10^-11`.", "reason": "'minimum excess > 1e-11' is PR1673's backoff; final minimum is 1e-30022"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-10", "keys": ["all_checks_pos"], "line": 11, "quote": "All claims are eventual in p; one fixed finite prefix of inputs can use the retained elementary fallback.", "reason": "eventual, astronomical cutoff"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-11", "keys": ["q_lt_a", "a_lt_b"], "line": 15, "quote": "lower the usable bit saving to `a_eff=(b+q)/2`; this keeps its historical convention `a_eff0` with `(1-t_stop)b>a_eff` and `q<(1-t_stop)b`.", "reason": "coverage: stop_pos = ledger stop_positive; leaf_gt_a = ledger leaf_saving_above_effective; q_lt_leaf = ledger q_below_leaf/lambda_prime_above_leaf"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-39", "keys": ["beta_pos"], "line": 70, "quote": "there are g local windows of size at most L=Theta(p^8), their rational origins have O(p/d) bits", "reason": "L = p^8 stale (p^128); setup O(p^2 log p) still polynomial"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-40", "keys": ["gamma_slack"], "line": 72, "quote": "with completed scalar range `O(d alpha^2)=o(p)`", "reason": "coverage: gamma_slack = ledger global_gamma_power_slack"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-41", "keys": ["poly_row"], "line": 72, "quote": "Packed polynomial products retain their saving epsilon.", "reason": "coverage: poly_row = ledger polynomial_products_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-42", "keys": ["beta_lt_eps"], "line": 76, "quote": "Let `h_w=1/2` and `h_K=beta+1-epsilon`.", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-43", "keys": ["gauss_row"], "line": 82, "quote": "| dense Gaussian groups | `epsilon-q*beta` | `(d/g) g^(1-q)` |", "reason": "coverage: gauss_row = ledger fused_gaussian_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-44", "keys": ["bitrouter_row"], "line": 83, "quote": "| grouped bit routing | `epsilon-a_eff*beta` | same grouping, bit supplier |", "reason": "coverage: bitrouter_row = ledger group_bit_router_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-45", "keys": ["scan_row"], "line": 84, "quote": "| one/fixed group scans | `epsilon-beta` | d/g groups |", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-46", "keys": ["uncapped_boundary"], "line": 85, "operative_keys": ["boundary_row"], "quote": "| boundary algebra | `(omega-1)*h_w` | batched w-column Strassen |", "reason": "uncapped boundary row (true at final, 29/32 < 1-kappa) superseded by the capped d/B row (CAPPED-INTERIORS l.37, l.41)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "line": 37}, {"file": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md", "line": 41}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-47", "keys": ["old_union_uncapped"], "line": 86, "operative_keys": ["union_row"], "quote": "| sparse union, basic movement | `beta+h_w` | V g w overall |", "reason": "superseded by CAPPED-INTERIORS and outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-48", "keys": ["full_key_uncapped"], "line": 87, "operative_keys": ["union_row"], "quote": "| sparse union, conservative key surcharge | `beta+h_w+h_K` | full active-group keys |", "reason": "full-key sort not used (MATRIX-COROLLARY l.70; outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125))", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md", "line": 70}, {"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-49", "keys": ["poly_row"], "line": 88, "quote": "| polynomial products | `1-epsilon` | retained short polynomial products |", "reason": "coverage: poly_row = ledger polynomial_products_above_kappa"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-50", "keys": ["face_row"], "line": 89, "quote": "| core-face corrections | `epsilon+beta+3-8+2` | old local maps on sparse copies, with a loose p² allowance |", "reason": "powers 3-8 -> 48-128"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-51", "keys": ["strassen"], "line": 91, "quote": "Use the rational upper bound `omega<45/16`, checked by `7^16<2^45`.", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/OUTER-AUDIT.md", "id": "pr1673a-52", "keys": ["gauss_eq_main_old"], "line": 91, "operative_keys": ["gauss_row", "main_row"], "quote": "The target balances the first and third rows exactly before a fixed 10^-11 absorption backoff.", "reason": "balance superseded by FINE-PADDING-COMPOSITION sec 2-3 (Gaussian exceeds main by delta(1-2q))", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-01", "keys": ["old_union_row"], "line": 4, "operative_keys": ["union_row"], "quote": "implementation with its stated `V g^2 W polylog(p)/d` per-group movement", "reason": "outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125); control old_g_factor_union_row", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-02", "keys": [], "line": 40, "quote": "lies within O(W) of the carved endpoints", "reason": "locality: boundary set E_i within O(W) of carved endpoints"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-03", "keys": ["xi_gt_half", "xi_lt_TH", "xi_lt_eps"], "line": 45, "quote": "mu := max_i |E_i|/L = O(W log d/d + W log d/L)", "reason": "mu formula uses cells of length d; capped density O((W/B) polylog) per UNION l.13, PR1786 l.236-240 (literal W/d would understate mu)"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-04", "keys": ["union_density"], "line": 56, "operative_keys": ["union_row"], "quote": "Then `|U|/L^g <= g mu`.", "reason": "inequality valid but vacuous (g mu > 1); sparsity not used (outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125) l.101-102, l.125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-05", "keys": [], "line": 91, "quote": "Its length is at most L=poly(p), so only O(log p) binary", "reason": ""}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-06", "keys": ["old_union_row"], "line": 107, "operative_keys": ["union_row"], "quote": "O(V [g^2 mu + g mu polylog p])", "reason": "per-axis U scan removed (outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125) l.17-18)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-07", "keys": ["pla_edge"], "line": 108, "operative_keys": ["union_row"], "quote": "O(V g^2 W polylog p/L)", "reason": "old window cost formula replaced (outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125) l.17-18); this edge term is true anyway", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-08", "keys": ["full_key_union"], "line": 112, "operative_keys": ["union_row"], "quote": "A more general radix implementation would still fit with extra", "reason": "not used; control full_key_sort", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-09", "keys": ["beta_lt_1"], "line": 120, "quote": "O(g log L) bits. A nonzero number of flags sends the whole record once to U;", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-10", "keys": [], "line": 124, "quote": "bitlength h=Theta(p/d), q_j inversion and phase-cell endpoint calculations", "reason": "definition of h and per-axis descriptor arithmetic O(h^2 polylog p)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-11", "keys": ["membership"], "line": 128, "quote": "`O(g h^2 polylog p)` per record, which is o(p) for", "reason": "coverage: membership = ledger membership_arithmetic_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-12", "keys": ["stale_g_param"], "line": 129, "operative_keys": ["membership", "beta_def"], "quote": "`g=p^(1-epsilon-r-zeta)`", "reason": "parameterisation superseded (FINE-PADDING-COMPOSITION sec 2: beta = 1 - 3 delta); operative condition is membership (true)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 15}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-13", "keys": ["eps_gt_2_3"], "line": 129, "operative_keys": ["membership"], "quote": "epsilon>2/3", "reason": "true, but sufficient only under the superseded g; the operative row is membership_arithmetic_fits_record"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-14", "keys": ["membership"], "line": 130, "quote": "power about 0.005", "reason": "eventual only (exponent margin membership=2E-30010)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-15", "keys": ["beta_pos", "eps_lt_1"], "line": 137, "quote": "are superpolynomial in p and amortize this polynomial setup. This avoids", "reason": "coverage: beta_pos = ledger group_positive; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-16", "keys": ["eps_lt_1", "beta_lt_eps"], "line": 146, "quote": "Their count R is superpolynomial.", "reason": "RHS count = spectators (source axes 2^(p^(1-eps)), L^(d-g))"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-17", "keys": [], "line": 149, "quote": "move only that polynomial-width row field", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-18", "keys": ["boundary_row", "strassen"], "line": 155, "quote": "`O(V W^(omega-1) polylog p)` boundary arithmetic.", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa; strassen = ledger strassen_integer_power_gap"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-19", "keys": ["TH_pos"], "line": 161, "quote": "is increasing", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-20", "keys": ["membership"], "line": 177, "quote": "The g membership tests cost O(g h^2 polylog p)=o(p) per p-bit record.", "reason": "coverage: membership = ledger membership_arithmetic_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-21", "keys": ["eps_lt_2"], "line": 178, "quote": "Partial tensor volumes remain bounded by the retained total T/S<2.", "reason": "coverage: eps_lt_2 implied by epsilon_below_one"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-22", "keys": ["halo_volume"], "line": 192, "quote": "Keep the retained dyadic target core side `L~p^8`.", "reason": "stale numeric: core_power_8 (final 128, at pr1673: 8 matches)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-23", "keys": ["halo_radius"], "line": 197, "quote": "fixed multiple of `A~p^3` from every artificial core edge.", "reason": "stale numeric: halo_power_3 (final 48, at pr1673: 3 matches)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-24", "keys": ["halo_volume"], "line": 201, "quote": "fraction O(gA/L).", "reason": "coverage: halo_volume = ledger microbox_halo_volume"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-25", "keys": ["beta_lt_eps"], "line": 213, "quote": "Actual keys use O(g log s) bits", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-26", "keys": ["pla_halo_path", "face_row"], "line": 215, "quote": "`polylog(p) p^delta (1+W^2/d)` plus boundary terms, with fixed small delta;", "reason": "evaluated with delta = 1 (worst admissible 'small' delta)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-27", "keys": ["core_gt_halo"], "line": 217, "quote": "A/L=O(p^-5).", "reason": "now p^-80"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-28", "keys": ["beta_pos"], "line": 218, "quote": "superpolynomial spectator/inner volume.", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-29", "keys": ["scan_row"], "line": 228, "quote": "group scans: O(V d/g polylog p),", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-30", "keys": ["old_union_uncapped"], "line": 229, "operative_keys": ["union_row"], "quote": "union movement: O(V g W polylog p),", "reason": "outer/UNION-SCHEDULE.md (radix schedule l.17-18, l.94-99; sec 5b l.122-125)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 17}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-31", "keys": ["boundary_row"], "line": 230, "quote": "boundary arithmetic: O(V W^(omega-1) polylog p),", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-32", "keys": ["face_row"], "line": 231, "quote": "microedge corrections: lower order by the p^-5 volume factor.", "reason": "stale numeric: halo_minus_core_m5 (final -80, at pr1673: -5 matches)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PHASE-LAYOUT-AUDIT.md", "id": "pr1673b-33", "keys": ["gauss_row", "bitrouter_row"], "line": 235, "quote": "`O(V d/g^q polylog p)` and `O(V d/g^a_bit polylog p)`", "reason": "coverage: gauss_row = ledger fused_gaussian_above_kappa; bitrouter_row = ledger group_bit_router_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/PROOF-AND-COVERAGE.md", "id": "pr1673a-53", "keys": ["tau_9_4_branch"], "line": 42, "operative_keys": ["strassen"], "quote": "Fix a rational exponent `tau` strictly between 9/4 and 5/2; `19/8` is sufficient.", "reason": "9/4 branch not used (FINE-PADDING-COMPOSITION l.13)", "superseded_by": [{"file": "outer/FINE-PADDING-COMPOSITION.md", "line": 13}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/PROOF-AND-COVERAGE.md", "id": "pr1673a-54", "keys": ["strassen"], "line": 44, "quote": "For rational `tau=a/d`, the exponent check is the integer inequality `r^d0.", "reason": "SPD extension hypothesis"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SHALLOW-TOEPLITZ.md", "id": "pr1673c-70", "keys": ["beta_lt_1"], "line": 197, "quote": "and g-axis tensorization adds O(g(u+1)log N) guard bits.", "reason": "u = O(log p) polylog: covered by 1-beta; the r0-absorbed variant 1-beta-r0 = 5e-30010 is true but is not a ledger row"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-34", "keys": ["gauss_row"], "line": 5, "quote": "O(V g^(1-q) polylog(p))", "reason": "coverage: gauss_row = ledger fused_gaussian_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-35", "keys": ["router_row"], "line": 7, "quote": "without the previously charged additive V p^(1-a), **provided the call is made globally on the complete dyadic tensor", "reason": "load-bearing NON-EXPONENT proviso: the supplier call must be global (CAPPED-INTERIORS l.66 says it is); a per-group V p^(1-a) charge would fail"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-36", "keys": [], "line": 9, "quote": "The full address still has O(p) bits.", "reason": "ambient binary address length n and descriptor/key length"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-37", "keys": ["eps_lt_1"], "line": 29, "quote": "Because the original axis length ell grows faster than log p, K+O(log p) infinity", "reason": "replaced by the finite guard (SSA l.61-64; SAA l.213-215)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "line": 61}, {"file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "line": 213}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-41", "keys": ["supp_K_guard"], "line": 61, "quote": "K >= G+4 ceil(log2 p)+10,", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-42", "keys": ["beta_lt_1"], "line": 76, "quote": "Three disjoint 3kG-bit reservoirs can be chosen when n>=9kG", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-43", "keys": ["beta_lt_1"], "line": 78, "quote": "if n>2(k+1)ell_s, a gap in its support contains a consecutive ell_s-bit field", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-44", "keys": ["beta_lt_1"], "line": 80, "quote": "n/(k log p) tends to infinity because g=p^beta with beta<1 while n is of order p in the retained full tensor.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md", "id": "pr1673b-45", "keys": ["q_lt_a", "leaf_gt_a", "q_lt_leaf"], "line": 98, "quote": "with q 2(k+1)L.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-61", "keys": ["beta_lt_1"], "line": 109, "quote": "In the application, n-L>=9kG holds with a wide", "reason": "'wide' margin is now 6e-30010"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-62", "keys": [], "line": 114, "quote": "This length exceeds every fixed", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-63", "keys": [], "line": 117, "quote": "O(V L^(1-a))=O(V polylog p)", "reason": ""}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-64", "keys": [], "line": 127, "quote": "n=O((k+1)polylog p), the old full-span construction gives the desired", "reason": "fallback regime for dense support"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-65", "keys": [], "line": 172, "quote": "phase's volume by twice its original volume", "reason": "row padding per deferred phase"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-66", "keys": ["beta_lt_1"], "line": 189, "quote": "The largest exposure moves k=O(gK)=O(p^.093 log p) binary coordinates.", "reason": "eventual only (exponent margin beta_lt_1=6E-30010)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-67", "keys": ["beta_lt_1"], "line": 193, "quote": "9kG = O(p^.093 log^2 p) = o(p).", "reason": "eventual only (exponent margin beta_lt_1=6E-30010)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-68", "keys": ["beta_lt_1"], "line": 199, "quote": "n/(kG) = Omega(p^.907/log^2 p) -> infinity,", "reason": "ratio p^(6e-30010)/log^2 p -> infinity only beyond an astronomical cutoff"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-69", "keys": ["beta_lt_1"], "line": 200, "quote": "n/((k+1)L) = Omega(p^.907/log^3 p) -> infinity.", "reason": "eventual only (exponent margin beta_lt_1=6E-30010)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-70", "keys": ["eps_lt_1"], "line": 210, "quote": "K + O(log p) < ell_axis = Theta(p^.002),", "reason": "eventual only (exponent margin eps_lt_1=2E-30010)"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-71", "keys": ["supp_K_guard"], "line": 215, "quote": "guard inequality K>=G+4ceil(log2 p)+10. K=128G satisfies it.", "reason": ""}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-72", "keys": [], "line": 221, "quote": "ceil(2hG/K) + ceil(hG/K) <= 3h/128 + 2.", "reason": "front/back control chunk count"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-73", "keys": [], "line": 225, "quote": "polylogarithmic cutoff this is at most h/16", "reason": "row stock + control chunks per phase"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ADVERSARIAL-AUDIT.md", "id": "pr1673b-74", "keys": ["divergence_gG_ell"], "line": 227, "quote": "gG/ell_axis=Theta(p^.091 log p) diverges", "reason": "divergence still true (exponent 1-8e-30010); the avoided per-axis fit is false, as intended"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-75", "keys": [], "line": 10, "quote": "Let a supplied permutation of `n=O(p)` binary address coordinates move at", "reason": "address length of the router"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-76", "keys": ["beta_lt_1"], "line": 13, "quote": "`n/(k log p) -> infinity`; short remaining cases can use the retained", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-77", "keys": ["bitrouter_row", "beta_pos"], "line": 17, "quote": "O(V (k+1)^(1-a) polylog p + poly(p)).", "reason": "coverage: bitrouter_row = ledger group_bit_router_above_kappa; beta_pos = ledger group_positive"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-78", "keys": ["supp_K_guard_64"], "line": 25, "quote": "and `K=64G`", "reason": "K = 64G here vs 128G in SSA (non-exponent inconsistency; both satisfy the finite guard)"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-79", "keys": ["beta_lt_1"], "line": 76, "quote": "bad density <= r [2/B + 8B/2^K] <= p [2/B + 8B/2^K].", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-80", "keys": ["beta_lt_1"], "line": 94, "quote": "span is at least 9H0.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-81", "keys": ["beta_lt_1"], "line": 115, "quote": "`n>2(k+1)ell`, a gap outside the moved support contains a contiguous ell-bit", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-82", "keys": [], "line": 122, "quote": "Its 2^ell complete values absorb the polynomial descriptor work", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/SUPPORT-ROUTER.md", "id": "pr1673b-83", "keys": ["beta_lt_1"], "line": 134, "quote": "requested gather to a coordinate permutation supported on at most 2k bits.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-84", "keys": [], "line": 13, "quote": "at most (8m+2)D simultaneous H calls", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-85", "keys": ["beta_lt_1"], "line": 21, "quote": "More generally depth D=polylog(p), B=poly(p), N=poly(p) gives an O(g polylog(p)) guard", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-86", "keys": ["full_cell_axis"], "line": 23, "operative_keys": ["chirp_guard"], "quote": "Therefore the retained phase-cell case Q_a=O(a d) uses", "reason": "full-cell Q_a not charged after recentering (CAPPED-GAUGE-AUDIT l.107; GAUGEFREE R1; PR1786 l.149)", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "line": 107}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 149}, {"file": "outer/GAUGEFREE-INTERIORS.md", "line": 15}]}, +{"classification": "OBSOLETE", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-87", "keys": ["gad_O_p"], "line": 27, "operative_keys": ["chirp_guard", "beta_lt_1"], "quote": "The condition g a d+g polylog(p)=O(p) is sufficient for O(p)-bit records.", "reason": "as pr1673b-50", "superseded_by": [{"file": "vendor/pr1673/capped-phase-fusion/CAPPED-GAUGE-AUDIT.md", "line": 107}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 149}]}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-88", "keys": ["beta_lt_1"], "line": 108, "quote": "using only the rough original bound Lambda<=(2B)^D gives exp(O(gD log B))", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-89", "keys": ["beta_lt_1", "chirp_guard"], "line": 110, "quote": "This costs O(g polylog(p)+sum Q_a) guard bits.", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record; chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-90", "keys": ["beta_pos"], "line": 130, "quote": "polynomial-time table construction is negligible per N^g block in the retained asymptotic regime g=p^beta tending to infinity", "reason": "coverage: beta_pos = ledger group_positive"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-92", "keys": [], "line": 147, "quote": "For D=polylog(p), N=poly(p), the compiler uses only polylog(p) such calls", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1673/capped-phase-fusion/TENSOR-COMPILER.md", "id": "pr1673b-91", "keys": ["q_lt_a", "a_lt_bit", "q_pos", "q_lt_1"], "line": 151, "quote": "When a_bit>q and 0 0.", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-76", "keys": ["eps_lt_1"], "line": 46, "quote": "Indeed `log x=Theta(p^(1-epsilon))` and epsilon<1 is fixed, so its positive", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-77", "keys": ["eps_lt_1"], "line": 48, "quote": "least `x/(8p^2 log x)` primes. This exceeds d, since x is exponential in", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-78", "keys": ["eps_pos"], "line": 56, "quote": "Its logarithm is `O(log p+p/d)=o(p)`", "reason": "coverage: eps_pos = ledger epsilon_positive"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-74", "keys": ["TH_pos"], "line": 62, "quote": "1/(4p^2) < theta_i <= 1/(2p^2-1) <= 1/p^2.", "reason": "coverage: TH_pos = ledger theta_positive_polynomial_power"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-79", "keys": ["eps_lt_2"], "line": 64, "quote": "Also `S/T > (1-1/(2p^2))^d >= 1-d/(2p^2) > 1/2` eventually, since", "reason": "coverage: eps_lt_2 implied by epsilon_below_one"}, +{"classification": "OBSOLETE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-80", "keys": ["theta_ge_1_over_d"], "line": 67, "operative_keys": ["TH_pos"], "quote": "bound on theta is explicit; we do not reuse the old `theta>=1/(4d)`.", "reason": "'we do not reuse the old theta >= 1/(4d)' (same line)", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 67}]}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-81", "keys": ["r_pos"], "line": 72, "quote": "`4 log(16p)<=a<=5 log(16p)` and alpha^2=Theta(log p).", "reason": "coverage: r_pos = ledger alpha_logarithm_absorption"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-82", "keys": ["TH_pos"], "line": 77, "quote": "For theta>=1/(4p^2), its row gap is at least `1/(8p^2)` eventually", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-83", "keys": ["exp_rho_lt_p2"], "line": 90, "quote": "factor is at most p^2 eventually, theta^-2<=16p^4, and alpha^5 is", "reason": ""}, +{"classification": "UNCOVERED_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-84", "keys": ["umbrella10"], "line": 95, "quote": "Thus a conservative common eventual bound p^10 covers", "reason": "true at THETA_POWER = 2 (exponent margin 3.5), but the umbrella power 10 is hard-coded (check_fine_padding.py norm_power) and drives 20/40/42/43 and the ledger's halo row 48 > 43; no ledger row ties it to THETA_POWER (it would fail silently for THETA_POWER >= 3.75)"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-85", "keys": ["xi_gt_half"], "line": 101, "quote": "disjoint future interiors separated by at least the bandwidth.", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-86", "keys": [], "line": 114, "quote": "the negative logarithm can now be as large as `a/(4 theta)=O(p^2 log p)`.", "reason": "fact motivating P_setup (THETA_POWER = 2 > 1)"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-87", "keys": [], "line": 121, "quote": "P_setup = C p + 64 p^2 L_p.", "reason": ""}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-88", "keys": [], "line": 123, "quote": "Eventually `a<=16 L_p`, so `a/(4 theta)<=16 p^2 L_p`. Since log 2>1/2,", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-89", "keys": ["beta_pos", "eps_lt_1"], "line": 133, "quote": "polynomial time in p. Schoolbook arithmetic and ordinary convergent series", "reason": "coverage: beta_pos = ledger group_positive; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-90", "keys": ["aW_o_p"], "line": 143, "quote": "range O(aW)=o(p). The truncation tail is bounded directly in the Gaussian", "reason": "W exponent 1/2 is not a ledger variable"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-91", "keys": ["aW_o_p"], "line": 145, "quote": "the exact Gaussian matrix by `poly(p) 2^(-(C-o(1))p)` in row and column norm.", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-92", "keys": ["chirp_axis_o1"], "line": 154, "quote": "most O(a B^2/p^2). The shifted Toeplitz kernels remain accretive: their shift", "reason": "coverage: chirp_axis_o1 implied by cap_below_cell+epsilon_below_one (xi < 1 and THETA_POWER = 2)"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-93", "keys": ["TH_pos", "beta_lt_1"], "line": 156, "quote": "polynomial inverse norms when theta^-1=O(p^2). Its accretive shallow-circuit", "reason": "coverage: TH_pos = ledger theta_positive_polynomial_power; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-94", "keys": ["chirp_guard", "chirp_guard_noR", "beta_lt_1"], "line": 165, "quote": "exp(O(g a B^2/p^2 + g polylog p)).", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack; chirp_guard_noR = ledger actual_logarithmic_group_guard; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-95", "keys": ["chirp_guard", "beta_lt_1"], "line": 169, "quote": "beta + 2 xi - 2 < 1, beta < 1.", "reason": "binding part is beta < 1 (margin 6e-30010, eventual)"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-96", "keys": ["chirp_guard", "beta_lt_1"], "line": 175, "quote": "constant number of completed factor stages, and through g tensor axes,", "reason": "coverage: chirp_guard = ledger group_gauge_power_slack; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-97", "keys": ["beta_pos", "eps_lt_1"], "line": 184, "quote": "preserves that argument: `L^g` and every full unused source-axis range exceed", "reason": "coverage: beta_pos = ledger group_positive; eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-98", "keys": ["normalizer100"], "line": 196, "quote": "additional dyadic factor of at most `2^ceil(100 log2 p)`. The conservative", "reason": ""}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-99", "keys": ["eps_lt_1"], "line": 201, "quote": "There are O(d) factors; the added shift has O(d log p)=o(p) bits because", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-100", "keys": ["eps_lt_1", "beta_lt_1", "chirp_guard"], "line": 203, "quote": "At a sufficiently large fixed C, data precision is `C p+o(p)=O(p)`.", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record; chirp_guard = ledger group_gauge_power_slack"}, +{"classification": "NON_EXPONENT", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-101", "keys": [], "line": 206, "quote": "these changes increases the semantic online dimension exponent C1=1.", "reason": "semantic online precision interface C1 = 1"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-102", "keys": ["scan_row"], "line": 210, "quote": "axis. A constant number of these operations per group is absorbed by the", "reason": "coverage: scan_row = ledger group_scans_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-103", "keys": [], "line": 215, "operative_keys": ["halo_radius", "halo_volume", "face_row"], "quote": "The old literal row-gap and locality constants must not be reused.", "reason": "old row gap / Cp^3 locality not reused (same line); replacement encoded", "superseded_by": [{"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 215}]}, +{"classification": "AUTO_TRUE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-104", "keys": ["neumann_exp"], "line": 221, "quote": "Its eigenvalues lie in `[0,1-p^-40]`. With `J=ceil(p^42)`, the polynomial", "reason": "power relations asserted in check_fine_padding.py, not in the ledger"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-105", "keys": ["halo_radius", "halo_neumann_sharp"], "line": 224, "quote": "Since W=O(sqrt(p) polylog p)

0`.", "reason": "coverage: face_row = ledger microbox_face_corrections_above_kappa; halo_volume = ledger microbox_halo_volume"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-109", "keys": ["xi_lt_TH"], "line": 240, "quote": "is `O(W log B/p^2)`, dominated when B<=p^2. Clipped physical period cuts and", "reason": "coverage: xi_lt_TH = ledger cap_below_phase_cell_power"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-110", "keys": ["xi_gt_half"], "line": 241, "quote": "holes remain boundary. Scalar Schur bandwidth stays O(W), since an eliminated", "reason": "coverage: xi_gt_half = ledger cap_above_band"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-111", "keys": ["eps_lt_1", "beta_lt_1"], "line": 244, "quote": "fields. Their source axes are still superpolynomial in p.", "reason": "coverage: eps_lt_1 = ledger epsilon_below_one/source_axis_superpolynomial/actual_logarithmic_gamma_guard; beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-112", "keys": ["strassen"], "line": 248, "quote": "Use the explicit Strassen circuit, with `7^16<2^45`, so choose fixed matrix", "reason": "coverage: strassen = ledger strassen_integer_power_gap"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-113", "keys": ["boundary_row", "boundary_eq"], "line": 253, "quote": "`epsilon-xi+(tau-1)/2` and its saving is `c+xi-epsilon`. This applies to general", "reason": "coverage: boundary_row = ledger boundary_algebraic_matrix_above_kappa; boundary_eq asserted (check_ledger.py l.195 assert)"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-114", "keys": ["beta_lt_1"], "line": 265, "quote": "moves an O(p)-bit record; flag extraction and O(g log L)-bit headers are absorbed", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record"}, +{"classification": "OBSOLETE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-115", "keys": ["tag_2beta"], "line": 266, "operative_keys": ["beta_lt_1"], "quote": "We use PR1758's per-visit argument, not the obsolete 2 beta<1.", "reason": "same line; control old_union_tag_2beta", "superseded_by": [{"file": "outer/GAUGEFREE-INTERIORS.md", "line": 108}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 266}]}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-116", "keys": ["union_row"], "line": 267, "quote": "Union cost power remains `epsilon+1/2-xi`.", "reason": "coverage: union_row = ledger sparse_union_movement_above_kappa"}, +{"classification": "OBSOLETE", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-117", "keys": ["union_density"], "line": 268, "operative_keys": ["union_row"], "quote": "is added, and no vanishing-union fraction is assumed.", "reason": "same line; row deleted (UNION-SCHEDULE 5b)", "superseded_by": [{"file": "outer/UNION-SCHEDULE.md", "line": 119}, {"file": "vendor/pr1786/FINE-PRIME-PADDING.md", "line": 268}]}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-118", "keys": ["r_pos", "slack_pos", "stop_pos", "q_lt_b"], "line": 276, "quote": "`r0=10^-64`, `zeta=10^-66`, layout slack `s=10^-64`, and stopped-recursion", "reason": "PR1786 slacks; final 1e-30010 etc."}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-119", "keys": ["eps_def", "beta_def"], "line": 280, "quote": "epsilon=9999999/10000000,", "reason": "stale numeric: eps_0_9999999 (final 1 - 2E-30010, at pr1786: 0.9999999 matches)"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-120", "keys": ["xi_def"], "line": 284, "quote": "Thus xi=0.90792965478815... . This is an explicit interior point; it does not", "reason": "PR1786 value; copied into FINE-PADDING-COMPOSITION l.28 and UNION-SCHEDULE l.121"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-121", "keys": ["beta_lt_eps", "eps_lt_1"], "line": 285, "quote": "Since beta0`. The global router also", "reason": "coverage: gauss_minus_main_id: rejecting control fires; router_row = ledger global_coordinate_router_above_kappa"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-129", "keys": ["beta_lt_1", "beta_def"], "line": 307, "quote": "1-beta=3 delta>0,", "reason": "coverage: beta_lt_1 = ledger support_router_span/union_header_fits_record/union_tag_work_per_visit_fits_record; beta_def asserted (check_ledger beta = 1 - 3 DELTA_E)"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-130", "keys": ["membership"], "line": 308, "quote": "1-beta-2(1-epsilon)=delta>0,", "reason": "coverage: membership = ledger membership_arithmetic_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-131", "keys": ["beta_lt_eps"], "line": 309, "quote": "epsilon-beta=2 delta>0,", "reason": "coverage: beta_lt_eps = ledger group_below_dimension/group_key_fits_record"}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-132", "keys": ["gamma_slack"], "line": 310, "quote": "1-epsilon-r0>0,", "reason": "coverage: gamma_slack = ledger global_gamma_power_slack"}, +{"classification": "STALE_TEXT_ONLY", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-133", "keys": ["chirp_guard"], "line": 311, "quote": "1-(2xi-2)-r0-beta=0.184140990423...>0,", "reason": "PR1786-point value; final 0.18414049008774891..."}, +{"classification": "COVERED", "file": "vendor/pr1786/FINE-PRIME-PADDING.md", "id": "pr1673c-134", "keys": ["xi_gt_half", "xi_lt_eps", "xi_lt_TH"], "line": 312, "quote": "1/20, 48>43.", "reason": "coverage: halo_volume = ledger microbox_halo_volume; halo_radius = ledger halo_covers_generic_inverse_radius"} +], +"counts":{"AMBIGUOUS": 0, "AUTO_TRUE": 53, "COVERED": 262, "FALSE_AT_POINT": 3, "NON_EXPONENT": 58, "OBSOLETE": 113, "STALE_TEXT_ONLY": 64, 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"Q(2**tau.numerator-7**tau.denominator)", "truth": {"final": true, "pr1673": true, "pr1673mc": false, "pr1786": true}}, +"strassen_gt_9_4":{"expr": "(7**4-2**9)", "final_value": "1889", "kind": "auto", "ledger_checks": [], "meaning": "log2 7 > 9/4 (Strassen exponent between 9/4 and 45/16)", "rel": ">0", "source_expr": "Q(7**4-2**9)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"supp_K_guard":{"expr": "(127*4-4)", "final_value": "504", "kind": "auto", "ledger_checks": [], "meaning": "K=128G >= G+4ceil(log2 p)+10 with G=4ceil(log2 p)+6 (coefficient of ceil(log2 p) in the difference)", "rel": ">0", "source_expr": "Q(127*4-4)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"supp_K_guard_64":{"expr": "(63*4-4)", "final_value": "248", "kind": "auto", "ledger_checks": [], "meaning": "K=64G >= G+4ceil(log2 p)+10 (SUPPORT-ROUTER variant)", "rel": ">0", "source_expr": "Q(63*4-4)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"tag_2beta":{"expr": "1-2*beta", "final_value": "-1.000000000000000000000000", "kind": "control", "ledger_checks": [], "meaning": "old union tag test 2 beta < 1", "rejecting_control": "old_union_tag_2beta", "rel": ">0", "truth": {"final": false, "pr1673": true, "pr1673mc": true, "pr1786": false}}, +"tau_9_4_branch":{"expr": ["tau-9/4", "5/2-tau"], "final_value": "-0.3125", "kind": "none", "ledger_checks": [], "meaning": "9/4 < tau < 5/2 (supplementary 9/4 branch)", "rel": ">0", "source_expr": "min(tau-Q(9,4),Q(5,2)-tau)", "truth": {"final": false, "pr1673": false, "pr1673mc": true, "pr1786": false}}, +"tau_gt_2":{"expr": "tau-2", "final_value": "0.8125", "kind": "auto", "ledger_checks": [], "meaning": "tau > 2", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"tau_gt_legall":{"expr": "tau-(23728639/10**7)", "final_value": "0.4396361", "kind": "auto", "ledger_checks": [], "meaning": "tau above Le Gall 2.3728639 (CLASSICAL row; obsolete)", "rel": ">0", "source_expr": "tau-Q(23728639,10**7)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"tau_lt_5_2":{"expr": "(5/2)-tau", "final_value": "-0.3125", "kind": "none", "ledger_checks": [], "meaning": "tau < 5/2 (CLASSICAL/RECT rows; PR1673 search-from-promise path)", "rel": ">0", "source_expr": "Q(5,2)-tau", "truth": {"final": false, "pr1673": false, "pr1673mc": true, "pr1786": false}}, +"theta_ge_1_over_4p":{"expr": "1-TH", "final_value": "-1", "kind": "none", "ledger_checks": [], "meaning": "theta >= 1/(4p)", "rel": ">=0", "truth": {"final": false, "pr1673": true, "pr1673mc": true, "pr1786": false}}, +"theta_ge_1_over_d":{"expr": "eps-TH", "final_value": "-1.000000000000000000000000", "kind": "none", "ledger_checks": [], "meaning": "theta >= 1/(4d), i.e. theta^-1 = O(d)", "rel": ">=0", "truth": {"final": false, "pr1673": true, "pr1673mc": true, "pr1786": false}}, +"tile_gauge":{"expr": "1-(beta+TH)", "final_value": "-2.000000000000000000000000", "kind": "none", "ledger_checks": [], "meaning": "HALO sec 6 tile gauge g a0/theta = o(p) at fine theta", "rel": ">0", "truth": {"final": false, "pr1673": false, "pr1673mc": false, "pr1786": false}}, +"tile_gauge_core":{"expr": "1-(beta+core-TH)", "final_value": "-126.0000000000000000000000", "kind": "none", "ledger_checks": [], "meaning": "HALO sec 6 tile gauge g a0 theta N = o(p) with N = p^128", "rel": ">0", "truth": {"final": false, "pr1673": false, "pr1673mc": false, "pr1786": false}}, +"u_ge_log2_8p":{"expr": "(14/5)-3", "final_value": "-0.2", "kind": "none", "ledger_checks": [], "meaning": "u = (4/pi) ln 16p >= log2(8p): needs 4 ln2 >= pi; upper bound 4(7/10) - 3 of 4ln2 - pi", "rel": ">=0", "source_expr": "Q(14,5)-3", "truth": {"final": false, "pr1673": false, "pr1673mc": false, "pr1786": false}}, +"umbrella10":{"expr": ["10-(2*TH+2)", "10-(5/2+2*TH)"], "final_value": "3.5", "implication": "hard-coded norm_power=10 in check_fine_padding.py; feeds 20/40/42/43 and halo 48; not derived from THETA_POWER in the ledger", "kind": "none", "ledger_checks": [], "meaning": "PR1786 umbrella p^10 >= broad ||K^-1|| ~ p^(2TH+5/3+o(1)) (<= p^(2TH+2)) and narrow ||N^-1|| ~ p^(5/2+2TH)", "rel": ">0", "source_expr": "10-max(2*TH+2,Q(5,2)+2*TH)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"uncapped_boundary":{"expr": "1-kappa-(tau-1)/2", "final_value": "0.09207024504387445547866433", "kind": "auto", "ledger_checks": [], "meaning": "uncapped PR1673 OUTER-AUDIT boundary row (omega-1)/2 < 1-kappa", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"union_density":{"expr": "xi-beta-(1/2)", "final_value": "-0.5920702450438744554786643", "kind": "none", "ledger_checks": [], "meaning": "sparse-union fraction g mu -> 0 (deleted row sparse_union_fraction_decays)", "rel": ">0", "source_expr": "xi-beta-Q(1,2)", "truth": {"final": false, "pr1673": true, "pr1673mc": true, "pr1786": false}}, +"union_eq":{"expr": "(xi+(1/2)-eps)-(eps*q+s+(tau-2)/2)", "final_value": "0", "implication": "check_ledger.py l.196 assert", "kind": "assert", "ledger_checks": [], "meaning": "union saving = main + s + (tau-2)/2 = main + s + 13/32", "rel": "==0", "source_expr": "(xi+Q(1,2)-eps)-(eps*q+s+(tau-2)/2)", "truth": {"final": true, "pr1673": true, "pr1673mc": false, "pr1786": true}}, +"union_row":{"expr": "xi+(1/2)-eps-kappa", "final_value": "0.4062500000000000000000000", "kind": "ledger", "ledger_checks": ["sparse_union_movement_above_kappa"], "meaning": "radix-union movement xi+1/2-eps above kappa", "rel": ">0", "source_expr": "xi+Q(1,2)-eps-kappa", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_def":{"expr": "xi-(eps*(1+q)-c+s)", "final_value": "0", "implication": "check_ledger definition (ledger_eval identity xi_formula)", "kind": "assert", "ledger_checks": [], "meaning": "xi = eps(1+q) - c + s", "rel": "==0", "truth": {"final": true, "pr1673": true, "pr1673mc": false, "pr1786": true}}, +"xi_free_c_half":{"expr": "(eps*(1+q)-(1/2)+s)-(1/2)", "final_value": "0.001679754956125544521335671", "kind": "none", "ledger_checks": [], "meaning": "claim: c = 1/2 gives xi = 0.5", "rel": "==0", "source_expr": "(eps*(1+q)-Q(1,2)+s)-Q(1,2)", "truth": {"final": false, "pr1673": false, "pr1673mc": false, "pr1786": false}}, +"xi_gt_half":{"expr": "xi-(1/2)", "final_value": "0.4079297549561255445213357", "kind": "ledger", "ledger_checks": ["cap_above_band"], "meaning": "cap B = p^xi above the band W ~ p^(1/2)", "rel": ">0", "source_expr": "xi-Q(1,2)", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_lt_1":{"expr": "1-xi", "final_value": "0.09207024504387445547866433", "identity": "C__cap_below_cell+C__epsilon_below_one", "kind": "implied", "ledger_checks": ["cap_below_cell", "epsilon_below_one"], "meaning": "xi < 1 (per-block aB = o(p); per-axis chirp o(1))", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_lt_TH":{"expr": "TH-xi", "final_value": "1.092070245043874455478664", "kind": "ledger", "ledger_checks": ["cap_below_phase_cell_power"], "meaning": "cap below the fine phase cell theta^-1 ~ p^2", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_lt_core":{"expr": "core-xi", "final_value": "127.0920702450438744554787", "identity": "C__cap_below_phase_cell_power+core-TH", "kind": "implied", "ledger_checks": ["cap_below_phase_cell_power"], "meaning": "W polylog <= L W/B (xi < core power)", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_lt_eps":{"expr": "eps-xi", "final_value": "0.09207024504387445547866433", "kind": "ledger", "ledger_checks": ["cap_below_cell"], "meaning": "cap below d (PR1673 cell scale)", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"xi_pos":{"expr": "xi", "final_value": "0.9079297549561255445213357", "identity": "C__cap_above_band+(1/2)", "kind": "implied", "ledger_checks": ["cap_above_band"], "meaning": "xi > 0", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}}, +"zeta_pos":{"expr": "zeta", "final_value": "1E-30012", "kind": "auto", "ledger_checks": [], "meaning": "zeta > 0 (stored, used by no ledger formula)", "rel": ">0", "truth": {"final": true, "pr1673": true, "pr1673mc": true, "pr1786": true}} +}, +"schema":"t74-side-condition-coverage-audit/inventory/v1", +"status":"local-only adversarial coverage audit of the pending PR #2044 T74 notes; exact rationals; not a proof of the T74 claim and not a multiplication theorem", +"verification_verdicts":[ +{"id": "outer-09", "note": "The keys are gauss_row (fused_gaussian_above_kappa, exact), gauss_window ((C_fg - C_main)/q identity, checked exactly; value delta(1/q-2) = 1.1866e-30007) and gauss_minus_main_id ((Gauss-main) = delta(1-2q), checked). A caveat on 'implied': positivity of the two checks does not by itself imply C_fg - C_main > 0. However, check_ledger.py asserts min(margins)==main_transform, which does cover Gaussian >= main. COVERED holds.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "outer-102", "note": "OBSOLETE is correct. FINE-PADDING-COMPOSITION.md:13 explicitly says the boundary is explicit Strassen tau=45/16, c=3/32, 'not the structured boundary', and that the file does not enter kappa. The file's own l.3 package note says the same. No keys are needed because no current check uses c=1/2.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "outer-115", "note": "COVERED with beta_lt_eps and eps_lt_1 is a valid sufficient translation and matches the note's own l.24 reasoning. RECT-BOUNDARY is a superseded fallback (l.1), but this premise is not specific to k=5 batching. The current explicit-Strassen boundary inherits PHASE-LAYOUT-AUDIT's batching of >=W RHS from a superpolynomial supply (RECT l.17), so not OBSOLETE is defensible. This matches the inventory's treatment of sibling outer-105/107 (COVERED, 'fallback file').", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "outer-19", "note": "No cost or precision row breaks, and the claimed kappa does not depend on this claim. The condition the proof uses is positivity of each row's margin above kappa (equivalently, main binds). It holds and is checked by the 9 '*_above_kappa' strict checks, including global_coordinate_router_above_kappa = 5.0336e-30011 > 0, and by check_ledger's assertion that main_transform is the minimum margin. The 1e-30010 figure is descriptive only. The router margin r0(1/2+2q) > 0 holds for every r0 > 0 and delta > 0. So sec. 3's conclusion (kappa = eps*q - 1e-30022, only delta moves it) is unaffected. Relat", "verdict": "CONFIRMED_FALSE", "verifier": "flag-rederive"}, +{"id": "outer-19", "note": "No cost or precision row breaks, and the claimed kappa does not depend on this sentence. kappa = floor(eps*q on the FLOOR grid) - BACKOFF is set by the main row alone. The router row is strictly above main for every delta >= 0, because a - eps*q = (a-q) + q*delta >= r0/2 > 0. The ledger checks this as global_coordinate_router_above_kappa = 5.0336e-30011 > 0, and independent_check.py checks it as eff > Ed*q in its delta sweep. Absorbing polylog factors only needs a strictly positive exponent gap. The main row's gap of 1e-30022 is far smaller than the router's, so no step can need a gap of at le", "verdict": "CONFIRMED_FALSE", "verifier": "flag-refute"}, +{"id": "outer-21", "note": "The claimed kappa does not depend on this. Only the literal sentence is false: \"using c = 1/2 would give xi = 0.5\", and, under the Strassen boundary actually used, \"xi ... free in (1/2, epsilon)\". Taken literally, xi = 0.5 at c = 1/2 breaks three rows: boundary_algebraic_matrix_above_kappa (-0.00168), sparse_union_movement_above_kappa (-0.00168) and cap_above_band (0, fails strict). The sentence sits in a counterfactual aside (sec. 3) about alternative boundaries that the package does not use. The kappa claim uses c = 3/32 and xi = eps(1+q) - 3/32 + s = 0.90793. There, every condition on xi th", "verdict": "CONFIRMED_FALSE", "verifier": "flag-rederive"}, +{"id": "outer-21", "note": "None. No cost or precision row breaks at the final #2044 point, and the claimed kappa 0.0016797549561255445... does not depend on the aside. The aside describes an unused alternative boundary (STRUCTURED-BOUNDARY.md is explicitly 'not used', 'does not enter kappa'), and kappa = floor(eps*q) - 1e-30022 is independent of c anyway. The only defect is cosmetic numeric text: 'xi = 0.5' should read 'xi ≈ 0.50168', and 'free in (1/2, eps)' should say that xi = eps(1+q) - c + s, with c ranging over (0.00168, 0.50168). Separate stale-text finding, not part of this flag: the decimal 'xi = 0.907929654788", "verdict": "ACTUALLY_COVERED", "verifier": "flag-refute"}, +{"id": "outer-36", "note": "Inventory COVERED with xi_lt_1 (1-xi, implied by cap_below_cell+epsilon_below_one) and chirp_axis_o1 (TH-2xi with identity 2*(cap_below_cell+epsilon_below_one)+TH-2, TH=2). I re-derived both identities; they are exact and give 0.0921 and 0.1841 > 0 at the final point. The fine-theta reading is correct because the package note on line 1 of the same file replaces theta>=1/(4d) by theta>=1/(4p^2). Minor nuance: the range bound uses the upper bound theta<=1/(2p^2-1), whereas TH encodes theta^-1=O(p^2); both hold for fine primes. The group total is the chirp guard, which the reason mentions but the", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "outer-71", "note": "No row breaks. Under every cost reading, the binding inequality is either already the strict ledger check membership_arithmetic_fits_record (1-beta-2(1-eps) = 2e-30010) or implied by union_header_fits_record or group_key_fits_record. The ledger also has the rejecting control beta_above_membership_window: at beta = 1 - 2delta the membership check fails, as it should. Kappa = eps*q is fixed by the main row; none of these rows binds kappa beyond restricting beta to the window (1 - delta(1+1/q), 1 - 2delta), and the chosen beta = 1 - 6delta lies inside it. Separate wording issue (not an exponent c", "verdict": "ACTUALLY_COVERED", "verifier": "flag-rederive"}, +{"id": "outer-71", "note": "None. No cost or precision row breaks. The worst-case reading needs beta + 2(1-eps) < 1, which the ledger already checks strictly as membership_arithmetic_fits_record, value 2e-30010. That row also enters the rejecting control beta_above_membership_window. The per-record cost is o(p) and is absorbed by reading the p-bit record once in the group-scan pass, so the group_scans row (1-eps+beta) is unchanged. The union row xi+1/2-eps, about 0.408, does not involve this cost at all. Kappa does not depend on it. The margin of 2e-30010 is the same r0-scale 'eventually' status that FINE-PADDING-COMPOSI", "verdict": "ACTUALLY_COVERED", "verifier": "flag-refute"}, +{"id": "outer-79", "note": "AUTO_TRUE with dense_union (auto, beta+1/2-xi) matches. No ledger check is needed because the sparsity row was dropped. I re-evaluated the value independently.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "outer-96", "note": "AUTO_TRUE with TH_pos (theta_positive_polynomial_power) is correct. Nuances: (1) BILATERAL-LDU states the '16 theta^-2' form only at a=1, and STRUCTURED-BOUNDARY l.64 cites it for N generally. The polynomial conclusion survives with a=Theta(log p). (2) STRUCTURED-BOUNDARY is unused at the final point (its l.3 and FINE-PADDING-COMPOSITION l.13), but the bound itself carries no stale number, so AUTO_TRUE rather than OBSOLETE is fine.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-02", "note": "check_ledger.py uses the identical literal for bit and checks actual_bit_above_effective. The inventory correctly avoided the c=3/32 clash. COVERED with a_lt_bit is right.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-107", "note": "These map exactly to cap_above_band, cap_below_cell, group_positive and group_below_dimension. The inventory resolved b->xi correctly. 'At the displayed parameters' refers to old PR1673 numbers, but the four generic inequalities are ledger checks that hold at the final point. COVERED is correct.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-122", "note": "OBSOLETE with key linear_guard (= the rejecting control old_linear_guard) is correct. GAUGEFREE-INTERIORS.md:1 (theta>=1/(4p^2) replaces 1/(4d); guard becomes beta+2xi-2<1) and FINE-PADDING-COMPOSITION.md:46 (the guard is superseded at fine theta) really supersede the g*a*Bcap term. FINE-PADDING-COMPOSITION:11 also names old_linear_guard. Caveat: the reason 'ad term true' and operative key gamma_slack for the ad term are inaccurate at the final regime. The literal a*d = o(p) is true, but the precision requirement it stood for became O(p^2 log p) setup precision. The inventory's own outer-12 re", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-141", "note": "OBSOLETE ('9/4 branch numerics') is correct. FINE-PADDING-COMPOSITION.md:13 fixes the boundary to explicit Strassen tau=45/16, which supersedes the 9/4 branch only implicitly. RECT-BOUNDARY.md:66 ('The unproven omega_C <= 9/4 premise is not used') is a more explicit citation. The same literal is the ledger's `old` in improvement_over_previous_local_final (kappa-old>0, true), which could be noted as a ledger link.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-162", "note": "This matches the ledger margin group_scans=1-eps+beta and the check group_scans_above_kappa exactly, and it is the same 'group scans O(V d/g)' row as PHASE-LAYOUT-AUDIT. COVERED with scan_row is correct.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-44", "note": "This matches the ledger margin group_bit_router=1-eps+a*beta and the check group_bit_router_above_kappa exactly. COVERED is correct, and I re-evaluated the positive margin.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-50", "note": "STALE_TEXT_ONLY with face_row is correct. The generic row is the ledger margin microbox_face_corrections with halo 48 / core 128 (PR1786 l.230-233), and only the numeric powers are stale.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673a-58", "note": "The inventory marks COVERED with the single key eps_lt_1 (epsilon_below_one / source_axis_superpolynomial / actual_logarithmic_gamma_guard). epsilon<1 neither implies nor encodes 'O(p)-bit entries, h=O(p), W=O(sqrt p polylog p)', and no identity is recorded. At most it reflects the PR1673-era (theta~1/d) global range O(d alpha^2)=o(p). At fine theta that is not what bounds the boundary-block entries, and outer-12's own reason says the fine-theta offline term is not this row. The inventory treats the same premises inconsistently: outer-111 ('O(P+h+log W)=O(p) ... P,h=O(p)') is NON_EXPONENT, pr1", "verdict": "DISAGREE_MISTRANSLATED", "verifier": "sample-seed72"}, +{"id": "pr1673a-79", "note": "STALE_TEXT_ONLY with halo_volume (microbox_halo_volume) is correct, and the reason 'now p^(beta-80)' is accurate. Arguably OBSOLETE, because PR1786 l.215-233 explicitly replaces the locality scale, but STALE_TEXT_ONLY fits the class definition.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-115", "note": "No cost or precision row breaks, and the claimed kappa does not depend on the false statement. The false clause, K0^2 = o(p), is only the optional \"metadata absorbed by records\" branch. The theorem itself offers the alternative at l.32 and l.44: pay O((gL/N) V K0^2/B) explicitly.\n\nAt the final point that explicit term has exponent -78 - 10*delta, which is 2 + 2*delta below the ledger row microbox_face_corrections. That row charges g*p^2 per copied bit, and its strict check microbox_face_corrections_above_kappa is positive at about 76.998. So the strict check covers the metadata term with room ", "verdict": "CONFIRMED_FALSE", "verifier": "flag-rederive"}, +{"id": "pr1673b-115", "note": "The literal text is false at the point, but nothing in the kappa derivation depends on it, so no cost or precision row breaks. The only consumer of HALO-THEOREM in the #2044 tree is PHASE-LAYOUT-AUDIT.md l.204-219 (git grep on pr/2044; the evidence/ copy has the same hash). That note uses it only as the movement lemma (\"source-driven first-boundary-axis rectangles ... Actual keys use O(g log s) bits, and all key passes are paid\"). It never uses sec 6's parameter set. The metadata and key passes it needs are paid inside the microbox_face_corrections row. That row has a margin of about 77 and do", "verdict": "OBSOLETE", "verifier": "flag-refute"}, +{"id": "pr1673b-23", "note": "STALE_TEXT_ONLY with halo_radius (halo_covers_generic_inverse_radius) is correct. The old numeric p^3 would fail at fine theta (3<43), but the generic condition with the current A=p^48 holds. PR1786 l.215 ('old literal row-gap and locality constants must not be reused') would also justify OBSOLETE, so the choice between the two classes is a convention.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-24", "note": "COVERED via halo_volume = microbox_halo_volume, which matches exactly. The surrounding paragraph uses the old A~p^3, L~p^8, but the quoted text 'fraction O(gA/L)' has no number, so COVERED rather than STALE_TEXT_ONLY is appropriate. This is consistent with the sibling pr1673a-79, which is STALE because it quotes p^3/p^8.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-30", "note": "OBSOLETE with old_union_uncapped (1/2-beta-kappa) and operative union_row matches. UNION-SCHEDULE.md:17-18 explicitly describes 'the audit's implementation' (PHASE-LAYOUT-AUDIT's per-axis scan of U, union row eps+beta+1/2-xi) and states 'Here the g-fold scan of U is removed'. So the superseder is valid. CAPPED-INTERIORS.md:41 is an intermediate superseder that could also be cited.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-52", "note": "These map exactly to group_positive, group_below_dimension and support_router_span (also union_header_fits_record). COVERED is correct.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-54", "note": "COVERED by eps_lt_1 = epsilon_below_one / source_axis_superpolynomial; these are exact. The margin is only 2e-30010, so 'eventually' means an astronomical cutoff, as FINE-PADDING-COMPOSITION sec. 4 acknowledges.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-62", "note": "AUTO_TRUE with no keys is correct.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673b-91", "note": "Inventory keys q_lt_a (q_below_effective; q_below_internal equals a-q here because sigma0, 1-eps>0) but not listed. That omission is harmless.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673c-13", "note": "AUTO_TRUE with no keys is correct, and the letter clash is handled. Mapping a to a_eff would have made it false (0.00168<1). The inventory did not do that.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673c-21", "note": "This is the same mapping as pr1673c-40: COVERED via r_pos = alpha_logarithm_absorption. a is correctly not mapped to a_eff (that would give a=0.00168, which contradicts Theta(log p)). Acceptable.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673c-40", "note": "COVERED via r_pos = alpha_logarithm_absorption (check value r0>0). The ledger names this check for exactly this absorption, so the mapping is reasonable. NON_EXPONENT would also be defensible. No letter-clash error: a is not mapped to a_eff.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673c-52", "note": "OBSOLETE with full_cell_gauge_d (1-eps-r-beta, not encoded) is the right translation, and I re-evaluated -1.0. The superseders are valid. vendor/pr1786/FINE-PRIME-PADDING.md:169 states the operative guard 'beta + 2 xi - 2 < 1, beta < 1'. GAUGEFREE-INTERIORS.md:15 (R1) replaces the local gauge by the chirp-only form. CAPPED-GAUGE-AUDIT, the anchored capped gauge, was the first superseder.", "verdict": "AGREE", "verifier": "sample-seed72"}, +{"id": "pr1673c-84", "note": "The condition is true at the final point, so no cost or precision row breaks. kappa does not depend on it: the binding row is main = eps*q. It does support the ledger's halo_covers_generic_inverse_radius row (48 > 43), the microbox_face_corrections and halo-volume rows (halo 48, core 128), and the PR1786 sec. 4 normalizer p^100 >> p^10. The gap is in what the ledger checks. Its only theta check is theta_positive_polynomial_power (T > 0). The number 43 is hard-coded in check_ledger.py and comes from norm_power = 10 in check_fine_padding.py, which never reads THETA_POWER. Changing THETA_POWER to", "verdict": "CONFIRMED_UNCOVERED_TRUE", "verifier": "flag-rederive"}, +{"id": "pr1673c-84", "note": "None at the final point. The inequality holds with exponent margin 7/2 or more and involves only fixed analytic constants, so no point row can break. It supports only the locality, halo and normalizer argument: halo 48 > radius 43, core 128, normalizer p^100. The ledger rows that depend on that chain are halo_covers_generic_inverse_radius (margin 5), microbox_halo_volume and microbox_face_corrections. None of them binds. The binding rows remain main transform, Strassen boundary (main + s) and union. The claimed kappa 0.0016797549561255445... therefore does not depend numerically on this condit", "verdict": "CONFIRMED_UNCOVERED_TRUE", "verifier": "flag-refute"}, +{"id": "pr1673c-88", "note": "AUTO_TRUE with no keys is correct. The step also uses the fine-prime lower bound theta>1/(4p^2) (TH=2). TH_pos could optionally be listed, but the classification is right.", "verdict": "AGREE", "verifier": "sample-seed72"} +], +"verification_verdicts_schema":"PLACEHOLDER for the main session: list of {\"id\": condition id, \"verifier\": label, \"verdict\": \"AGREE\"|\"DISAGREE\"|..., \"note\": text}; two independent adversarial verdicts per flagged id; verify.py reports, never enforces" +} diff --git a/research/t74-side-condition-coverage-audit/POINTS.json b/research/t74-side-condition-coverage-audit/POINTS.json new file mode 100644 index 0000000000..3b815d3fba --- /dev/null +++ b/research/t74-side-condition-coverage-audit/POINTS.json @@ -0,0 +1,465 @@ +{ + "note": "Exact parameter points. Definitions are evaluated in order by verify.py with the ast-whitelisted evaluator; {\"exact\": literal} is a decimal/rational literal; {\"floor_grid\",\"grid\",\"minus\"} is floor(x*grid)/grid - minus. Variables not defined at a point make a key n/a (null) there.", + "points": { + "final": { + "definitions": [ + [ + "b_cert", + { + "exact": 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484" + } + ], + [ + "r", + "1/10**30010" + ], + [ + "zeta", + "1/10**30012" + ], + [ + "s", + "r" + ], + [ + "stop", + "1/10**30016" + ], + [ + "backoff", + "1/10**30022" + ], + [ + "eps", + "1-2*r" + ], + [ + "beta", + "1-6*r" + ], + [ + "b", + "b_cert-r" + ], + [ + "q", + "b-r" + ], + [ + "a", + "(q+b)/2" + ], + [ + "TH", + "2" + ], + [ + "halo", + "48" + ], + [ + "core", + "128" + ], + [ + "tau_num", + "45" + ], + [ + "tau_den", + "16" + ], + [ + "tau", + "tau_num/tau_den" + ], + [ + "c", + "(3-tau)/2" + ], + [ + "xi", + "eps*(1+q)-c+s" + ], + [ + "kappa_formula", + { + "floor_grid": "eps*q", + "grid": "10**30046", + "minus": "backoff" + } + ], + [ + "kappa", + "kappa_formula" + ], + [ + "W", + "1/2" + ], + [ + "bit", + { + "exact": "0.001733427039589844234749" + } + ] + ], + "eq_tolerance": null, + "fingerprints": { + "a": "963df143320f66112561da2dd2f79bc3f64e51bd789cee250154f53bb9eb2222", + "b": "06796e3f793ea16d8b3569b5f13c5877f476b094fb03bd38d8ff49088d7a8d87", + "b_cert": "1a2dc418276ed2f1b6cad151892b3fa0578e514b2e4154cb9fc7d7522ba62c96", + "beta": "0d3124ffab59f94fac1e53fda22be4d0fd636bf5cb745ea23f1c2d4a7dec0ea8", + "eps": "3214df512cc0dad0e4dba96d2d492f7f89d88d23d95f0129106327bf961e00ab", + "kappa": "40345649a43d970dba6f4e9472a1e95907a48e83b73bf347d91a3e117a4245ea", + "q": "987b95787c6d7f1e2b57179b4d148619ad140259b6ef44a19a326d1f04aabaad", + "r": "e3f119a50d9c05222e4a4bcf1d562294ccc1dce676f2c8412c2eb812b39efcfa", + "s": "e3f119a50d9c05222e4a4bcf1d562294ccc1dce676f2c8412c2eb812b39efcfa", + "xi": "d5c80c50859049b25d2bdee06c7b500a9672c333001992fc80aa3e1fcf42c9c3", + "zeta": "4828224c12b6dab715d5b8308b2855cb4d6f270c401a9c2ff9ef559dd0fab810" + }, + "irreducible_input": "b_cert = LEDGER.json complex_lower_pinned (= new/SPEC.json expected.complex_lower), exact terminating decimal", + "ledger_derived": [ + "MINCHECK", + "MIN_NONMAIN_MARGIN", + "MIN_MARGIN_ABOVE_KAPPA" + ], + "ledger_floor_grid": "10**30046", + "ledger_map": { + "a": "rows.*.a", + "b": "complex_lower_short", + "b_cert": "complex_lower_pinned", + "beta": "rows.*.beta", + "eps": "rows.*.epsilon", + "kappa": "rows.*.kappa", + "q": "rows.*.q", + "r": "rows.*.r0", + "s": "rows.*.slack", + "xi": "rows.*.xi", + "zeta": "rows.*.zeta" + }, + "source": "PR #2044 head 322949a5 research/capped-fusion-t74-k554/outer/LEDGER.json row struct_boundary_radix_union; closed forms transcribed from outer/check_ledger.py l.24-33 (DIG=30000: R0=10^-(DIG+10), ZETA=10^-(DIG+12), SLACK=GAP=B_GAP=R0, STOP=10^-(DIG+16), FLOOR=10^(DIG+46), BACKOFF=10^-(DIG+22), DELTA_E=2 R0, EPS=1-DELTA_E, BETA=1-3 DELTA_E), l.49-54 (bit, b=certified_complex-B_GAP, q=b-GAP, a=(q+b)/2) and ledger() l.110-121 (c=(3-tau_eff)/2, xi=eps(1+q)-c+slack, kappa=floor(eps q FLOOR)/FLOOR-BACKOFF); geometry from LEDGER.json geometry_changes (theta 2, halo 48, core 128, tau 45/16)" + }, + "pr1673": { + "definitions": [ + [ + "eps", + { + "exact": "0.9984838711085557536432677624420451614" + } + ], + [ + "xi", + { + "exact": "0.9064167934681446247757331487619919695" + } + ], + [ + "beta", + { + "exact": "0.0935821965318553752242668512380080305" + } + ], + [ + "q", + "(16729223595888711324653863199468081/10**37)/eps" + ], + [ + "b", + "q+1/10**10" + ], + [ + "a", + "(q+b)/2" + ], + [ + "r", + "1/10**6" + ], + [ + "zeta", + "1/10**8" + ], + [ + "s", + "1/10**5" + ], + [ + "stop", + "1/10**9" + ], + [ + "kappa", + { + "exact": "0.001672922349588871" + } + ], + [ + "TH", + "eps" + ], + [ + "halo", + "3" + ], + [ + "core", + "8" + ], + [ + "tau_num", + "45" + ], + [ + "tau_den", + "16" + ], + [ + "tau", + "tau_num/tau_den" + ], + [ + "c", + "3/32" + ], + [ + "bit", + { + "exact": "0.001733427039589844234749" + } + ], + [ + "W", + "1/2" + ] + ], + "eq_tolerance": "1/10**30", + "source": "vendor/pr1673/capped-phase-fusion/CAPPED-INTERIORS.md l.48-61 point from its displayed 37-digit decimals: q = kappa_limit/eps, b = q+1e-10, r=1e-6, zeta=1e-8 (OUTER-AUDIT l.17), s=1e-5, stop=1e-9, theta ~ 1/d (TH = eps), halo 3, core 8 (OUTER-AUDIT l.19), tau=45/16; as defined in the local-only match.py l.77-86. ==0 keys use |v| < 1e-30 (displayed decimals)" + }, + "pr1673mc": { + "definitions": [ + [ + "eps", + { + "exact": "0.998745145709950482" + } + ], + [ + "xi", + { + "exact": "0.750213747912678130" + } + ], + [ + "beta", + { + "exact": "0.249785242087321870" + } + ], + [ + "q", + "(16729223595888711324653863199468081/10**37)/(9984838711085557536432677624420451614/10**37)" + ], + [ + "b", + "q+1/10**10" + ], + [ + "a", + "(q+b)/2" + ], + [ + "r", + "1/10**6" + ], + [ + "zeta", + "1/10**8" + ], + [ + "s", + "1/10**5" + ], + [ + "stop", + "1/10**9" + ], + [ + "kappa", + { + "exact": "0.001673360105405778" + } + ], + [ + "TH", + "eps" + ], + [ + "halo", + "3" + ], + [ + "core", + "8" + ], + [ + "tau_num", + "19" + ], + [ + "tau_den", + "8" + ], + [ + "tau", + "tau_num/tau_den" + ], + [ + "c", + "5/16" + ], + [ + "bit", + { + "exact": "0.001733427039589844234749" + } + ], + [ + "W", + "1/2" + ] + ], + "eq_tolerance": "1/10**16", + "source": "vendor/pr1673/capped-phase-fusion/MATRIX-COROLLARY.md l.25-49 (9/4 branch) point from displayed 18-digit decimals; q, b, a as at pr1673; tau=19/8, c=5/16, theta ~ 1/d (TH = eps), halo 3, core 8; as defined in the local-only match.py l.87-93. ==0 keys use |v| < 1e-16" + }, + "pr1786": { + "definitions": [ + [ + "b_cert", + { + "exact": "335950991225108904267/200000000000000000000000" + } + ], + [ + "r", + "1/10**64" + ], + [ + "zeta", + "1/10**66" + ], + [ + "s", + "1/10**64" + ], + [ + "stop", + "1/10**70" + ], + [ + "eps", + { + "exact": "9999999/10000000" + } + ], + [ + "beta", + { + "exact": "9999997/10000000" + } + ], + [ + "b", + "b_cert-1/10**64" + ], + [ + "q", + "b-1/10**64" + ], + [ + "a", + "(q+b)/2" + ], + [ + "TH", + "2" + ], + [ + "halo", + "48" + ], + [ + "core", + "128" + ], + [ + "tau_num", + "45" + ], + [ + "tau_den", + "16" + ], + [ + "tau", + "tau_num/tau_den" + ], + [ + "c", + "3/32" + ], + [ + "xi", + "eps*(1+q)-c+s" + ], + [ + "kappa", + { + "exact": "0.0016797547881500489087805478664999999999999999999999999999999998000000199999" + } + ], + [ + "W", + "1/2" + ], + [ + "bit", + { + "exact": "0.001733427039589844234749" + } + ] + ], + "eq_tolerance": null, + "source": "vendor/pr1786/FINE-PRIME-PADDING.md sec 7 (l.271-321) explicit point, exact: eps=9999999/10^7, beta=9999997/10^7, r0=s=1e-64, zeta=1e-66, stop=1e-70, b=b_cert-1e-64, q=b-1e-64, xi=eps(1+q)-3/32+s, kappa = PR1786 exact kappa (check_ledger.py KAPPA_1786); as defined in the local-only match.py l.66-75" + } + }, + "schema": "t74-side-condition-coverage-audit/points/v1", + "vocabulary": { + "MINCHECK": "min of the LEDGER strict checks (ledger-derived; final only)", + "MIN_MARGIN_ABOVE_KAPPA": "min over all cost rows of margin - kappa (ledger-derived; final only)", + "MIN_NONMAIN_MARGIN": "min over non-main cost rows of margin - kappa (ledger-derived; final only)", + "TH": "phase-cell power: theta^-1 ~ p^TH", + "W": "band exponent: W ~ p^(1/2)", + "a": "a_eff = (q+b)/2", + "b": "complex supplier saving used", + "b_cert": "certified complex supplier endpoint", + "backoff": "kappa backoff below the FLOOR grid", + "beta": "group exponent: g = p^beta", + "bit": "certified bit-supplier saving", + "c": "boundary constant (3 - tau)/2", + "core": "core power", + "eps": "epsilon: d = p^eps", + "halo": "halo power", + "kappa": "claimed kappa", + "kappa_formula": "floor(eps q * grid)/grid - backoff", + "q": "supplier saving used (q = b - gap)", + "r": "r0 slack", + "s": "layout slack", + "stop": "t_stop", + "tau": "matrix exponent tau_eff", + "tau_den": "denominator of tau", + "tau_num": "numerator of tau", + "xi": "cap exponent: B = p^xi", + "zeta": "zeta slack" + } +} diff --git a/research/t74-side-condition-coverage-audit/README.md b/research/t74-side-condition-coverage-audit/README.md new file mode 100644 index 0000000000..0ac9b60fcf --- /dev/null +++ b/research/t74-side-condition-coverage-audit/README.md @@ -0,0 +1,259 @@ +# Side-condition coverage audit of the pending T74 capped-fusion outer at PR #2044 + +**Status: adversarial audit and research note — no counterexample found. No new κ, no frontier change, and no +claim that the audited arguments are proved.** + +The pending T74 family (#1673 → #1758 → #1786 → #1905/#1928 → #1992 → #2044) claims the conditional +κ = 0.0016797549561255445…, which is 0.43% above the selected record. Its final parameter point puts the group exponent +and the axis exponent within 10⁻³⁰⁰¹⁰ of 1: β = 1 − 6·10⁻³⁰⁰¹⁰ and ε = 1 − 2·10⁻³⁰⁰¹⁰. Many of the inherited +PR1673 notes were written at β ≈ 0.09 and ε ≈ 0.998. + +This audit asks one question: + +> Is every asymptotic side condition written into the 28 notes of the PR #2044 head either encoded as a ledger strict +> check and true at that final point, true there for an elementary reason, or explicitly superseded? Side conditions +> here are exponent inequalities and claims of the form "o(p)", "fits the record" and "eventually". + +A condition that silently fails at the final point would invalidate the claimed κ, because the ledger only checks what it +encodes. Maintainer reviews of #1673, #1758, #1876 and #1928 leave these shared parameter-inequality interfaces open. + +## Result + +Four independent extractors read all 28 Markdown notes of `research/capped-fusion-t74-k554` at +`322949a53488d64023fedb89a6774927707e57ba`. They recorded 554 side conditions; 280 are distinct after +de-duplication. Each one was translated into the ledger's variables (d = p^ε, g = p^β, B = p^ξ, W ≈ p^½, +θ ≈ p⁻², halo p⁴⁸, core p¹²⁸). Each was then evaluated exactly at the #2044 final point, and also at the PR1786 and +PR1673 points as sanity controls. + +| Classification | Count | Meaning | +|---|---:|---| +| COVERED | 262 | equals or is implied by named ledger strict checks (exact equality or a recorded identity) | +| AUTO_TRUE | 53 | true at the point for an elementary reason (constant inequality, polylog, structural) | +| OBSOLETE | 113 | explicitly superseded by a later note (file:line cited); many are false at the point, as intended | +| STALE_TEXT_ONLY | 64 | quotes an old numeric exponent or margin; the generic condition holds | +| NON_EXPONENT | 58 | a proof obligation not reducible to an exponent inequality (listed, not assessed) | +| FALSE_AT_POINT | 3 | a current statement that is false at the point, but **not load-bearing** | +| UNCOVERED_TRUE | 1 | true at the point but not tied to any ledger check | +| AMBIGUOUS | 0 | (one matcher item resolved as COVERED by two verifiers) | + +**No load-bearing side condition is false at the final point.** Every condition the final chain needs is a ledger +check, implied by one, or elementary. Every condition that fails at the point is explicitly superseded. Examples are the +linear gauge guard, the `2β < 1` union-tag test, `β < 1 − ε`, the old g-factor union row, the union-density row and +`θ ≥ 1/(4d)`. Each of those held at PR1673's own point, which serves as a sanity control. + +The smallest exponent margins are 10⁻³⁰⁰²², 10⁻³⁰⁰¹⁰, 2·10⁻³⁰⁰¹⁰, 4·10⁻³⁰⁰¹⁰ and 6·10⁻³⁰⁰¹⁰. These rows hold only +*eventually*, for astronomically large p. That suffices for an asymptotic exponent statement, but it is not a practical +cutoff. + +### Text defects found (none changes κ) + +1. **`outer/FINE-PADDING-COMPOSITION.md:37`.** The note says every non-main row exceeds κ by at least 10⁻³⁰⁰¹⁰. This is + false: `global_coordinate_router_above_kappa` is 5.03·10⁻³⁰⁰¹¹, and several supplier checks are smaller still. What + the proof needs is that every margin is positive, which the ledger checks. Both verifiers confirmed the statement + is false. +2. **`outer/FINE-PADDING-COMPOSITION.md:38`.** The aside "ξ free in (1/2, ε); c = 1/2 gives ξ = 0.5" is false as + written. With c = 3/32, ξ is pinned at ε(1+q) − c + s. With c = 1/2, ξ = 0.50168, and ξ = 0.5 would violate the + boundary row and the strict cap. It describes an unused alternative boundary. +3. **`vendor/pr1673/capped-phase-fusion/HALO-THEOREM.md:205`.** "K₀² = o(p)" belongs to the theorem's §6 + instantiation, which assumes g = p^(1−ε−ζ), ε > 5/6 and L = O(p polylog p). At the final point it fails, since + 1 − 2(β+1−ε) = −1 + 8·10⁻³⁰⁰¹⁰. The theorem's own l.32/l.44 alternative, which pays the explicit metadata term + O((gL/N)V K₀²/B), does hold: its exponent lies 2 + 2δ below the ledger's `microbox_face_corrections` row. + **No final note records that branch choice.** Its only consumer at #2044 is `PHASE-LAYOUT-AUDIT.md` l.204–219. +4. **Uncovered constant.** The PR1786 umbrella exponent p¹⁰ (vendor `FINE-PRIME-PADDING.md`, polynomial norm bounds at + θ ≈ p⁻²) holds with margin 7/2. No ledger check ties it to `THETA_POWER`; the ledger's only θ check is that the + power is positive. +5. **Stale numbers.** `outer/FINE-PADDING-COMPOSITION.md:28` and `outer/UNION-SCHEDULE.md:121` quote + ξ = 0.90792965…, which is PR1786's δ = 10⁻⁷ point. The pinned point is ξ = 0.90792975…. The other 62 STALE_TEXT_ONLY + items are similar old margins and exponents. + +### The two open review items + +Both are resolved. Item 1 independently corroborates philippeVV's earlier reconciliation on #1897; see +"Relation to concurrent work" below. Details, file:line citations and the sweep table are in +[REVIEW-ITEMS.md](REVIEW-ITEMS.md), and `review_items.py` checks them exactly. + +1. **The disabled `or True` assertion (`outer/check_gaugefree.py:23`; #1876/#1897).** The line checks the + s = −δ/λ substitution against `δ² + δ²/λ − 2δ(1−λ)y`. The correct bracket is + `(1−λ)x² − λ(1−λ)y² + δ² − δ²/λ + 2δ(1−λ)y`, which is #1876's supplemental identity. So the constant and the + y-linear signs are both wrong, and the line would fail if it were made live. However: + - **No live check depends on it.** The proof uses s = −δ(1−θ) for the broad block and s = −β₀/ρ for the narrow + block, and both are checked by live assertions. The s = −δ/λ variant appears only in a parenthetical, and its + linear coefficients are checked correctly by live line 25. + - **Neither the ledger nor `run_outer.py` uses it.** `check_ledger.py` never uses the identity, and `run_outer.py` + only runs the script. + - **Lemmas 2.1 and 2.2 hold exactly**, as do the normalisation and the shrunk-shift coefficients. + + The #2044 head still ships the wrong line, and a second vacuous `or True` sits at `outer/struct_check.py:130`; the + check it disables does not enter κ. The fix is to make line 23 a live assert with the correct bracket, or to + delete it. +2. **"Confirm no other place charges g² per record" (GAUGEFREE-INTERIORS §7).** At the final point, no *active* + step charges g² (or g·|F|) against one record: + - **Superseded charges** cover every hit of the old per-axis U scan, the `1 − 2β` tag test, the full-key sort, + g·a·d precision bits and the linear gauge. Each is superseded and rejected by a ledger control. + - **Active charges** are per-visit tag work and header (1 − β = 6·10⁻³⁰¹⁰), membership (2·10⁻³⁰¹⁰), keys and the + support router, and the halo g-fold passes (face-correction margin ≈ 77). All are ledger-encoded and true. + - **One false option remains:** HALO-THEOREM's "K₀² = O(B)" option (defect 3 above). The package must use the + explicit-metadata branch. + +### Further observations + +- **Offline precision at fine θ.** The offline term a/(4θ) = Θ(p² log p) is not o(p). The written argument handles it + in PR1786 §3 (separate setup precision P_setup = Cp + 64p²L_p; `research/pr1786-fine-prime-transfer-audit` checked + that section), but no ledger row encodes it. `global_gamma_power_slack` (1 − ε − r) is the θ ≈ 1/d version of a + different bound. +- **Unused ζ.** ζ is stored in the ledger, but no ledger formula uses it. +- **Load-bearing removals.** The removals of `β < 1 − ε`, `g < √B` and union sparsity are load-bearing: all three + conditions are false at the final point, so the stack depends on the arguments that removed them. These are + SUPPLIER-SUPPORT §8, the gauge-free chirp guard and the per-visit union schedule. +- **Calling conventions that must hold.** The support-local supplier must be called globally. Charging V p^(1−a) per + group would need a − (ε − β) > κ, which is false (−3.5·10⁻³⁰⁰¹⁰). Setup and online precision must likewise stay + separate. + +## Verification + +- **Flagged items.** Every flagged item (FALSE_AT_POINT, UNCOVERED_TRUE, AMBIGUOUS) was checked by two independent + agents. One tried to refute the flag; the other re-derived the condition from the argument it supports and evaluated + it exactly. +- **Sampled re-check.** A seeded random sample (seed 72) of 28 non-flagged classifications (15 COVERED, 5 AUTO_TRUE, + 5 OBSOLETE, 3 STALE_TEXT_ONLY) was re-translated by a separate agent before it looked at the inventory. It agreed on + 27. The one disagreement mapped two structural premises (`h = O(p)`, `W = O(√p polylog p)`) to ε < 1. Those two + items, pr1673a-58 and pr1673a-133, are now NON_EXPONENT, which does not change any truth value. +- **Verdict log.** All 38 verdicts are recorded in `INVENTORY.json`, under `verification_verdicts`. + +## Reproduce + +From the repository root, Python 3.10+ standard library only, about 30 s: + +```sh +python3 -I -B research/t74-side-condition-coverage-audit/verify.py +python3 -I -B research/t74-side-condition-coverage-audit/review_items.py +``` + +Expected last line of `verify.py`: + +```text +PASS_T74_SIDE_CONDITION_COVERAGE conditions=554 keys=133 covered=262 auto_true=53 obsolete=113 stale_text_only=64 non_exponent=58 false_at_point=3 uncovered_true=1 ambiguous=0 load_bearing_false=0 negative_controls=14 source_root=skipped +``` + +and for `review_items.py` (about 6 s): + +```text +PASS_T74_REVIEW_ITEMS checks=88 mode=default item1_random_points=1500 seed=20441876 item2_records=18 active=11 superseded=6 false_option=1 cites=skipped ... +``` + +The verifier: + +- rebuilds the exact #2044 final point from one pinned 30,000-digit rational (`complex_lower_pinned`) and the + closed forms of `outer/check_ledger.py`, with SHA-256 fingerprints of 11 rebuilt rationals; +- evaluates all 133 condition keys at four points with an AST-whitelisted exact evaluator (no `eval`); +- checks every classification rule (for example, COVERED keys must hold at the point, OBSOLETE items must cite a + superseding file:line, and FALSE_AT_POINT items must record `load_bearing: false` with true operative keys); +- recomputes 49 ledger strict checks and 7 rejecting-control rows from transcribed formulas; +- runs 14 negative controls: flipped classes, a corrupted β, undefined variables, forbidden AST nodes and others. + +The audited sources live in the open PR, not on main. To re-check them, export that head into a new empty directory: + +```sh +git fetch origin pull/2044/head +mkdir /new/empty/dir +git archive 322949a53488d64023fedb89a6774927707e57ba research/capped-fusion-t74-k554 | tar -x -C /new/empty/dir +python3 -I -B research/t74-side-condition-coverage-audit/verify.py --source-root /new/empty/dir +python3 -I -B research/t74-side-condition-coverage-audit/review_items.py --source-root /new/empty/dir +``` + +This re-hashes all 32 files in `SOURCES-T74.json` (blob id and SHA-256). It locates each of the 554 quotes within +±2 lines, checks the rebuilt parameters and the 49 checks against `LEDGER.json`, and runs two more source controls. + +## Scope and limits + +- **Checked:** the *written* side conditions and their exact truth at the final point. **Not checked:** the arguments + themselves, including: + - the accretive Toeplitz circuit theorem; + - the SHALLOW-TOEPLITZ recursion; + - the union-schedule correctness; + - the locality/halo constructions; + - the Trudgian prime step; + - the all-size compiler, hosting and precision/tape interfaces; + - the T74 supplier admission. + + The 58 NON_EXPONENT items list such obligations without assessing them. +- **Extraction coverage.** Extraction is exhaustive over the 28 notes, but it is a reading by language models, + cross-checked by de-duplication, two verifiers per flag and a sample. A condition that no extractor recognised is not + covered. Code-only assumptions in `check_*.py`, and the evidence archives under `vendor/pr1673/.../evidence/`, were + not extracted. +- **Pinned head.** The result is pinned to the #2044 head. Later heads, and siblings such as #2161 and #2180 that + change only ε-slack arithmetic, would need their final point re-substituted. `POINTS.json` makes this a small + change. +- **Provenance of the inventory.** `INVENTORY.json` was produced in a local session from the extractor and matcher + outputs, which are not retained. Every entry carries its file, line and verbatim quote so it can be re-checked + against the pinned sources. + +## Open next questions + +1. **Record the HALO branch at the final point.** *Why it matters:* the stack relies on HALO-THEOREM's explicit + metadata branch, but the only written instantiation (§6) assumes the obsolete PR1673 regime. *First step:* add a + short note to the family's outer stating the K₀ instantiation, either as a ledger row or by citing + `microbox_face_corrections`. *Blocked by:* author or maintainer action on the pending stack. +2. **Tie the p¹⁰ umbrella to `THETA_POWER`.** *Why it matters:* it is the only side condition found that is true but + unchecked, and a future change to the θ power would not be caught. *First step:* a ledger strict check deriving + the umbrella exponent from `THETA_POWER`. *Blocked by:* nothing. +3. **Extend coverage to code-only assumptions.** *Why it matters:* this audit reads prose only. *First step:* the + same inventory method applied to the assertions in `outer/check_*.py` and `run_outer.py`. *Blocked by:* nothing; it + is about the same size as this audit. + +## Relation to concurrent work (philippeVV) + +Philippe Van Velzen (philippeVV) published a closely related audit of the same #2044 head while this one was running. +It appears as PR comments and fork commits, which `scripts/find_overlap.py` does not index, so this audit's 00:30 UTC +overlap check missed it. That work has priority on the points below, and this package independently corroborates +them: + +- **Broad-shift reconciliation** ([#1897 comment, 2026-10-14 19:40 UTC](https://github.com/CrocSwap/integer-mult-bounds/pull/1897); + fork `philippeVV/integer-mult-bounds@a3c40a6f`, `research/t74-broad-shift-reconcile/`). It shows the disabled + `or True` line is in a branch the proof does not use and corrects GAUGEFREE :31/:84 (the linear leftover is + 3b₀θB, not 2b₀θB). This package reaches the same conclusions by a different method: an exact Laurent certificate + with no sympy (`review_items.py`). +- **Outer-layer audit and PR1673 fusion cost census** (#2044 comments, 2026-10-15 00:04–00:46 UTC; fork commits + `e6bc8393`, `bc4ed55b`, `76af2562`, `d1e01310`): + - an exact knockout showing the lift rests on PR1673's removal of the per-axis Vd row; + - every PR1673 cost term evaluated at the #2044 point; + - the same HALO `K₀² = O(B)` finding; + - the support-local H-call and layout-contract follow-ups; + - the CRLF, stage-E and self-authenticated cache issues. + +This package does **not** repeat the knockout, the cost census, the H-call analysis or the release-path issues. +It adds: + +- **Scope:** a machine-checkable inventory of *all* written side conditions in all 28 notes (554 items, 133 + exact keys), not only the PR1673 cost terms. It covers the outer, PR1758 and PR1786 notes as well, and maps each + condition to the 62 ledger strict checks. +- **Exact re-check:** a registered standard-library verifier that re-evaluates every classification exactly at + four points, with negative controls and source-pinned quotes. +- **Findings not in those comments:** + - the false margin claim at `FINE-PADDING-COMPOSITION.md:37`; + - the false aside at `FINE-PADDING-COMPOSITION.md:38`; + - the PR1786 p¹⁰ umbrella that no ledger row ties to `THETA_POWER`; + - the unused ζ; + - the offline fine-θ precision term that no ledger row encodes; + - the second vacuous `or True` at `outer/struct_check.py:130`; + - the stale ξ digits; + - the per-record g² sweep table. + +## Credit and provenance + +- **Audited work:** + - Vlado Vojdanovski (PR1673, capped phase-cell fusion and its audits); + - Jeremy Kothe and the PR1758/PR1839/PR2044 contributors (gauge-free interiors, union schedule, structured + boundary, final ledger); + - Chafik Boukhalfa (PR1786, fine-prime padding); + - Rohan Arun and M6LI (PR1876, PR1897: the broad-shift identity and the discovery of the `or True` guard); + - LeverRank (`sched_review.py`). +- **Overlap:** the nearest prior audit is `research/pr1786-fine-prime-transfer-audit`, which covers the fine-prime + lemmas only and explicitly excludes the union schedule and layout. The concurrent philippeVV audit is described + above. +- **Assignment and claim:** base `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, priority revision 4. Sprint track 60–74 + (adversarial audit), OS assignment seed 72. No pinned coordination issue existed, so the claim was recorded locally. +- **AI assistance:** prepared for Sagar Thakrar with substantial AI assistance (Claude Code, Anthropic). Subagents did + the extraction, ledger re-evaluation, matching, adversarial verification, sampled re-check and verifier + construction. The main session checked GAUGEFREE Lemmas 2.1, 3.1–3.3 and Theorem 4.1(a)(b) by hand and reran every + command. Apache-2.0. diff --git a/research/t74-side-condition-coverage-audit/REVIEW-ITEMS.md b/research/t74-side-condition-coverage-audit/REVIEW-ITEMS.md new file mode 100644 index 0000000000..b468c2bb8e --- /dev/null +++ b/research/t74-side-condition-coverage-audit/REVIEW-ITEMS.md @@ -0,0 +1,124 @@ +# Review items on PR #2044: the disabled `or True` assertion and the per-record g^2 sweep + +Scope: two review items on `research/capped-fusion-t74-k554` at PR #2044 head `322949a5`. All paths below are +relative to that directory. This is a read-only audit. It is not a proof of the T74 claim and not a multiplication theorem. +Replay: `python3 -I -B research/t74-side-condition-coverage-audit/review_items.py`. This default mode is self-contained. +It runs 88 exact checks in about 6 s, using only the standard library. Add `--source-root DIR` to also re-check the file-level facts below. +That mode checks SHA-256 and git-blob pins, exact line text, `ast` parses and 108 file:line anchors within +-2 lines. With it, the run has 122 checks. +Credit: the disabled assertion was found by PR1897 (M6LI). The corrected s = -dl/lam bracket is PR1876's supplemental identity (Rohan Arun). + +## Item 1: `outer/check_gaugefree.py:23` (`... or True`) + +**What line 23 asserts.** Line 20 sets `claim = -b0*[bracket]`, the general-s Lemma 2.1 identity, and line 21 asserts it live. +Line 22 sets `sub = expand(claim.subs(s, -dl/lam))`. Line 23 then asserts +`sub == -b0*[(1-lam)x^2 - lam(1-lam)y^2 + dl^2 + dl^2/lam + 0*x - 2dl(1-lam)y - 2dl^2*0]` and appends `or True`. +The `ast` scan confirms that the test is vacuous. + +**Correct bracket.** At s = -dl/lam, (x - lam y + dl)^2 - lam(x - y - s)^2 equals +**(1-lam)x^2 - lam(1-lam)y^2 + dl^2 - dl^2/lam + 2dl(1-lam)y**. +- The constant term dl^2 - dl^2/lam equals -theta dl^2 when lam = 1/(1+theta). +- The x-linear term is 0. + +This is certified by an exact Laurent-polynomial expansion over Q. It is also checked at 1500 random rational points with seed 20441876. + +**The two sign errors in the disabled expression:** +- **Constant term:** it has `+dl^2/lam`; the correct term is `-dl^2/lam`. +- **y-linear term:** it has `-2dl(1-lam)y`; the correct term is `+2dl(1-lam)y`. + +The residual `sub - (-b0)D` equals `2 b0 dl^2/lam - 4 b0 dl(1-lam) y`, which is not zero, so without `or True` the assertion would fail. +The quadratic and x-linear parts agree, so these are the only two differences. + +Three mutation controls are rejected at every random point: the full disabled bracket, a constant-only flip and a y-linear-only flip. +With `--source-root`, line 23's bracket is parsed from the file by `ast`. It equals the transcription above and differs from the certified bracket. + +**Nothing depends on it.** +- The proof never uses s = -dl/lam: + - The broad block uses s = -delta(1-theta) (`outer/GAUGEFREE-INTERIORS.md:31`), checked live at `check_gaugefree.py:44-46`. + - The narrow block uses s = -beta0/rho (`GAUGEFREE-INTERIORS.md:37`), checked live at `check_gaugefree.py:35`. + - s = -delta/lambda appears only in the parenthetical at `GAUGEFREE-INTERIORS.md:32`. That parenthetical makes two claims: an x-coefficient of 0, and a y-coefficient of 2 b0 delta(1-lambda) in the b0-bracket convention. +- **Live line 25 certifies both claims** with the correct sign. The parsed expected slope `(-b0)(-2lam(dl-dl/lam))` equals -b0 times the certified y-coefficient, so line 25 contradicts the disabled line 23. +- **The constant term is never used.** It is an absorbed scalar. +- **`outer/check_ledger.py` does not touch the identity.** + - It imports only fractions, decimal, pathlib, math, hashlib, json, sys and gmpy2. + - It never names `check_gaugefree` and has no `dl`, `b0`, `claim` or `sub` symbols. + - Its only `lam` is the supplier lambda = 1-(q_+a)/2 at line 126. +- **`outer/run_outer.py:19` is the only reference** to the script in any `*.py`. It runs `check_gaugefree.py` as a pass/fail subprocess with stdout discarded, and the script writes nothing. + +PR1876's supplemental `check_broad_shift.py` is not in #2044, so the release still ships the wrong disabled expression. +Fix: make line 23 live with the correct bracket, or delete it. + +**Minor gaps.** +- **Stage B covers only s = -dl/lam.** The "600 exact rational mixed-difference checks" (`GAUGEFREE-INTERIORS.md:30`) all use `S=-D/L` (`check_gaugefree.py:53`). Separability for every s follows from live line 21, which has no x*y term (certified). +- **The narrow kernel completion is not asserted.** k(h) = e^{a be0^2/rho} e^{-gamma(h-s)^2} appears only as an OUT string (`check_gaugefree.py:36`). It is certified here, together with 1-2|s| >= theta/rho >= theta/2. +- **Constants only.** `GAUGEFREE-INTERIORS.md:31` gives the summed linear range as "<= 2 b0 theta B (total)", and `:84` gives "<= 2 b0 theta B'". The exact sum is 3 b0 theta B/(1+theta), which is larger than 2 b0 theta B for theta < 1/2. Each axis separately is <= 2 b0 theta B, and Section 5 (`:92`) uses 4 b0 theta B, so the exponents are unaffected. +- **A second vacuous assertion.** `outer/struct_check.py:130` also ends in `or True`; it is the only other one in `outer/*.py`. It belongs to the structured boundary, which does not enter kappa (`outer/FINE-PADDING-COMPOSITION.md:13`). +- **Undocumented dependencies.** `check_gaugefree.py:12` imports sympy, mpmath and numpy. `README.md:16` mentions only SymPy, and only for the vendored PR1673 checks. + +Also certified exactly: +- Lemma 2.1 (general s, no cross term); +- Lemma 2.2; +- the normalisation identity; +- the old-weights identities (`check_gaugefree.py:40`, `:42`); +- the shrunk-shift coefficients 4 dl theta/(1+theta) and -2 dl theta/(1+theta), together with |cx| <= 2theta, |cy| <= theta and 1-2|s| >= theta. + +## Item 2: per-record g^2 / g|F| / 2beta / g-fold charges at the final point + +Final point: rebuilt from `POINTS.json` (11 SHA-256 fingerprints). +- eps = 1-2r, beta = 1-6r, r = r0 = 1e-30010, zeta = 1e-30012. +- xi = eps(1+q) - 3/32 + r = 0.9079... +- kappa = floor(eps q 10^30046)/10^30046 - 1e-30022, so 0 < eps q - kappa < 1e-30020. + +A condition holds iff its value is > 0. Values are exact; the closed forms are checked by `review_items.py`. +`V/` = `vendor/pr1673/capped-phase-fusion/`. `FPP` = `vendor/pr1786/FINE-PRIME-PADDING.md`. + +**Superseded (false at the final point; a rejecting control in `outer/LEDGER.json` fires for each).** + +| id | charge | file:line | condition | value | control | +|---|---|---|---|---|---| +| U1 | old union row (g-fold scan of U, g^2 per window) | V/PHASE-LAYOUT-AUDIT.md:4,86,103-108,229; V/CAPPED-SIGNOFF.md:30-31; V/CAPPED-INTERIORS.md:38,41; V/OUTER-AUDIT.md:86; V/MATRIX-LAYOUT-SIGNOFF.md:19-21,31-33; outer/UNION-SCHEDULE.md:17-18,98,110,122; outer/RECT-BOUNDARY.md:65; outer/FINE-PADDING-COMPOSITION.md:12; outer/check_ledger.py:139 | 1-(eps+beta+1/2-xi)-kappa | -19/32+7r+(eps q-kappa) = -0.5937 | `old_g_factor_union_row` | +| U2 | g\|F\| <= g^2 tag work charged to one record | outer/GAUGEFREE-INTERIORS.md:17,103-104,110; outer/UNION-SCHEDULE.md:103,124; outer/RECT-BOUNDARY.md:66; outer/FINE-PADDING-COMPOSITION.md:12; FPP:266; outer/check_ledger.py:193,220; verify_release.py:112 | 1-2beta | -1+12r | `old_union_tag_2beta` | +| U7 | full-key sort surcharge (V/CAPPED-SIGNOFF.md:49 "remains below the target" is stale) | V/CAPPED-SIGNOFF.md:49-50; V/OUTER-AUDIT.md:87; V/CAPPED-INTERIORS.md:43,64; V/MATRIX-LAYOUT-SIGNOFF.md:34-35 | (xi+1/2-eps)-(beta+1-eps)-kappa | -19/32+5r+(eps q-kappa) = -0.5937 | `full_key_sort` | +| U11 | g a d precision bits | V/TENSOR-COMPILER.md:25-27; V/LOG-A-PHASE-SCHUR-AUDIT.md:112; V/SUPPLIER-SUPPORT-AUDIT.md:109 (superseded per V/CAPPED-GAUGE-AUDIT.md:67,107); outer/check_ledger.py:190 | 1-(beta+eps) | -1+8r | `full_cell_gauge` | +| U12 | linear gauge g a B | V/CAPPED-GAUGE-AUDIT.md:99-107; V/CAPPED-INTERIORS.md:68; outer/GAUGEFREE-INTERIORS.md:17 | 1-xi-r-beta | -0.9079 | `old_linear_guard` | +| U13 | GAUGEFREE bold guard beta+2xi-eps <= 1-r-zeta | outer/GAUGEFREE-INTERIORS.md:17,93-95,101; superseded per :1 and outer/FINE-PADDING-COMPOSITION.md:46 | 1-(2xi-eps)-r-zeta-beta | -0.8159 | `old_theta_chirp_guard` | + +**Active and encoded (true; each is equal to a `check_ledger.py` strict-check row, recomputed and compared with LEDGER.json).** + +| id | charge | file:line | condition | value | ledger row | +|---|---|---|---|---|---| +| U3 | tag O(g) per visit; header O(g log L) | outer/UNION-SCHEDULE.md:11,46-47,58,103; outer/GAUGEFREE-INTERIORS.md:110; FPP:264-266; V/PHASE-LAYOUT-AUDIT.md:119-120 | 1-beta | 6r | `union_tag_work_per_visit_fits_record`, `union_header_fits_record` | +| U4 | new union row (no g^2, no per-axis scan) | outer/UNION-SCHEDULE.md:94-98 | xi+1/2-eps-kappa | 13/32+r+(eps q-kappa) = 0.4063 | `sparse_union_movement_above_kappa` | +| U5 | membership g h^2 per record | V/PHASE-LAYOUT-AUDIT.md:123-130,177; V/CAPPED-SIGNOFF.md:44-47; V/CAPPED-INTERIORS.md:64; V/MATRIX-LAYOUT-SIGNOFF.md:20 | 1-beta-2(1-eps) | 2r | `membership_arithmetic_fits_record` | +| U6 | group key g h | V/CAPPED-SIGNOFF.md:48; V/OUTER-AUDIT.md:62,76; V/HALO-THEOREM.md:31,150 | 1-(beta+1-eps) | 4r | `group_key_fits_record` | +| U8b | halo metadata K0^2 within the p^2 face allowance | V/HALO-THEOREM.md:44,150-157; V/CAPPED-INTERIORS.md:43 | 2-2(beta+1-eps) | 8r | 2 x `group_below_dimension` | +| U8c | halo metadata term (explicit-metadata branch) | V/HALO-THEOREM.md:44 | 1-kappa-[(eps-beta)+(beta+48-128)+2(beta+1-eps)-1] | 79+10r-kappa | covered by the face row | +| U9 | g sequential passes on halo copies (g^2 A/L) | V/OUTER-AUDIT.md:58-62,89; V/PHASE-LAYOUT-AUDIT.md:213-219; V/HALO-THEOREM.md:185-186; V/CAPPED-INTERIORS.md:43; V/CAPPED-SIGNOFF.md:63-65; FPP:230-233; outer/check_ledger.py:137 | 1-(eps+beta+48-128+2)-kappa | 77+8r-kappa | `microbox_face_corrections_above_kappa` | +| U10 | support router O(g polylog p) | V/CAPPED-SIGNOFF.md:52-57; V/CAPPED-INTERIORS.md:66; V/SUPPLIER-SUPPORT-AUDIT.md:121; V/SUPPORT-ADVERSARIAL-AUDIT.md:189-200,227; outer/UNION-SCHEDULE.md:123 | 1-beta | 6r | `support_router_span` | +| U14 | fine chirp g a theta B^2 | outer/GAUGEFREE-INTERIORS.md:1,41,94; FPP:163-169 | 1-(2xi-2)-r-beta (also with -zeta, outer/GAUGEFREE-INTERIORS.md:95 form) | 0.1841 | `group_gauge_power_slack` | +| U15 | linear leftover dominated by the chirp | outer/GAUGEFREE-INTERIORS.md:96,101 | xi > 0 (via xi-1/2) | 0.4079 | `cap_above_band` | + +The §6.1 row names `shift_leftover_linear_dominated_by_chirp` and `shift_gap_theta_polynomial` are absent from LEDGER.json. +Their conditions are implied by `cap_above_band` and `theta_positive_polynomial_power`. + +**False option (must not be the branch used).** +- U8a: `V/HALO-THEOREM.md:31-32` offers "Require `K0^2=O(B)`", where K0^2 = g^2 h^2. The condition 1-2(beta+1-eps) evaluates to -1+8r, so it is **false**. +- The package should state that it uses the explicit-metadata alternative at `V/HALO-THEOREM.md:44` (U8b/U8c), which holds because eps > beta. + +**Non-exponent obligations** (listed, not evaluated): +- the head-travel bookkeeping of UNION-SCHEDULE §2.3 (`outer/UNION-SCHEDULE.md:85`) and the requirement that every visit moves the full record; +- `outer/GAUGEFREE-INTERIORS.md:96` still says "a d = o(p)". Under fine theta the offline term a/theta ~ a p^2 is moved to an amortized P_setup (`FPP:159-187`); +- Theorem 4.1 rests on SHALLOW-TOEPLITZ (`outer/GAUGEFREE-INTERIORS.md:72`); +- the dependencies of `check_gaugefree.py` (see Item 1). + +**Stale numeric text** (anchors checked): `outer/STRUCTURED-BOUNDARY.md:97`, `V/CAPPED-SIGNOFF.md:63-65,75-78`, `V/PHASE-LAYOUT-AUDIT.md:128-130` (assumes g = p^(1-epsilon-r-zeta) and epsilon > 2/3), `V/SUPPORT-ADVERSARIAL-AUDIT.md:189-227`, `outer/RECT-BOUNDARY.md:65-66`, `outer/GAUGEFREE-INTERIORS.md:105,117` (labelled pkg8-era). + +**Conclusion.** No active step charges g^2 or g|F| against one p-bit record. +- **Union schedule.** The worst-case total tag work g|F| <= g^2 per record does exceed one record (2beta > 1). It is paid per visit instead: each visit moves the record at Theta(p), so only beta < 1 is required, and that is encoded. +- **Halo/core-face path.** The g^2-type charges that remain active sit on this path, which carries sparse volume p^(beta-80); they fit with a margin of about 77. +- **One false condition to fix.** The HALO "K0^2 = O(B)" option is false at the final point and should be disowned in the text. + +**Prior and concurrent work.** Philippe Van Velzen (philippeVV) posted an independent exact broad-shift reconciliation +for this head before this audit. It is a #1897 comment from 2026-10-14 19:40 UTC (fork +`philippeVV/integer-mult-bounds@a3c40a6f`, `research/t74-broad-shift-reconcile/`), and it reaches the same Item 1 +conclusion, including the 3b₀θB correction to :31/:84. His #2044 comments of 2026-10-15 also report the HALO +`K₀² = O(B)` issue. 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"package": "research/capped-fusion-t74-k554", + "paths_relative_to": "research/capped-fusion-t74-k554", + "pr": 2044, + "repository": "CrocSwap/integer-mult-bounds", + "schema": "t74-side-condition-coverage-audit/sources/v1" +} diff --git a/research/t74-side-condition-coverage-audit/SOURCES.json b/research/t74-side-condition-coverage-audit/SOURCES.json new file mode 100644 index 0000000000..392737aa2a --- /dev/null +++ b/research/t74-side-condition-coverage-audit/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "e8870e5917057d59b730eb14721a778639eca050", + "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7" + } + ] +} diff --git a/research/t74-side-condition-coverage-audit/TASK.json b/research/t74-side-condition-coverage-audit/TASK.json new file mode 100644 index 0000000000..c96d56bc62 --- /dev/null +++ b/research/t74-side-condition-coverage-audit/TASK.json @@ -0,0 +1,72 @@ +{ + "schema_version": 1, + "task_id": "uniform-transfer-audit", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "uniform-transfer-audit", + "question": "Can one exact all-size/compiler, precision, hosting or restoration implication be proved or falsified?", + "starting_points": [ + "certificates/selected-result.json", + "docs/audit.md" + ], + "methods": [ + "Prove one missing implication with explicit quantified hypotheses.", + "Find an exact counterexample at the claimed interface boundary." + ], + "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the selected review scope and choose one exact all-size or precision implication.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write its quantified inputs and conclusion; find a missing hypothesis or construct a minimal exact adversarial instance.", + "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.", + "allowed_variations": [ + "Choose one tape, precision, hosting or restoration lemma." + ], + "scope_change_triggers": [ + "Replacing a quantified obligation with another finite smoke test." + ], + "overlap_terms": [ + "uniform transfer", + "all-size", + "precision" + ] + }, + "scope_status": "changed", + "actual_scope": "Coverage audit of the stated asymptotic side conditions (exponent inequalities, o(p)/fits-the-record/eventually claims) of the pending T74 capped-fusion outer at PR #2044 head 322949a5: are all conditions written in the 28 inherited notes (PR1673 capped phase-cell fusion, PR1758 gauge-free interiors and union schedule, PR1786 fine-prime padding, structured/Strassen boundary) encoded as ledger strict checks and true at the family's final parameter point (eps = 1-2e-30010, beta = 1-6e-30010)? Plus the open review items on the disabled `or True` guard and per-record g^2 charges.", + "scope_change_reason": "The card asks to prove or falsify one implication. Maintainer reviews of #1673/#1758/#1876/#1928 leave the shared parameter-inequality interfaces and the `or True` / g^2-per-record items open, and the family's final point moved beta and eps to within 1e-30010 of 1, far from the point at which PR1673's notes were written. A complete exact inventory of the written side conditions at that point decides whether any stated condition silently fails there. It does not prove the arguments themselves.", + "bottleneck_link": "Audit of the leading pending frontier candidate (claimed kappa 0.0016797549..., +0.43% over the selected record). A false load-bearing side condition would invalidate the stack; none was found in the written text, which narrows the remaining review to the non-exponent obligations listed in the inventory.", + "budget_minutes": 180, + "stop_rule": "All 28 md notes of the #2044 outer/vendor tree extracted once by four independent extractors; every one of the 554 extracted conditions classified and exactly evaluated at four points; every flagged item double-checked (refute + re-derive); a seeded random sample of 28 non-flagged classifications independently re-translated.", + "outcome": "completed", + "evidence": "verify.py: PASS_T74_SIDE_CONDITION_COVERAGE conditions=554 keys=133 covered=262 auto_true=53 obsolete=113 stale_text_only=64 non_exponent=58 false_at_point=3 uncovered_true=1 ambiguous=0 load_bearing_false=0 (default mode, 14 negative controls; --source-root mode re-hashes 32 #2044 files, locates all 554 quotes, equates rebuilt parameters and 49 ledger checks with LEDGER.json, 16 controls). Two independent verdicts per flagged item and a seeded 28-item sampled re-check (27 agree; the one disagreement corrected) are recorded in INVENTORY.json.", + "author": "Sagar Thakrar", + "ai_assistance": "Substantial AI assistance: Claude Code (Anthropic, Claude Opus 5.5) orchestrated subagents for extraction, ledger re-evaluation, matching, adversarial verification, sampled re-checks and package construction; the main session spot-checked the key lemmas by hand and reran the verifier.", + "open_questions": [ + { + "question": "Which HALO-THEOREM branch does the final T74 chain use, and where is it recorded?", + "why_it_matters": "The written section 6 instantiation (K0^2 = o(p)) assumes PR1673's obsolete regime and is false at the final point; the explicit metadata branch holds but is unrecorded.", + "first_step": "Add a short instantiation note or ledger row for the K0 metadata term citing microbox_face_corrections.", + "blocked_by": "Author or maintainer action on the pending stack." + }, + { + "question": "Can the PR1786 p^10 umbrella exponent be tied to THETA_POWER by a ledger strict check?", + "why_it_matters": "It is the only true-but-unchecked side condition found; a future change of the theta power would not be caught.", + "first_step": "Derive the umbrella exponent from THETA_POWER and add a strict check.", + "blocked_by": "Nothing." + }, + { + "question": "Do the code-only assertions in outer/check_*.py and run_outer.py carry side conditions absent from the prose?", + "why_it_matters": "This audit inventories prose only.", + "first_step": "Apply the same inventory and exact-evaluation method to the checker assertions.", + "blocked_by": "Nothing; similar size to this audit." + } + ] +} diff --git a/research/t74-side-condition-coverage-audit/VERIFY.json b/research/t74-side-condition-coverage-audit/VERIFY.json new file mode 100644 index 0000000000..0c8667cc36 --- /dev/null +++ b/research/t74-side-condition-coverage-audit/VERIFY.json @@ -0,0 +1,29 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "rebuild the exact #2044 final point from one pinned rational and closed forms; evaluate 133 condition keys at 4 points; classification consistency for 554 conditions; recompute 49 ledger strict checks and 7 rejecting-control rows; 14 negative controls" + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/review_items.py" + ], + "timeout_seconds": 300, + "checks": "exact Laurent-polynomial certificates for the disabled `or True` bracket (two sign errors), Lemmas 2.1/2.2, normalisation and shrunk-shift coefficients with mutation controls; final-point exponent checks for every per-record g^2 sweep item" + } + ] +} diff --git a/research/t74-side-condition-coverage-audit/review_items.py b/research/t74-side-condition-coverage-audit/review_items.py new file mode 100644 index 0000000000..11d91c42b7 --- /dev/null +++ b/research/t74-side-condition-coverage-audit/review_items.py @@ -0,0 +1,798 @@ +#!/usr/bin/env python3 +"""Exact checks for two review items on PR #2044 (research/capped-fusion-t74-k554, head 322949a5). + +Item 1: the disabled `... or True` assertion at outer/check_gaugefree.py:23 (the s = -dl/lam bracket), + Lemma 2.1 / Lemma 2.2 of outer/GAUGEFREE-INTERIORS.md, the narrow-kernel completion, the + normalisation identity and the shrunk-shift coefficients. Exact Laurent-polynomial expansion + over Q (a certificate), independent Fraction evaluation at random rational points (fixed + seed) and three mutation controls that must be rejected. +Item 2: every per-record g^2 / g|F| / 2beta / g-fold charge found in the sweep, evaluated exactly at + the final point rebuilt from this package's POINTS.json (same evaluator and SHA-256 + fingerprints as verify.py), with expected truth values, independent ledger-row formulas + transcribed from outer/check_ledger.py, and rejecting controls. + +Default mode (no arguments) is self-contained: it reads only POINTS.json next to this file. +--source-root DIR (an export containing research/capped-fusion-t74-k554 at #2044 head) adds file +level checks: SHA-256/git-blob pins, exact text of the cited check_gaugefree.py lines, the line-23 +bracket parsed by `ast` and compared with the certified bracket, the vacuous-assert scan of outer/*.py, +check_ledger.py / run_outer.py dependence facts, every cited file:line anchor (+-2 lines), and the +LEDGER.json values of every ledger row and rejecting control used below. + +Standard library only; Python 3.10+; run as `python3 -I -B review_items.py [--source-root DIR]`. +-O is refused (exit 2). No network, no subprocess, no git. Writes nothing. +""" +import sys + +if sys.flags.optimize: + sys.stderr.write('review_items.py refuses to run under -O/-OO\n') + sys.exit(2) + +import argparse +import ast +import hashlib +import json +import random +import time +from decimal import Decimal, localcontext +from fractions import Fraction as Fr +from pathlib import Path + +if hasattr(sys, 'set_int_max_str_digits'): + sys.set_int_max_str_digits(0) + +HERE = Path(__file__).resolve().parent +PKG_REL = 'research/capped-fusion-t74-k554' +HEAD = '322949a53488d64023fedb89a6774927707e57ba' +RANDOM_SEED = 20441876 +NPTS = 1500 + +RESULTS = [] # (section, name, ok, info) +SECTION = ['?'] + + +def check(name, ok, info=''): + RESULTS.append((SECTION[0], name, bool(ok), info)) + + +# ================================================================ exact Laurent polynomials over Q +VARS = ('x', 'y', 'dl', 'lam', 's', 'b0', 'th', 'rho', 'a', 'be0', 'ti', 'h', 'i', 'j', 'c', 'u') +IDX = {v: k for k, v in enumerate(VARS)} +NV = len(VARS) +ZERO = (0,) * NV + + +class P: + """Laurent polynomial {exponent tuple (ints, may be negative): Fraction}.""" + __slots__ = ('t',) + + def __init__(self, t=None): + self.t = {k: Fr(v) for k, v in (t or {}).items() if v != 0} + + @staticmethod + def lift(o): + return o if isinstance(o, P) else P({ZERO: Fr(o)}) + + def __add__(self, o): + o = P.lift(o) + r = dict(self.t) + for k, v in o.t.items(): + r[k] = r.get(k, 0) + v + return P(r) + __radd__ = __add__ + + def __neg__(self): + return P({k: -v for k, v in self.t.items()}) + + def __sub__(self, o): + return self + (-P.lift(o)) + + def __rsub__(self, o): + return P.lift(o) - self + + def __mul__(self, o): + o = P.lift(o) + r = {} + for k1, v1 in self.t.items(): + for k2, v2 in o.t.items(): + k = tuple(p + q for p, q in zip(k1, k2)) + r[k] = r.get(k, 0) + v1 * v2 + return P(r) + __rmul__ = __mul__ + + def __pow__(self, n): + if not (isinstance(n, int) and n >= 0): + raise ValueError('only non-negative integer powers') + r = P.lift(1) + for _ in range(n): + r = r * self + return r + + def inv(self): + if len(self.t) != 1: + raise ValueError('only monomials are invertible here') + (k, v), = self.t.items() + return P({tuple(-e for e in k): 1 / v}) + + def __truediv__(self, o): + return self * P.lift(o).inv() + + def __rtruediv__(self, o): + return P.lift(o) * self.inv() + + def iszero(self): + return not self.t + + def __eq__(self, o): + return (self - P.lift(o)).iszero() + + __hash__ = None + + def subs(self, name, val): + val = P.lift(val) + ix = IDX[name] + r = P() + for k, v in self.t.items(): + e = k[ix] + k0 = list(k) + k0[ix] = 0 + f = val ** e if e >= 0 else val.inv() ** (-e) + r = r + P({tuple(k0): v}) * f + return r + + def coeff(self, name, power): + ix = IDX[name] + return P({tuple(0 if n == ix else e for n, e in enumerate(k)): v + for k, v in self.t.items() if k[ix] == power}) + + def __repr__(self): + parts = [] + for k, v in sorted(self.t.items()): + mon = '*'.join(VARS[n] + ('^%d' % e if e != 1 else '') for n, e in enumerate(k) if e) + parts.append(str(v) + ('*' + mon if mon else '')) + return ' + '.join(parts) or '0' + + +V = {n: P({tuple(1 if m == IDX[n] else 0 for m in range(NV)): 1}) for n in VARS} +x, y, dl, lam, s, b0, th, rho, a, be0, ti, h, i_, j_, c_, u = (V[n] for n in VARS) + +# Lemma 2.1, general s (the identity asserted live at check_gaugefree.py:21; claim = -b0 * RHS at :20) +LHS = (x - lam * y + dl) ** 2 - lam * (x - y - s) ** 2 +RHS = ((1 - lam) * x ** 2 - lam * (1 - lam) * y ** 2 + dl ** 2 - lam * s ** 2 + + 2 * (dl + lam * s) * x - 2 * lam * (dl + s) * y) +# s = -dl/lam: the correct bracket (PR1876, Rohan Arun) and the expression disabled at check_gaugefree.py:23 +CORRECT = (1 - lam) * x ** 2 - lam * (1 - lam) * y ** 2 + dl ** 2 - dl ** 2 / lam + 2 * dl * (1 - lam) * y +DISABLED = ((1 - lam) * x ** 2 - lam * (1 - lam) * y ** 2 + dl ** 2 + dl ** 2 / lam + 0 * x + - 2 * dl * (1 - lam) * y - 2 * dl ** 2 * 0) + + +def item1_symbolic(): + SECTION[0] = 'item1-symbolic' + check('Lemma 2.1 identity for general s', LHS == RHS) + check('Lemma 2.1 has no x*y cross term (separable for every s)', LHS.coeff('x', 1).coeff('y', 1).iszero()) + sub_b = RHS.subs('s', -dl / lam) + check('s=-dl/lam: RHS.subs == (1-lam)x^2-lam(1-lam)y^2+dl^2-dl^2/lam+2dl(1-lam)y', sub_b == CORRECT) + check('s=-dl/lam: LHS.subs == same bracket', LHS.subs('s', -dl / lam) == CORRECT) + diff = CORRECT - DISABLED + check('disabled bracket differs from the correct one', not diff.iszero(), repr(diff)) + check('correct - disabled == -2 dl^2/lam + 4 dl (1-lam) y', diff == -2 * dl ** 2 / lam + 4 * dl * (1 - lam) * y) + cc, cd = CORRECT.coeff('x', 0).coeff('y', 0), DISABLED.coeff('x', 0).coeff('y', 0) + lc, ld = CORRECT.coeff('x', 0).coeff('y', 1), DISABLED.coeff('x', 0).coeff('y', 1) + check('sign error 1, constant: correct dl^2-dl^2/lam, disabled dl^2+dl^2/lam', + cc == dl ** 2 - dl ** 2 / lam and cd == dl ** 2 + dl ** 2 / lam) + check('constant at lam=1/rho, rho=1+th equals -th dl^2', cc.subs('lam', rho.inv()).subs('rho', 1 + th) == -th * dl ** 2) + check('sign error 2, y-linear: correct +2dl(1-lam), disabled -2dl(1-lam)', + lc == 2 * dl * (1 - lam) and ld == -2 * dl * (1 - lam)) + check('x-linear and all quadratic parts agree (only the two terms above differ)', + CORRECT.coeff('x', 1) == DISABLED.coeff('x', 1) and CORRECT.coeff('x', 2) == DISABLED.coeff('x', 2) + and CORRECT.coeff('x', 0).coeff('y', 2) == DISABLED.coeff('x', 0).coeff('y', 2) + and CORRECT.coeff('x', 1).iszero()) + resid = (-b0) * sub_b - (-b0) * DISABLED + check('line-23 residual sub-(-b0)D == 2 b0 dl^2/lam - 4 b0 dl (1-lam) y (non-zero: fails without `or True`)', + resid == 2 * b0 * dl ** 2 / lam - 4 * b0 * dl * (1 - lam) * y and not resid.iszero()) + sub = (-b0) * sub_b + lin_x, lin_y = sub.coeff('x', 1).coeff('y', 0), sub.coeff('y', 1).coeff('x', 0) + check('live line 25: d/dx sub at 0 == 0', lin_x.iszero()) + check('live line 25: d/dy sub at 0 == (-b0)(-2lam(dl-dl/lam)) == -2 b0 dl (1-lam)', + lin_y == (-b0) * (-2 * lam * (dl - dl / lam)) and lin_y == -2 * b0 * dl * (1 - lam)) + check('line 25 confirms the correct y-sign, contradicts the disabled one', lin_y == (-b0) * lc and not lin_y == (-b0) * ld) + # shrunk shift s = -dl(1-th), lam = 1/(1+th): Laurent in rho with th = rho-1 (check_gaugefree.py:44-46) + shr = RHS.subs('s', -dl * (1 - th)).subs('lam', rho.inv()).subs('th', rho - 1) + cx, cy = shr.coeff('x', 1).coeff('y', 0), shr.coeff('y', 1).coeff('x', 0) + check('shrunk shift x-linear == 4 dl th/(1+th)', cx * rho == 4 * dl * (rho - 1)) + check('shrunk shift y-linear == -2 dl th/(1+th)', cy * rho == -2 * dl * (rho - 1)) + check('shrunk shift: x-lin = 2(dl+lam s), y-lin = -2 lam th dl (note line 31 form)', + cx == 2 * dl * (1 - rho.inv() * (1 - (rho - 1))) and cy == -2 * rho.inv() * (rho - 1) * dl) + check('shrunk shift quadratic: x^2 coeff th/(1+th), y^2 coeff -th/(1+th)^2', + shr.coeff('x', 2).coeff('y', 0) * rho == rho - 1 and shr.coeff('y', 2).coeff('x', 0) * rho * rho == -(rho - 1)) + # Lemma 2.2 (narrow, check_gaugefree.py:35) and the kernel completion that is only an OUT string (:36) + bi, bj = be0 + th * ti, be0 + th * (ti + h) + EN = ((1 + th) * h + bi) ** 2 - bj ** 2 + check('Lemma 2.2: (rho h+beta_i)^2-beta_{i+h}^2 == (1+2th)h^2 + 2 beta_i h', EN == (1 + 2 * th) * h ** 2 + 2 * bi * h) + check('Lemma 2.2: -a EN == -a rho h^2 - 2 a be0 h + a th (ti^2 - tj^2)', + (-a) * EN == -a * (1 + th) * h ** 2 - 2 * a * be0 * h + a * th * (ti ** 2 - (ti + h) ** 2)) + sN, gam = -be0 / rho, a * rho + check('kernel completion: -a rho h^2 - 2a be0 h == a be0^2/rho - gamma (h-s)^2, s=-be0/rho', + -a * rho * h ** 2 - 2 * a * be0 * h == a * be0 ** 2 / rho - gam * (h - sN) ** 2) + check('normalisation: gamma s^2 - gamma (u-s)^2 == -gamma u^2 + 2 gamma s u', + gam * s ** 2 - gam * (u - s) ** 2 == -gam * u ** 2 + 2 * gam * s * u) + bI, bJ = th * i_ - c_, th * j_ - c_ + check('old-weights log ratio (check_gaugefree.py:40)', + ((-a) * (Fr(1, 4) - bI ** 2) / th) - ((-a) * (Fr(1, 4) - bJ ** 2) / th) == a * (i_ - j_) * (bI + bJ)) + check('old weights = -a/(4th) + a th (i - c/th)^2 (OUT string :42)', + (-a) * (Fr(1, 4) - bI ** 2) / th == -a / (4 * th) + a * th * (i_ - c_ / th) ** 2) + + +def item1_random(): + SECTION[0] = 'item1-random' + rng = random.Random(RANDOM_SEED) + + def rq(lo, hi): + den = rng.choice([1, 2, 3, 7, 10, 97, 1000, 65537, 10 ** 9 + 7]) + return Fr(rng.randint(int(lo * den), int(hi * den)), den) + + keys = ('general', 'correct', 'disabled_rejected', 'const_flip_rejected', 'lin_flip_rejected', 'shrunk', 'bounds', + 'lemma22', 'kernel') + cnt = dict.fromkeys(keys, 0) + for _ in range(NPTS): + X, Y, D, Sv = rq(-50, 50), rq(-50, 50), rq(-Fr(1, 2), Fr(1, 2)), rq(-3, 3) + T = rq(Fr(1, 10 ** 6), Fr(1, 2)) or Fr(1, 3) + L = 1 / (1 + T) + lhs = (X - L * Y + D) ** 2 - L * (X - Y - Sv) ** 2 + rhs = (1 - L) * X ** 2 - L * (1 - L) * Y ** 2 + D ** 2 - L * Sv ** 2 + 2 * (D + L * Sv) * X - 2 * L * (D + Sv) * Y + cnt['general'] += lhs == rhs + S1 = -D / L + e1 = (X - L * Y + D) ** 2 - L * (X - Y - S1) ** 2 + q0 = (1 - L) * X ** 2 - L * (1 - L) * Y ** 2 + D ** 2 + corr = q0 - D ** 2 / L + 2 * D * (1 - L) * Y + dis = q0 + D ** 2 / L - 2 * D * (1 - L) * Y # mutation control 1: line 23 as written + m_const = q0 + D ** 2 / L + 2 * D * (1 - L) * Y # mutation control 2: constant sign only + m_lin = q0 - D ** 2 / L - 2 * D * (1 - L) * Y # mutation control 3: y-linear sign only + cnt['correct'] += e1 == corr + cnt['disabled_rejected'] += e1 != dis or D == 0 + cnt['const_flip_rejected'] += e1 != m_const or D == 0 + cnt['lin_flip_rejected'] += e1 != m_lin or D == 0 or Y == 0 + S2 = -D * (1 - T) + + def f(XX, YY): + return (XX - L * YY + D) ** 2 - L * (XX - YY - S2) ** 2 + cxv, cyv = (f(1, 0) - f(-1, 0)) / 2, (f(0, 1) - f(0, -1)) / 2 # exact for quadratics + cnt['shrunk'] += cxv == 4 * D * T / (1 + T) and cyv == -2 * D * T / (1 + T) + ok = abs(cxv) <= 2 * T and abs(cyv) <= T and abs(S2) <= (1 - T) / 2 and 1 - 2 * abs(S2) >= T + cnt['bounds'] += ok and (1 - L) <= T and L * (1 - L) <= T + A, BE, TI, HH = rq(1, 60), rq(-Fr(1, 2), Fr(1, 2)), rq(-500, 500), rq(-40, 40) + R = 1 + T + l22 = (R * HH + BE + T * TI) ** 2 - (BE + T * (TI + HH)) ** 2 + cnt['lemma22'] += (l22 == (1 + 2 * T) * HH ** 2 + 2 * (BE + T * TI) * HH + and -A * l22 == -A * R * HH ** 2 - 2 * A * BE * HH + A * T * (TI ** 2 - (TI + HH) ** 2)) + sn = -BE / R + cnt['kernel'] += (-A * R * HH ** 2 - 2 * A * BE * HH == A * BE ** 2 / R - A * R * (HH - sn) ** 2 + and 1 - 2 * abs(sn) >= T / R >= T / 2) + labels = {'general': 'general-s identity', 'correct': 'correct s=-dl/lam bracket', + 'disabled_rejected': 'mutation control 1 (disabled line-23 bracket) rejected', + 'const_flip_rejected': 'mutation control 2 (constant sign only) rejected', + 'lin_flip_rejected': 'mutation control 3 (y-linear sign only) rejected', + 'shrunk': 'shrunk-shift coefficients 4dl th/(1+th), -2dl th/(1+th)', + 'bounds': '|cx|<=2th, |cy|<=th, |s|<=(1-th)/2, 1-2|s|>=th, quadratic coeffs <= th', + 'lemma22': 'Lemma 2.2 identities', 'kernel': 'kernel completion and 1-2|s| >= th/rho >= th/2'} + for k in keys: + check('random (seed %d, %d points): %s' % (RANDOM_SEED, NPTS, labels[k]), cnt[k] == NPTS, '%d/%d' % (cnt[k], NPTS)) + T0 = Fr(1, 100) + L0 = 1 / (1 + T0) + check('s=-dl/lam at dl=1/2 has |s| = 1/2 + th/2 > 1/2 (why the note shrinks the shift)', abs(-Fr(1, 2) / L0) == Fr(1, 2) + T0 / 2) + tot = 4 * Fr(1, 2) * T0 / (1 + T0) + 2 * Fr(1, 2) * T0 / (1 + T0) + check('note line 31 "(total) <= 2 b0 th B" understates the summed range 3th/(1+th) (th=1/100)', + tot == 3 * T0 / (1 + T0) and tot > 2 * T0, str(tot)) + check('...but each axis is <= 2 b0 th B and the Section-5 bound 4 b0 th B holds', tot <= 4 * T0 + and 4 * Fr(1, 2) * T0 / (1 + T0) <= 2 * T0) + + +# ================================================================ final point (same rebuild as verify.py) +_BINOPS = (ast.Add, ast.Sub, ast.Mult, ast.Div, ast.Pow) +_UNOPS = (ast.UAdd, ast.USub) + + +def _parse(src): + if not isinstance(src, str) or len(src) > 4000: + raise ValueError('expression must be a short string') + tree = ast.parse(src, mode='eval') + for node in ast.walk(tree): + if isinstance(node, (ast.Expression, ast.Load, ast.Name) + _BINOPS + _UNOPS): + continue + if isinstance(node, ast.BinOp) and isinstance(node.op, _BINOPS): + continue + if isinstance(node, ast.UnaryOp) and isinstance(node.op, _UNOPS): + continue + if isinstance(node, ast.Constant) and type(node.value) is int: + continue + raise ValueError('%s not allowed in %r' % (type(node).__name__, src)) + return tree + + +def _ev(node, env, vocab): + if isinstance(node, ast.Expression): + return _ev(node.body, env, vocab) + if isinstance(node, ast.Constant): + return Fr(node.value) + if isinstance(node, ast.Name): + if node.id not in vocab or node.id not in env: + raise ValueError('unknown/undefined name %s' % node.id) + return env[node.id] + if isinstance(node, ast.UnaryOp): + v = _ev(node.operand, env, vocab) + return -v if isinstance(node.op, ast.USub) else v + l, r = _ev(node.left, env, vocab), _ev(node.right, env, vocab) + if isinstance(node.op, ast.Add): + return l + r + if isinstance(node.op, ast.Sub): + return l - r + if isinstance(node.op, ast.Mult): + return l * r + if isinstance(node.op, ast.Div): + if r == 0: + raise ValueError('division by zero') + return l / r + if r.denominator != 1 or abs(r.numerator) > 100000 or (l == 0 and r < 0): + raise ValueError('bad power') + return l ** int(r) + + +def seval(src, env, vocab): + return Fr(_ev(_parse(src), env, vocab)) + + +def exact_literal(sv): + body = sv[1:] if sv[:1] == '-' else sv + num, _, den = body.partition('/') + ip, _, fp = num.partition('.') + if not (ip.isdigit() and (fp == '' or fp.isdigit()) and (den == '' or den.isdigit())): + raise ValueError('bad exact literal %r' % sv[:40]) + return Fr(sv) + + +def build_point(pt, vocab): + env = {} + for name, val in pt['definitions']: + if name not in vocab or name in env: + raise ValueError('bad/duplicate definition %s' % name) + if isinstance(val, str): + env[name] = seval(val, env, vocab) + elif isinstance(val, dict) and set(val) == {'exact'}: + env[name] = exact_literal(val['exact']) + elif isinstance(val, dict) and set(val) == {'floor_grid', 'grid', 'minus'}: + g = seval(val['grid'], env, vocab) + if g.denominator != 1 or g <= 0: + raise ValueError('grid must be a positive integer') + xv = seval(val['floor_grid'], env, vocab) + env[name] = Fr((xv * g).__floor__(), g.numerator) - seval(val['minus'], env, vocab) + else: + raise ValueError('bad definition form for %s' % name) + return env + + +def frac_sha(v): + return hashlib.sha256(str(Fr(v)).encode()).hexdigest() + + +R0_EXP = 30010 + + +def show(v): + """Display: integer part plus an exact offset in units of 1e-30010, else 4 correctly rounded significant digits.""" + unit = Fr(1, 10 ** R0_EXP) + n = round(v) + off = (v - n) / unit + if off.denominator == 1 and abs(off) < 10 ** 6: + o = int(off) + if n == 0: + return '%de-%d' % (o, R0_EXP) if o else '0' + return '%d%s' % (n, ('%+de-%d' % (o, R0_EXP)) if o else '') + with localcontext() as cx: # correctly rounded (half-even) to 4 significant digits from the exact value + cx.prec = 4 + return str(+(Decimal(v.numerator) / Decimal(v.denominator))) + + +# Item 2 records. group: superseded | active | false-option. cond: exact condition (> 0 means it holds). +# ledger: (strict-check row, formula transcribed from outer/check_ledger.py ledger()). +# control: (control flag, control row, formula from check_ledger.py) -- must be <= 0. +HITS = [ + dict(id='U1', group='superseded', what='old union row: g-fold scan of U, g^2 per window', + cond='1-(eps+beta+1/2-xi)-kappa', holds=False, show='-0.5937', exact='-19/32+7*r+(eps*q-kappa)', + control=('old_g_factor_union_row', 'old_g_factor_union_row_above_kappa', '(1-eps-beta-1/2+xi)-kappa')), + dict(id='U2', group='superseded', what='g|F| <= g^2 tag work charged to one record', cond='1-2*beta', holds=False, + show='-1+12e-30010', exact='-1+12*r', + control=('old_union_tag_2beta', 'old_union_tag_2beta', '1-2*beta')), + dict(id='U3', group='active', what='tag O(g) per visit; header O(g log L)', cond='1-beta', holds=True, show='6e-30010', + exact='6*r', ledger=[('union_tag_work_per_visit_fits_record', '1-beta'), ('union_header_fits_record', '1-beta')]), + dict(id='U4', group='active', what='new union row', cond='xi+1/2-eps-kappa', holds=True, show='0.4063', exact='13/32+r+(eps*q-kappa)', + ledger=[('sparse_union_movement_above_kappa', '(xi+1/2-eps)-kappa')]), + dict(id='U5', group='active', what='membership g h^2 per record', cond='1-beta-2*(1-eps)', holds=True, show='2e-30010', exact='2*r', + ledger=[('membership_arithmetic_fits_record', '1-beta-2*(1-eps)')]), + dict(id='U6', group='active', what='group key g h', cond='1-(beta+1-eps)', holds=True, show='4e-30010', exact='4*r', + ledger=[('group_key_fits_record', '1-(beta+1-eps)')]), + dict(id='U7', group='superseded', what='full-key sort surcharge (not used)', cond='(xi+1/2-eps)-(beta+1-eps)-kappa', + holds=False, show='-0.5937', exact='-19/32+5*r+(eps*q-kappa)', + control=('full_key_sort', 'unnecessary_full_key_sort_above_kappa', '((xi+1/2-eps)-(beta+1-eps))-kappa')), + dict(id='U8a', group='false-option', what='HALO option K0^2 = g^2 h^2 = O(B)', cond='1-2*(beta+1-eps)', holds=False, + show='-1+8e-30010', exact='-1+8*r'), + dict(id='U8b', group='active', what='halo metadata K0^2 within the p^2 face allowance', cond='2-2*(beta+1-eps)', + holds=True, show='8e-30010', exact='8*r', ledger=[('group_below_dimension', '(eps-beta)')], ledger_scale=2), + dict(id='U8c', group='active', what='halo metadata term (HALO-THEOREM:44 branch)', + cond='1-kappa-((eps-beta)+(beta+halo-core)+2*(beta+1-eps)-1)', holds=True, show='79.00', exact='79+10*r-kappa'), + dict(id='U9', group='active', what='g sequential passes on halo copies', cond='1-(eps+beta+halo-core+2)-kappa', + holds=True, show='77.00', exact='77+8*r-kappa', + ledger=[('microbox_face_corrections_above_kappa', '(1-(eps+beta+halo-core+2))-kappa')]), + dict(id='U10', group='active', what='support router O(g polylog p)', cond='1-beta', holds=True, show='6e-30010', exact='6*r', + ledger=[('support_router_span', '1-beta')]), + dict(id='U11', group='superseded', what='g a d precision bits', cond='1-(beta+eps)', holds=False, show='-1+8e-30010', exact='-1+8*r', + control=('full_cell_gauge', 'unrecentered_group_gauge', '1-TH-r-beta')), + dict(id='U12', group='superseded', what='linear gauge g a B', cond='1-xi-r-beta', holds=False, show='-0.9079', + control=('old_linear_guard', 'old_linear_guard', '1-xi-r-beta')), + dict(id='U13', group='superseded', what='GAUGEFREE bold guard beta+2xi-eps <= 1-r-zeta', + cond='1-(2*xi-eps)-r-zeta-beta', holds=False, show='-0.8159', + control=('old_theta_chirp_guard', 'old_theta_chirp_guard', '1-(2*xi-eps)-r-beta')), + dict(id='U14', group='active', what='fine chirp g a theta B^2 (ledger form)', cond='1-(2*xi-TH)-r-beta', holds=True, + show='0.1841', ledger=[('group_gauge_power_slack', '1-(2*xi-TH)-r-beta')]), + dict(id='U14b', group='active', what='fine chirp guard with zeta (GAUGEFREE:95 form)', cond='1-(2*xi-TH)-r-zeta-beta', + holds=True, show='0.1841'), + dict(id='U15', group='active', what='linear leftover dominated by chirp (xi > 0)', cond='xi-1/2', holds=True, + show='0.4079', ledger=[('cap_above_band', 'xi-1/2')]), +] + + +def item2(points_path): + SECTION[0] = 'item2-final-point' + PTS = json.loads(Path(points_path).read_text()) + vocab = set(PTS['vocabulary']) + fin = PTS['points']['final'] + Pt = build_point(fin, vocab) + fps = fin['fingerprints'] + bad = [n for n, hsh in fps.items() if frac_sha(Pt[n]) != hsh] + check('final point rebuilt from POINTS.json: %d SHA-256 fingerprints match' % len(fps), not bad and len(fps) >= 11, + 'mismatch: %s' % bad if bad else '') + r = Fr(1, 10 ** R0_EXP) + check('eps = 1-2e-30010, beta = 1-6e-30010, r0 = 1e-30010, zeta = 1e-30012', + Pt['eps'] == 1 - 2 * r and Pt['beta'] == 1 - 6 * r and Pt['r'] == r and Pt['zeta'] == r / 100) + check('xi = eps(1+q) - 3/32 + r0 (Strassen c = 3/32), theta power 2, halo 48, core 128', + Pt['xi'] == Pt['eps'] * (1 + Pt['q']) - Fr(3, 32) + r and Pt['c'] == Fr(3, 32) + and (Pt['TH'], Pt['halo'], Pt['core']) == (2, 48, 128)) + vals = {} + for H in HITS: + v = seval(H['cond'], Pt, vocab) + vals[H['id']] = v + check('%s %s: %s %s at the final point (= %s)' % (H['id'], H['what'], H['cond'], '> 0' if H['holds'] else '<= 0', show(v)), + (v > 0) == H['holds'] and show(v) == H['show'], 'value %s, expected display %s' % (show(v), H['show'])) + if 'exact' in H: + check('%s: exact closed form %s' % (H['id'], H['exact']), seval(H['exact'], Pt, vocab) == v) + for row, form in H.get('ledger', ()): + lv = seval(form, Pt, vocab) + check('%s: ledger row %s (%s) agrees with the sweep condition and is > 0' % (H['id'], row, form), + lv * H.get('ledger_scale', 1) == v and lv > 0) + if 'control' in H: + flag, row, form = H['control'] + cv = seval(form, Pt, vocab) + check('%s: rejecting control %s.%s (%s) is <= 0' % (H['id'], flag, row, form), cv <= 0, show(cv)) + groups = {g: [H['id'] for H in HITS if H['group'] == g] for g in ('superseded', 'active', 'false-option')} + check('every active record holds and every superseded/false-option record fails', + all(vals[i] > 0 for i in groups['active']) and all(vals[i] <= 0 for i in groups['superseded'] + groups['false-option'])) + check('every superseded record has a rejecting control', all('control' in H for H in HITS if H['group'] == 'superseded')) + return Pt, vocab + + +# ================================================================ --source-root +EXTRA_PINS = { # files not in SOURCES-T74.json; from `git show pr/2044:research/capped-fusion-t74-k554/` + 'outer/run_outer.py': ('cb46c44c70d05597bda3375517ed4f5a3f93294d30aff356c5ad5fe6d03b5aeb', + '8a9434e5b5d877c0b26976b379180cf5d9508d7e'), + 'outer/struct_check.py': ('f13c6a166394549a25b6e727c4a43c0a34ae270c9498a9697683d63e0e5f9971', + 'a541e93ae70acfa62998cfb833ef35d0a5900a41'), + 'verify_release.py': ('bd8e9373edfe1062e7d6e8c2dc962fd4b5a4d05272f283ed85be3401a8d9463c', + '65b4cdef75eb3f713e58b7081f25b630492e22f3'), +} +CG_LINES = { # outer/check_gaugefree.py at #2044 head, exact text + 20: 'claim=-b0*((1-lam)*x**2-lam*(1-lam)*y**2+dl**2-lam*s**2+2*(dl+lam*s)*x-2*lam*(dl+s)*y)', + 21: 'assert sp.simplify(res-claim)==0', + 22: 'sub=sp.expand(claim.subs(s,-dl/lam))', + 23: 'assert sp.simplify(sub-(-b0)*((1-lam)*x**2-lam*(1-lam)*y**2+dl**2+dl**2/lam+0*x-2*dl*(1-lam)*y- 2*dl**2*0))==0 or True', + 24: 'lin_x=sp.simplify(sp.diff(sub,x).subs({x:0,y:0})); lin_y=sp.simplify(sp.diff(sub,y).subs({x:0,y:0}))', + 25: 'assert sp.simplify(lin_x)==0 and sp.simplify(lin_y-(-b0)*(-2*lam*(dl-dl/lam)))==0', + 35: 'assert sp.simplify(sp.expand(EN-EKer-EChirp))==0', + 40: 'assert sp.simplify((-a*(sp.Rational(1,4)-b_i**2)/th)-(-a*(sp.Rational(1,4)-b_j**2)/th)-a*(i_-j_)*(b_i+b_j))==0', + 44: 'shr=sp.expand(claim.subs(s,-dl*(1-th)).subs(lam,1/(1+th)))', + 45: 'cx=sp.simplify(sp.diff(shr,x).subs({x:0,y:0})/(-b0)); cy=sp.simplify(sp.diff(shr,y).subs({x:0,y:0})/(-b0))', + 46: 'assert sp.simplify(cx-2*dl*2*th/(1+th))==0 and sp.simplify(cy-(-2*dl*th/(1+th)))==0', + 53: ' B0=rnd(Fr(1,50),2); L=1/(1+rnd(Fr(1,200),Fr(1,10))); D=rnd(-Fr(1,2),Fr(1,2)); S=-D/L', +} +RUN_OUTER_19 = "subprocess.run([sys.executable, '-B', str(P / 'outer/check_gaugefree.py')], check=True, stdout=subprocess.DEVNULL)" +STRUCT_130 = (' assert all(x == 0 for r in S[(p, q)] for x in r) or True # far blocks are tiny/zero or ' + 'ignored by the tridiagonal solve below (checked via full solve)') + +VP = 'vendor/pr1673/capped-phase-fusion/' +PLA, CS, CI, OA, MLS, HT = (VP + n for n in ('PHASE-LAYOUT-AUDIT.md', 'CAPPED-SIGNOFF.md', 'CAPPED-INTERIORS.md', + 'OUTER-AUDIT.md', 'MATRIX-LAYOUT-SIGNOFF.md', 'HALO-THEOREM.md')) +US, GF, RB, FPC = 'outer/UNION-SCHEDULE.md', 'outer/GAUGEFREE-INTERIORS.md', 'outer/RECT-BOUNDARY.md', 'outer/FINE-PADDING-COMPOSITION.md' +FPP, CL = 'vendor/pr1786/FINE-PRIME-PADDING.md', 'outer/check_ledger.py' +# (tag, file, lines, anchor): the anchor must occur within +-2 lines of the cited line (range). +CITES = [ + ('I1', GF, '30', '600 exact rational mixed-difference checks'), + ('I1', GF, '31', 'Choose **s = -delta (1-theta)**'), + ('I1', GF, '31', 'logarithmic range <= 2 b0 theta B (total)'), + ('I1', GF, '32', '(With s = -delta/lambda the linear terms vanish in x and are 2 b0 delta (1-lambda) in y'), + ('I1', GF, '37', '**gamma = a rho, s = -beta0/rho**'), + ('I1', GF, '84', "the linear leftover is <= 2 b0 theta B'"), + ('I1', GF, '92', '4 b0 theta B (linear leftover)'), + ('I1', 'outer/check_gaugefree.py', '36', 'exp(a be0^2/rho) exp(-gamma (h-s)^2)'), + ('I1', 'outer/check_gaugefree.py', '42', 'log w_i = const + a th (i - c/th)^2'), + ('I1', FPC, '13', 'the unproved stability claim of STRUCTURED-BOUNDARY.md is dispensable'), + ('U1', PLA, '4', 'V g^2 W polylog(p)/d'), ('U1', PLA, '86', 'Scan U once'), + ('U1', PLA, '103-108', 'O(V [g^2 mu + g mu polylog p])'), ('U1', PLA, '229', 'union movement:'), + ('U1', CS, '30-31', 'per group: O(V g^2 W/B polylog p)'), + ('U1', CI, '38', 'sparse union movement | `epsilon+beta+1/2-b`'), + ('U1', CI, '41', 'For the sparse union, its fraction within a group'), + ('U1', OA, '86', 'sparse union, basic movement'), + ('U1', MLS, '19-21', 'epsilon + beta + 1/2 - xi < 1-kappa'), ('U1', MLS, '31-33', 'It scans U once per axis'), + ('U1', US, '17-18', 'the g-fold scan of U is removed'), ('U1', US, '98', 'Old audit row: `eps + beta + 1/2 - xi`'), + ('U1', US, '110', 'reinstating the old row `1 - eps - beta - 1/2 + xi`'), + ('U1', US, '122', 'the old row 1-eps-beta-1/2+xi = -0.5921 fails'), + ('U1', RB, '65', 'the old g-factor union row would be -0.341'), + ('U1', FPC, '12', 'control `old_g_factor_union_row`'), + ('U1', CL, '139', "margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi"), + ('U2', GF, '17', 'union tag check 1-2 beta > 0'), ('U2', GF, '103-104', '`union_tag_work_fits_record` (1 - 2 beta)'), + ('U2', GF, '110', 'o(p) because 2 beta < 1'), ('U2', US, '103', 'a record is visited at most |F| <= g times'), + ('U2', US, '124', 'union tag work per visit 1-beta = 6e-30010'), ('U2', RB, '66', 'union tag work 1 - 2 beta = 0.158'), + ('U2', FPC, '12', '2 beta < 1 fails (control `old_union_tag_2beta`)'), + ('U2', FPP, '266', 'not the obsolete 2 beta<1'), ('U2', CL, '193', "checks['old_union_tag_2beta']=1-2*beta"), + ('U2', CL, '220', "('old_union_tag_2beta',{'old_tag':True})"), ('U2', 'verify_release.py', '112', 'the old 2*beta tag test'), + ('U3', US, '11', 'a header of O(g log L) bits'), ('U3', US, '46-47', 'tag work per visit is O(g) bit operations'), + ('U3', US, '58', 'O(g log L) bits per comparison'), ('U3', US, '103', 'tag work is at most O(g) per visit'), + ('U3', GF, '110', 'is per visit'), ('U3', FPP, '264-266', 'O(g log L)-bit headers are absorbed'), + ('U3', PLA, '119-120', 'O(g log L) bits'), + ('U4', US, '94-98', 'no factor g^2 and no per-axis scan of U'), + ('U5', PLA, '123-130', '`O(g h^2 polylog p)` per record'), + ('U5', PLA, '177', 'The g membership tests cost O(g h^2 polylog p)=o(p) per p-bit record.'), + ('U5', CS, '44-47', 'is O(g h^2 polylog p), h=Theta(p/d)'), + ('U5', CI, '64', 'per-record phase metadata exponent `beta+2(1-epsilon)`'), ('U5', MLS, '20', 'beta + 2(1-epsilon) < 1'), + ('U6', CS, '48', 'coordinate headers use O(g log p) bits'), ('U6', OA, '62', 'group-key length `K=O(g p/d)`'), + ('U6', OA, '76', '`h_K=beta+1-epsilon`'), ('U6', HT, '31', '`K0=O(g(h+b)+log g)=O(gh)`'), + ('U6', HT, '150', 'These are K0=O(gh) bits.'), + ('U7', CS, '49-50', 'sparse sort with O(gh)-bit keys remains below the target'), + ('U7', OA, '87', 'sparse union, conservative key surcharge'), + ('U7', CI, '43', 'full active-group key surcharge adds only `beta+1-epsilon`'), + ('U7', CI, '64', 'optional full-key surcharge leaves it below 0.781'), + ('U7', MLS, '34-35', 'correctly rejected in the new ledger'), + ('U8a', HT, '31-32', 'Require `K0^2=O(B)` or retain the explicit extra metadata term below.'), + ('U8b', HT, '44', 'O((gL/N)V K0^2/B)'), ('U8b', HT, '150-157', 'O(K0^2) safe metadata work per copy'), + ('U8b', CI, '43', 'Sparse core-face corrections'), + ('U9', OA, '58-62', '`O(V (g A/L) g [1+w^2/d] polylog p)` per group'), ('U9', OA, '89', '`epsilon+beta+3-8+2`'), + ('U9', PLA, '213-219', 'g sequential such passes on this sparse volume'), + ('U9', HT, '185-186', 'Summing over rectangles costs `O(M g polylog p)`'), + ('U9', CS, '63-65', 'O(g p^-5), now about p^-4.9064'), ('U9', FPP, '230-233', '`epsilon+beta+48-128+2`'), + ('U9', CL, '137', "'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2)"), + ('U10', CS, '52-57', 'router uses O(g polylog p) moved/control bits'), + ('U10', CI, '66', 'even though gK is larger than one axis width'), + ('U10', VP + 'SUPPLIER-SUPPORT-AUDIT.md', '121', 'gK=O(p^beta log p) bit positions'), + ('U10', VP + 'SUPPORT-ADVERSARIAL-AUDIT.md', '189-200', 'k=O(gK)=O(p^.093 log p)'), + ('U10', VP + 'SUPPORT-ADVERSARIAL-AUDIT.md', '227', 'gG/ell_axis=Theta(p^.091 log p)'), + ('U10', US, '123', 'support router span 1-beta = 6e-30010 > 0'), + ('U11', VP + 'TENSOR-COMPILER.md', '25-27', 'g a d+g polylog(p)=O(p)'), + ('U11', VP + 'LOG-A-PHASE-SCHUR-AUDIT.md', '112', 'exp(O(g*a*d))'), + ('U11', VP + 'SUPPLIER-SUPPORT-AUDIT.md', '109', 'O(g) extra magnitude and error allowance'), + ('U11', VP + 'CAPPED-GAUGE-AUDIT.md', '67', '**ad cost occurs in offline coefficient accuracy**'), + ('U11', VP + 'CAPPED-GAUGE-AUDIT.md', '107', 'no remaining full-cell term g*a*d may be charged'), + ('U11', CL, '190', "checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta"), + ('U12', VP + 'CAPPED-GAUGE-AUDIT.md', '99-107', '`O(g a Bcap + g polylog p)`'), + ('U12', CI, '68', '`1-b-r-beta=zeta>0`'), ('U12', GF, '17', 'ledger guard beta + xi <= 1-r-zeta'), + ('U13', GF, '17', 'guard beta + 2 xi - eps <= 1-r-zeta'), ('U13', GF, '93-95', '**beta + 2 xi - eps <= 1 - r - zeta**'), + ('U13', GF, '101', '**1 - (2 xi - eps) - r - beta**'), + ('U13', FPC, '46', 'superseded by `beta + 2 xi - 2 < 1` at fine theta'), + ('U14', GF, '1', 'the chirp range becomes O(a B^2/p^2)'), ('U14', GF, '41', 'e^{O(g (a theta B^2 + polylog))}'), + ('U14', GF, '94', 'O(g a theta B^2)'), ('U14', FPP, '163-169', 'beta + 2 xi - 2 < 1'), + ('U15', GF, '96', 'is dominated by the chirp (exponent beta + 2 xi - eps) since xi > 0'), + ('U15', GF, '101', '`shift_leftover_linear_dominated_by_chirp`: xi > 0'), + ('NX', US, '85', 'the total is O(p (log g + log L + 1) * sum_r |S_r|)'), + ('NX', GF, '96', 'The offline accuracy term a d = o(p) is unchanged.'), + ('NX', FPP, '159-187', 'Setup arithmetic at P_setup is separate from these records.'), + ('NX', GF, '72', 'Identical to SHALLOW-TOEPLITZ sec. 4, 5, 6, 9'), + ('NX', 'README.md', '16', 'SymPy 1.14.0 is only needed for the vendored PR1673 evidence checks'), + ('NX', 'outer/check_gaugefree.py', '12', 'import sympy as sp, mpmath as mp, numpy as np'), + ('STALE', 'outer/STRUCTURED-BOUNDARY.md', '97', 'beta = 0.99665, union tag work per visit 1 - beta = 0.00335'), + ('STALE', CS, '75-78', 'membership descriptor power = .0966144543147439.'), + ('STALE', PLA, '128-130', '`g=p^(1-epsilon-r-zeta)` and epsilon>2/3'), + ('STALE', GF, '105', 'pkg8-era package, superseded by outer/FINE-PADDING-COMPOSITION.md'), + ('STALE', GF, '117', '(pkg8-era, superseded by the fine-padding point beta = 1 - 6e-100)'), +] + + +def _to_poly(node): + """ast of a sympy-free arithmetic expression over x,y,lam,dl,b0 (ints, + - * / **int) -> P.""" + if isinstance(node, ast.Name) and node.id in ('x', 'y', 'lam', 'dl', 'b0', 's'): + return V[node.id] + if isinstance(node, ast.Constant) and type(node.value) is int: + return P.lift(node.value) + if isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub): + return -_to_poly(node.operand) + if isinstance(node, ast.BinOp): + lt = _to_poly(node.left) + if isinstance(node.op, ast.Pow): + if not (isinstance(node.right, ast.Constant) and type(node.right.value) is int): + raise ValueError('non-integer power') + return lt ** node.right.value + rt = _to_poly(node.right) + op = type(node.op) + if op is ast.Add: + return lt + rt + if op is ast.Sub: + return lt - rt + if op is ast.Mult: + return lt * rt + if op is ast.Div: + return lt / rt + raise ValueError('unsupported node %s' % type(node).__name__) + + +def _vacuous(node): + t = node.test + return (isinstance(t, ast.BoolOp) and isinstance(t.op, ast.Or) + and any(isinstance(v, ast.Constant) and v.value is True for v in t.values)) + + +def source_root(dirarg, Pt, vocab): + SECTION[0] = 'source-root' + d = Path(dirarg) + root = d / PKG_REL if (d / PKG_REL / 'outer').is_dir() else d + if not (root / 'outer' / 'check_gaugefree.py').is_file(): + check('--source-root contains %s' % PKG_REL, False, str(d)) + return + SRC = json.loads((HERE / 'SOURCES-T74.json').read_text()) + check('SOURCES-T74.json pins PR #2044 head %s' % HEAD[:8], SRC.get('head_sha') == HEAD and SRC.get('package') == PKG_REL) + pins = {k: (m['sha256'], m['git_blob']) for k, m in SRC['files'].items()} + for k, v in EXTRA_PINS.items(): + pins.setdefault(k, v) + used = sorted({c[1] for c in CITES} | {'outer/check_gaugefree.py', 'outer/run_outer.py', 'outer/struct_check.py', + CL, 'outer/LEDGER.json'}) + text = {} + nbad = [] + for rel in used: + p = root / rel + if rel not in pins or not p.is_file(): + nbad.append(rel + ' (unpinned or missing)') + continue + data = p.read_bytes() + if (hashlib.sha256(data).hexdigest(), hashlib.sha1(b'blob %d\0' % len(data) + data).hexdigest()) != pins[rel]: + nbad.append(rel) + if rel != 'outer/LEDGER.json': + text[rel] = data.decode('utf-8').splitlines() + check('%d used source files match their SHA-256 + git-blob pins (%d from SOURCES-T74.json, %d in-file)' + % (len(used), len([r for r in used if r in SRC['files']]), len([r for r in used if r not in SRC['files']])), + not nbad, '; '.join(nbad)) + cg = text.get('outer/check_gaugefree.py', []) + wrong = [n for n, t in CG_LINES.items() if len(cg) < n or cg[n - 1] != t] + check('check_gaugefree.py lines %s have the exact pinned text' % sorted(CG_LINES), not wrong, str(wrong)) + tree = ast.parse('\n'.join(cg)) + asserts = {nd.lineno: _vacuous(nd) for nd in ast.walk(tree) if isinstance(nd, ast.Assert)} + check('check_gaugefree.py:23 is an assert whose test is `... or True` (vacuous)', asserts.get(23) is True) + check('check_gaugefree.py:21,25,35,40,46 are live (non-vacuous) asserts', all(asserts.get(n) is False for n in (21, 25, 35, 40, 46))) + try: + a23 = next(nd for nd in ast.walk(tree) if isinstance(nd, ast.Assert) and nd.lineno == 23) + call = a23.test.values[0].left # sp.simplify(sub - (-b0)*(BRACKET)) + br = _to_poly(call.args[0].right.right) + claim = _to_poly(next(nd for nd in ast.walk(tree) if isinstance(nd, ast.Assign) and nd.lineno == 20).value) + a25 = next(nd for nd in ast.walk(tree) if isinstance(nd, ast.Assert) and nd.lineno == 25) + lin_y_expected = _to_poly(a25.test.values[1].left.args[0].right) + ok_parse = True + except (StopIteration, AttributeError, IndexError, ValueError) as e: + ok_parse = False + check('parse check_gaugefree.py lines 20/23/25 with ast', False, repr(e)) + if ok_parse: + check('line 20 claim (parsed) == -b0 * Lemma 2.1 bracket', claim == -b0 * RHS) + check('line 23 bracket (parsed) == DISABLED transcription and != certified bracket', br == DISABLED and not br == CORRECT) + check('line 25 expected y-slope (parsed) == -b0 * (y-linear of certified bracket)', + lin_y_expected == -b0 * CORRECT.coeff('x', 0).coeff('y', 1)) + vac = [] + for py in sorted((root / 'outer').glob('*.py')): + try: + tr = ast.parse(py.read_text(encoding='utf-8')) + except SyntaxError: + vac.append('outer/%s:unparsable' % py.name) + continue + vac += ['outer/%s:%d' % (py.name, nd.lineno) for nd in ast.walk(tr) if isinstance(nd, ast.Assert) and _vacuous(nd)] + check('vacuous asserts in outer/*.py are exactly check_gaugefree.py:23 and struct_check.py:130', + vac == ['outer/check_gaugefree.py:23', 'outer/struct_check.py:130'], str(vac)) + sc_l = text.get('outer/struct_check.py', []) + check('struct_check.py:130 exact text (second vacuous `or True`)', len(sc_l) >= 130 and sc_l[129] == STRUCT_130) + cl_tree = ast.parse('\n'.join(text.get(CL, []))) + mods = set() + for nd in ast.walk(cl_tree): + if isinstance(nd, ast.Import): + mods.update(al.name for al in nd.names) + elif isinstance(nd, ast.ImportFrom): + mods.add(nd.module) + names = {nd.id for nd in ast.walk(cl_tree) if isinstance(nd, ast.Name)} + strs = [nd.value for nd in ast.walk(cl_tree) if isinstance(nd, ast.Constant) and isinstance(nd.value, str)] + lam_assign = [(nd.lineno, ast.dump(nd.value)) for nd in ast.walk(cl_tree) if isinstance(nd, ast.Assign) + and any(isinstance(tg, ast.Name) and tg.id == 'lam' for tg in nd.targets)] + check('check_ledger.py imports only fractions/decimal/pathlib/math/hashlib/json/sys/gmpy2 (no sympy, subprocess, ' + 'runpy, importlib)', mods == {'fractions', 'decimal', 'pathlib', 'math', 'hashlib', 'json', 'sys', 'gmpy2'}, str(mods)) + check('check_ledger.py never names check_gaugefree / GAUGEFREE-INTERIORS and never calls exec/eval/__import__', + not any('check_gaugefree' in sv or 'GAUGEFREE' in sv for sv in strs) + and not names & {'exec', 'eval', '__import__', 'compile', 'runpy', 'subprocess', 'importlib'}) + check('check_ledger.py has none of the identity symbols (dl, b0, claim, sub, sp, s=-dl/lam); its only `lam` is the ' + 'supplier lambda = 1-(q_+a)/2 at line 126', + not names & {'dl', 'b0', 'claim', 'sub', 'sp', 'sympy', 'shr', 'cx', 'cy'} + and lam_assign == [(126, ast.dump(ast.parse('1-(q_+a)/2', mode='eval').body))], str(lam_assign)) + refs = [] + for py in sorted(root.rglob('*.py')): + for n, line in enumerate(py.read_text(encoding='utf-8', errors='replace').splitlines(), 1): + if 'check_gaugefree' in line: + refs.append('%s:%d' % (py.relative_to(root).as_posix(), n)) + check('only reference to check_gaugefree in any *.py is run_outer.py:19 (besides its own docstring)', + refs == ['outer/check_gaugefree.py:5', 'outer/run_outer.py:19'], str(refs)) + ro = text.get('outer/run_outer.py', []) + check('run_outer.py:19 only runs it as a pass/fail subprocess with stdout discarded', + len(ro) >= 19 and ro[18] == RUN_OUTER_19) + bad = [] + for tag, rel, spec, anchor in CITES: + L = text.get(rel) + for part in spec.split(','): + lo, _, hi = part.partition('-') + lo, hi = int(lo), int(hi or lo) + if L is None or anchor not in '\n'.join(L[max(0, lo - 3):hi + 2]): + bad.append('%s %s:%s' % (tag, rel, part)) + check('%d cited file:line anchors found within +-2 lines' % len(CITES), not bad, '; '.join(bad)) + LED = json.loads((root / 'outer' / 'LEDGER.json').read_bytes()) + row = LED['rows']['struct_boundary_radix_union'] + R = lambda nd: Fr(nd['rational']) # noqa: E731 + stored = {'eps': row['epsilon'], 'beta': row['beta'], 'xi': row['xi'], 'r': row['r0'], 'zeta': row['zeta'], + 'kappa': row['kappa'], 'q': row['q']} + check('LEDGER.json row struct_boundary_radix_union equals the rebuilt point (eps,beta,xi,r0,zeta,kappa,q)', + all(R(v) == Pt[k] for k, v in stored.items())) + sc = row['strict_checks'] + rc = LED['rejecting_controls']['struct_boundary_radix_union'] + for H in HITS: + for name, form in H.get('ledger', ()): + check('%s: LEDGER strict check %s == recomputed' % (H['id'], name), + name in sc and R(sc[name]) == seval(form, Pt, vocab)) + if 'control' in H: + flag, name, form = H['control'] + check('%s: LEDGER rejecting control %s.%s == recomputed and <= 0' % (H['id'], flag, name), + name in rc.get(flag, {}) and R(rc[flag][name]) == seval(form, Pt, vocab) and R(rc[flag][name]) <= 0) + absent = ('shift_leftover_linear_dominated_by_chirp', 'shift_gap_theta_polynomial') + check('GAUGEFREE 6.1 row names %s are absent from LEDGER; cap_above_band, theta_positive_polynomial_power present' % (absent,), + not any(n in sc for n in absent) and 'cap_above_band' in sc and 'theta_positive_polynomial_power' in sc) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__.split('\n')[0]) + ap.add_argument('--source-root', help='export containing %s at PR #2044 head' % PKG_REL) + args = ap.parse_args() + t0 = time.time() + try: + item1_symbolic() + item1_random() + Pt, vocab = item2(HERE / 'POINTS.json') + if args.source_root: + source_root(args.source_root, Pt, vocab) + except (ValueError, KeyError, OSError, json.JSONDecodeError) as e: + check('unexpected error', False, '%s: %s' % (type(e).__name__, e)) + sections = [] + for sec, _, _, _ in RESULTS: + if sec not in sections: + sections.append(sec) + for sec in sections: + rs = [r for r in RESULTS if r[0] == sec] + print('[%s] %d/%d checks pass' % (sec, sum(r[2] for r in rs), len(rs))) + for _, name, ok, info in rs: + if not ok: + print(' FAIL: %s %s' % (name, ('(' + info + ')') if info else '')) + fails = [r for r in RESULTS if not r[2]] + mode = 'source-root' if args.source_root else 'default' + groups = {g: sum(1 for H in HITS if H['group'] == g) for g in ('superseded', 'active', 'false-option')} + if fails: + print('FAIL_T74_REVIEW_ITEMS failed=%d checks=%d mode=%s' % (len(fails), len(RESULTS), mode)) + sys.exit(1) + print('PASS_T74_REVIEW_ITEMS checks=%d mode=%s item1_random_points=%d seed=%d item2_records=%d ' + 'active=%d superseded=%d false_option=%d cites=%s runtime=%.1fs' + % (len(RESULTS), mode, NPTS, RANDOM_SEED, len(HITS), groups['active'], groups['superseded'], + groups['false-option'], len(CITES) if args.source_root else 'skipped', time.time() - t0)) + + +if __name__ == '__main__': + main() diff --git a/research/t74-side-condition-coverage-audit/verify.py b/research/t74-side-condition-coverage-audit/verify.py new file mode 100644 index 0000000000..aee4d1170b --- /dev/null +++ b/research/t74-side-condition-coverage-audit/verify.py @@ -0,0 +1,649 @@ +#!/usr/bin/env python3 +"""Replay of the T74 side-condition coverage audit (pending PR #2044 head 322949a5). + +Scope: an adversarial *coverage* audit of the asymptotic side conditions quoted in the +notes of research/capped-fusion-t74-k554/ (PR #2044). It is NOT a proof of the T74 +claim, NOT a re-certification of the supplier endpoint and NOT a multiplication theorem. +It checks a recorded classification against exact rational arithmetic: + + (a) rebuild the final parameter point from ONE irreducible input (the certified complex + endpoint b_cert of LEDGER.json `complex_lower_pinned`) and closed-form definitions + transcribed from outer/check_ledger.py; check SHA-256 fingerprints of the rebuilt + rationals (recorded from LEDGER.json); + (b) evaluate every canonical condition key at every point exactly (ast-whitelisted + evaluator: Expression/BinOp(+,-,*,/,**int)/UnaryOp/Name/int Constant only) and + require the recorded truth values; + (c) require classification consistency; + (d) recompute the 49 non-comparison LEDGER strict checks (and 7 rejecting-control rows) + from formulas transcribed from check_ledger.py and require every COVERED mapping; + (e) run negative controls that must be rejected; + (f) optional --source-root DIR: re-hash every audited source file, re-locate every quote + within +-2 lines, and compare the rebuilt point / checks / controls with LEDGER.json. + +Standard library only; Python 3.10-3.14; run as `python3 -I -B verify.py`. -O is refused. +""" +import sys + +if sys.flags.optimize: + sys.stderr.write('verify.py refuses to run under -O/-OO\n') + sys.exit(2) + +import argparse +import ast +import copy +import hashlib +import json +import time +from decimal import Decimal, localcontext +from fractions import Fraction +from pathlib import Path + +if hasattr(sys, 'set_int_max_str_digits'): + sys.set_int_max_str_digits(0) + +HERE = Path(__file__).resolve().parent +PKG_REL = 'research/capped-fusion-t74-k554' +POINT_NAMES = ('final', 'pr1786', 'pr1673', 'pr1673mc') +CLASSES = ('COVERED', 'AUTO_TRUE', 'FALSE_AT_POINT', 'UNCOVERED_TRUE', 'STALE_TEXT_ONLY', + 'OBSOLETE', 'NON_EXPONENT', 'AMBIGUOUS') +FLAG_CLASSES = ('FALSE_AT_POINT', 'UNCOVERED_TRUE', 'AMBIGUOUS', 'STALE_TEXT_ONLY') +LIVE_CLASSES = ('COVERED', 'AUTO_TRUE', 'STALE_TEXT_ONLY', 'UNCOVERED_TRUE', 'AMBIGUOUS') +ENCODED_KINDS = ('ledger', 'implied', 'assert', 'control') +MAX_POW = 100000 + + +class Fail(Exception): + pass + + +class Unknown(Exception): + """name outside the declared vocabulary (hard error)""" + + +class Undefined(Exception): + """vocabulary name not defined at this point (truth value n/a)""" + + +class Forbidden(Exception): + """expression uses a node outside the whitelist""" + + +def need(ok, msg): + if not ok: + raise Fail(msg) + + +# ---------------------------------------------------------------- safe exact evaluator +_BINOPS = (ast.Add, ast.Sub, ast.Mult, ast.Div, ast.Pow) +_UNOPS = (ast.UAdd, ast.USub) + + +def parse(src): + if not isinstance(src, str) or len(src) > 4000: + raise Forbidden('expression must be a short string') + try: + tree = ast.parse(src, mode='eval') + except SyntaxError as e: + raise Forbidden(f'syntax: {e}') from None + for node in ast.walk(tree): + if isinstance(node, (ast.Expression, ast.Load, ast.Name) + _BINOPS + _UNOPS): + continue + if isinstance(node, ast.BinOp) and isinstance(node.op, _BINOPS): + continue + if isinstance(node, ast.UnaryOp) and isinstance(node.op, _UNOPS): + continue + if isinstance(node, ast.Constant) and type(node.value) is int: + continue + raise Forbidden(f'{type(node).__name__} not allowed in {src!r}') + return tree + + +def _ev(node, env, vocab): + if isinstance(node, ast.Expression): + return _ev(node.body, env, vocab) + if isinstance(node, ast.Constant): + return Fraction(node.value) + if isinstance(node, ast.Name): + if node.id not in vocab: + raise Unknown(node.id) + if node.id not in env: + raise Undefined(node.id) + return env[node.id] + if isinstance(node, ast.UnaryOp): + v = _ev(node.operand, env, vocab) + return -v if isinstance(node.op, ast.USub) else v + if isinstance(node, ast.BinOp): + x = _ev(node.left, env, vocab) + y = _ev(node.right, env, vocab) + op = node.op + if isinstance(op, ast.Add): + return x + y + if isinstance(op, ast.Sub): + return x - y + if isinstance(op, ast.Mult): + return x * y + if isinstance(op, ast.Div): + if y == 0: + raise Forbidden('division by zero') + return x / y + if isinstance(op, ast.Pow): + if y.denominator != 1 or abs(y.numerator) > MAX_POW: + raise Forbidden('** needs a bounded integer exponent') + if x == 0 and y < 0: + raise Forbidden('0 ** negative') + return x ** int(y) + raise Forbidden(type(node).__name__) + + +def seval(src, env, vocab): + return Fraction(_ev(parse(src), env, vocab)) + + +def exact_literal(s): + """'123', '-1/7', '0.00173' -> Fraction (decimal/rational literal only).""" + need(isinstance(s, str) and s and len(s) < 100000, 'bad exact literal') + body = s[1:] if s[0] == '-' else s + num, _, den = body.partition('/') + ip, _, fp = num.partition('.') + need(ip.isdigit() and (fp == '' or fp.isdigit()) and (den == '' or den.isdigit()), f'bad exact literal {s[:40]!r}') + return Fraction(s) + + +def dec(x, prec=25): + with localcontext() as cx: + cx.prec = prec + return str(Decimal(x.numerator) / Decimal(x.denominator)) + + +def frac_sha(x): + return hashlib.sha256(str(Fraction(x)).encode()).hexdigest() + + +# ---------------------------------------------------------------- points +def build_point(pt, vocab, overrides=None): + env = {} + for name, val in pt['definitions']: + need(name in vocab, f'definition of unknown variable {name}') + need(name not in env, f'duplicate definition {name}') + if overrides and name in overrides: + env[name] = overrides[name] + continue + if isinstance(val, str): + env[name] = seval(val, env, vocab) + elif isinstance(val, dict) and set(val) == {'exact'}: + env[name] = exact_literal(val['exact']) + elif isinstance(val, dict) and set(val) == {'floor_grid', 'grid', 'minus'}: + # floor(x * grid) / grid - minus (check_ledger.py l.121: kappa) + g = seval(val['grid'], env, vocab) + need(g.denominator == 1 and g > 0, 'grid must be a positive integer') + x = seval(val['floor_grid'], env, vocab) + env[name] = Fraction((x * g).__floor__(), g.numerator) - seval(val['minus'], env, vocab) + else: + raise Fail(f'bad definition form for {name}') + return env + + +# ---------------------------------------------------------------- ledger transcription +# Transcribed from PR #2044 outer/check_ledger.py ledger() (lines 110-196) at the final point. +# Only exact edits: Q(n,d) -> n/d, Q(x) -> x, tau_eff.numerator/denominator -> tau_num/tau_den. +# The 13 comparison-only checks (improvement_over_*) are kappa minus other packages' kappas; +# they are not side conditions and are only re-checked from LEDGER.json in --source-root mode. +LEDGER_VOCAB = {'eps', 'beta', 'q_', 'a', 'b', 'r', 'stop', 'slack', 'zeta', 'tau_eff', 'tau_num', 'tau_den', + 'THETA_POWER', 'halo_power', 'core_power', 'bit', 'c', 'xi', 'saving', 'kappa', 'tau', 'sigma', + 'internal', 'leaf', 'lam', 'key', 'sparse_union_movement'} +MARGINS = [ # check_ledger.py lines 128-136 + ('main_transform', 'saving'), + ('global_coordinate_router', 'a'), + ('fused_gaussian', '1-eps+q_*beta'), + ('group_bit_router', '1-eps+a*beta'), + ('group_scans', '1-eps+beta'), + ('boundary_algebraic_matrix', 'c+xi-eps'), + ('sparse_union_movement', 'xi+1/2-eps'), + ('polynomial_products', 'eps'), + ('microbox_face_corrections', '1-(eps+beta+halo_power-core_power+2)'), +] +CHECKS = [ # check_ledger.py lines 142-181 (comparison-only rows omitted) + ('actual_bit_above_effective', 'bit-a'), + ('complex_above_effective', 'b-a'), + ('q_positive', 'q_'), + ('complex_endpoint', 'b-q_'), + ('q_below_effective', 'a-q_'), + ('stop_positive', 'stop'), + ('stop_below_one', '1-stop'), + ('leaf_saving_above_effective', '(1-stop)*b-a'), + ('q_below_internal', '1-internal-q_'), + ('q_below_leaf', '1-leaf-q_'), + ('lambda_above_tau', 'lam-tau'), + ('lambda_above_sigma', 'lam-sigma'), + ('lambda_above_internal', 'lam-internal'), + ('lambda_prime_above_lambda', '1-q_-lam'), + ('lambda_prime_above_leaf', '1-q_-leaf'), + ('epsilon_positive', 'eps'), + ('epsilon_below_one', '1-eps'), + ('cap_above_band', 'xi-1/2'), + ('cap_below_cell', 'eps-xi'), + ('group_positive', 'beta'), + ('group_below_dimension', 'eps-beta'), + ('support_router_span', '1-beta'), + ('group_gauge_power_slack', '1-(2*xi-THETA_POWER)-r-beta'), + ('actual_logarithmic_group_guard', '1-(2*xi-THETA_POWER)-beta'), + ('global_gamma_power_slack', '1-eps-r'), + ('actual_logarithmic_gamma_guard', '1-eps'), + ('alpha_logarithm_absorption', 'r'), + ('group_key_fits_record', '1-key'), + ('membership_arithmetic_fits_record', '1-beta-2*(1-eps)'), + ('microbox_halo_volume', 'core_power-halo_power-beta'), + ('positive_layout_slack', 'slack'), + ('short_record_fallback', 'eps-a'), + ('complex_below_one_over_32', '1/32-b'), + ('strassen_integer_power_gap', '2**tau_num-7**tau_den'), + ('theta_positive_polynomial_power', 'THETA_POWER'), + ('cap_below_phase_cell_power', 'THETA_POWER-xi'), + ('halo_covers_generic_inverse_radius', 'halo_power-43'), + ('union_tag_work_per_visit_fits_record', '1-beta'), + ('union_header_fits_record', '1-beta'), + ('source_axis_superpolynomial', '1-eps'), +] +COMPARISON_CHECKS = ['improvement_over_online_final', 'improvement_over_previous_local_final', + 'improvement_over_pr1786', 'improvement_over_pr1828', 'improvement_over_pr1839', + 'improvement_over_pr1875', 'improvement_over_pr1876', 'improvement_over_pr1897', + 'improvement_over_pr1758', 'improvement_over_pr1699', 'improvement_over_pr1712', + 'improvement_over_previous_package', 'improvement_over_pkg_k2'] +# rejecting-control rows that the ledger adds under a flag (check_ledger.py lines 137-139, 183-186) +CONTROL_ROWS = { + 'old_g_factor_union_row_above_kappa': ('old_g_factor_union_row', '(1-eps-beta-1/2+xi)-kappa'), + 'old_per_axis_scan_above_kappa': ('old_per_axis_scan', '(1-eps)-kappa'), + 'unnecessary_full_key_sort_above_kappa': ('full_key_sort', '(sparse_union_movement-key)-kappa'), + 'unrecentered_group_gauge': ('full_cell_gauge', '1-THETA_POWER-r-beta'), + 'old_theta_chirp_guard': ('old_theta_chirp_guard', '1-(2*xi-eps)-r-beta'), + 'old_linear_guard': ('old_linear_guard', '1-xi-r-beta'), + 'old_union_tag_2beta': ('old_union_tag_2beta', '1-2*beta'), +} + + +def ledger_recompute(P, floor_grid): + """P: rebuilt final point. Returns (checks, margins, control_rows, kappa).""" + V = LEDGER_VOCAB + env = {'eps': P['eps'], 'beta': P['beta'], 'q_': P['q'], 'a': P['a'], 'b': P['b'], 'r': P['r'], + 'stop': P['stop'], 'slack': P['s'], 'zeta': P['zeta'], 'tau_eff': P['tau'], + 'tau_num': Fraction(P['tau'].numerator), 'tau_den': Fraction(P['tau'].denominator), + 'THETA_POWER': P['TH'], 'halo_power': P['halo'], 'core_power': P['core'], 'bit': P['bit']} + env['c'] = seval('(3-tau_eff)/2', env, V) + env['xi'] = seval('eps*(1+q_)-c+slack', env, V) + env['saving'] = seval('eps*q_', env, V) + env['kappa'] = Fraction((env['saving'] * floor_grid).__floor__(), floor_grid) - P['backoff'] + env['tau'] = seval('1-a', env, V) + env['sigma'] = seval('1-b', env, V) + env['internal'] = env['tau'] + (1 - env['stop']) * max(env['sigma'] - env['tau'], Fraction(0)) + env['leaf'] = seval('sigma+stop*(1-sigma)', env, V) + env['lam'] = seval('1-(q_+a)/2', env, V) + env['key'] = seval('beta+1-eps', env, V) + margins = {n: seval(f, env, V) for n, f in MARGINS} + env['sparse_union_movement'] = margins['sparse_union_movement'] + checks = {n: seval(f, env, V) for n, f in CHECKS} + for n, v in margins.items(): + checks[n + '_above_kappa'] = v - env['kappa'] + need(margins['boundary_algebraic_matrix'] == env['saving'] + env['slack'], 'check_ledger l.195 identity') + need(margins['sparse_union_movement'] == env['saving'] + env['slack'] + (env['tau_eff'] - 2) / 2, + 'check_ledger l.196 identity') + ctrl = {n: seval(f, env, V) for n, (_, f) in CONTROL_ROWS.items()} + return checks, margins, ctrl, env + + +# ---------------------------------------------------------------- key evaluation +def key_value(kd, env, vocab): + exprs = kd['expr'] if isinstance(kd['expr'], list) else [kd['expr']] + need(exprs, 'empty key expression') + return min(seval(e, env, vocab) for e in exprs) + + +def truth(v, rel, tol): + if rel == '>0': + return v > 0 + if rel == '>=0': + return v >= 0 + if rel == '==0': + return v == 0 if tol is None else abs(v) < tol + raise Fail(f'bad relation {rel}') + + +def truth_table(keys, envs, vocab, tols): + out = {} + for name, kd in keys.items(): + row = {} + for pt in POINT_NAMES: + try: + row[pt] = truth(key_value(kd, envs[pt], vocab), kd['rel'], tols[pt]) + except Undefined: + row[pt] = None + out[name] = row + return out + + +# ---------------------------------------------------------------- classification consistency +def consistency_errors(inv, tt, files): + err = [] + keys = inv['keys'] + for c in inv['conditions']: + cid, cls = c['id'], c['classification'] + if cls not in CLASSES: + err.append(f'{cid}: unknown class {cls}') + continue + for k in c['keys'] + c.get('operative_keys', []): + if k not in keys: + err.append(f'{cid}: unknown key {k}') + if any(k not in keys for k in c['keys'] + c.get('operative_keys', [])): + continue + fin = [tt[k]['final'] for k in c['keys']] + if cls in LIVE_CLASSES and not all(v is True for v in fin): + err.append(f'{cid}: {cls} but a condition key is not true at final') + if cls == 'COVERED' and not any(keys[k]['kind'] in ENCODED_KINDS or keys[k]['kind'] == 'auto' for k in c['keys']): + err.append(f'{cid}: COVERED without any key') + if cls == 'COVERED' and any(keys[k]['kind'] == 'none' for k in c['keys']): + err.append(f'{cid}: COVERED but uses an unencoded key') + if cls == 'UNCOVERED_TRUE' and any(keys[k]['kind'] in ('ledger', 'implied') for k in c['keys']): + err.append(f'{cid}: UNCOVERED_TRUE but a key is ledger-encoded') + if cls == 'FALSE_AT_POINT': + if not any(v is False for v in fin): + err.append(f'{cid}: FALSE_AT_POINT without a failing key at final') + if c.get('load_bearing') is not False: + err.append(f'{cid}: FALSE_AT_POINT must record load_bearing=false with operative keys') + if not c.get('operative_keys'): + err.append(f'{cid}: FALSE_AT_POINT without operative keys') + if cls in ('FALSE_AT_POINT', 'OBSOLETE'): + for k in c.get('operative_keys', []): + if tt[k]['final'] is not True: + err.append(f'{cid}: operative key {k} not true at final') + if cls == 'OBSOLETE': + sup = c.get('superseded_by') or [] + if not sup: + err.append(f'{cid}: OBSOLETE without superseding citation') + for s in sup: + if s.get('file') not in files or not isinstance(s.get('line'), int) or not 1 <= s['line'] <= files[s['file']]['lines']: + err.append(f'{cid}: bad superseding citation {s}') + if cls == 'NON_EXPONENT' and not c.get('reason'): + err.append(f'{cid}: NON_EXPONENT without description') + if c['file'] not in files or not 1 <= c['line'] <= files[c['file']]['lines']: + err.append(f'{cid}: bad file/line') + return err + + +def load_bearing_false(inv, tt): + n = 0 + for c in inv['conditions']: + if c['classification'] in LIVE_CLASSES and any(tt[k]['final'] is not True for k in c['keys']): + n += 1 + if c['classification'] == 'FALSE_AT_POINT' and c.get('load_bearing') is not False: + n += 1 + return n + + +# ---------------------------------------------------------------- source-root checks +def resolve_root(d): + d = Path(d) + if (d / PKG_REL / 'outer' / 'LEDGER.json').is_file(): + return d / PKG_REL + if (d / 'outer' / 'LEDGER.json').is_file(): + return d + raise Fail(f'--source-root {d}: no {PKG_REL}/outer/LEDGER.json') + + +def source_errors(root, srcs, inv): + err = [] + texts = {} + for rel, meta in srcs['files'].items(): + p = root / rel + if not p.is_file(): + err.append(f'missing source {rel}') + continue + data = p.read_bytes() + if hashlib.sha256(data).hexdigest() != meta['sha256']: + err.append(f'sha256 mismatch {rel}') + if hashlib.sha1(b'blob %d\0' % len(data) + data).hexdigest() != meta['git_blob']: + err.append(f'git blob mismatch {rel}') + if rel.endswith('.md'): + texts[rel] = data.decode('utf-8').split('\n') + for c in inv['conditions']: + lines = texts.get(c['file']) + if lines is None: + err.append(f"{c['id']}: file {c['file']} not hashed") + continue + L = c['line'] + if c['quote'] not in '\n'.join(lines[max(0, L - 3):L + 2]): + err.append(f"{c['id']}: quote not within +-2 lines of {c['file']}:{L}") + return err + + +def ledger_errors(root, P, points, checks, ctrl): + err = [] + L = json.loads((root / 'outer' / 'LEDGER.json').read_bytes()) + row = L['rows']['struct_boundary_radix_union'] + R = lambda node: Fraction(node['rational']) # noqa: E731 + stored = {'eps': row['epsilon'], 'xi': row['xi'], 'beta': row['beta'], 'q': row['q'], 'a': row['a'], + 'r': row['r0'], 'zeta': row['zeta'], 's': row['slack'], 'kappa': row['kappa'], + 'b': L['complex_lower_short'], 'b_cert': L['complex_lower_pinned']} + for n, node in stored.items(): + if R(node) != P[n]: + err.append(f'LEDGER {n} != rebuilt') + g = L['geometry_changes'] + if (R(g['theta_power']), Fraction(g['halo_power']), Fraction(g['core_power']), R(g['matrix_exponent'])) != \ + (P['TH'], P['halo'], P['core'], P['tau']): + err.append('LEDGER geometry != rebuilt') + sc = row['strict_checks'] + if len(sc) != 62 or set(sc) != set(checks) | set(COMPARISON_CHECKS): + err.append('LEDGER strict-check names differ from transcription + comparison list') + for n, v in checks.items(): + if n not in sc or R(sc[n]) != v: + err.append(f'LEDGER strict check {n} != recomputed') + allv = [R(x) for x in sc.values()] + if not all(v > 0 for v in allv): + err.append('LEDGER has a non-positive strict check') + if min(allv) != P['MINCHECK']: + err.append('LEDGER min strict check != MINCHECK') + for n in COMPARISON_CHECKS: + if n in sc and R(sc[n]) <= P['MINCHECK']: + err.append(f'comparison row {n} below MINCHECK') + rc = L['rejecting_controls']['struct_boundary_radix_union'] + for n, (cname, _) in CONTROL_ROWS.items(): + if n not in rc.get(cname, {}) or R(rc[cname][n]) != ctrl[n]: + err.append(f'LEDGER rejecting control {cname}.{n} != recomputed') + return err + + +# ---------------------------------------------------------------- main +def main(): + ap = argparse.ArgumentParser() + ap.add_argument('--source-root', help='checkout/archive of PR #2044 head (contains research/capped-fusion-t74-k554)') + args = ap.parse_args() + t0 = time.time() + POINTS = json.loads((HERE / 'POINTS.json').read_text()) + INV = json.loads((HERE / 'INVENTORY.json').read_text()) + SRC = json.loads((HERE / 'SOURCES-T74.json').read_text()) + vocab = set(POINTS['vocabulary']) + files = SRC['files'] + + # (a) final point + ledger recomputation + fin = POINTS['points']['final'] + envs = {} + P = build_point(fin, vocab) + floor_grid = int(seval(fin['ledger_floor_grid'], {}, vocab)) + checks, margins, ctrl, lenv = ledger_recompute(P, floor_grid) + need(lenv['kappa'] == P['kappa'] and lenv['xi'] == P['xi'] and lenv['c'] == P['c'], 'point vs ledger kappa/xi/c') + need(len(checks) == 49, f'expected 49 non-comparison checks, got {len(checks)}') + P['MINCHECK'] = min(checks.values()) + P['MIN_NONMAIN_MARGIN'] = min(v - P['kappa'] for k, v in margins.items() if k != 'main_transform') + P['MIN_MARGIN_ABOVE_KAPPA'] = min(v - P['kappa'] for v in margins.values()) + for n, h in fin['fingerprints'].items(): + need(frac_sha(P[n]) == h, f'final fingerprint mismatch for {n}') + envs['final'] = P + tols = {'final': None} + for pt in POINT_NAMES[1:]: + envs[pt] = build_point(POINTS['points'][pt], vocab) + tol = POINTS['points'][pt].get('eq_tolerance') + tols[pt] = seval(tol, {}, vocab) if tol else None + print(f'[a] final point rebuilt from b_cert ({len(str(P["b_cert"].numerator))}-digit numerator); ' + f'{len(fin["fingerprints"])} fingerprints match; kappa = {dec(P["kappa"], 30)}') + + # (b) truth table + keys = INV['keys'] + need(len(keys) == INV['counts']['keys'], 'key count') + tt = truth_table(keys, envs, vocab, tols) + bad = [(k, pt) for k in keys for pt in POINT_NAMES if tt[k][pt] != keys[k]['truth'][pt]] + need(not bad, f'recorded truth mismatch: {bad[:5]}') + for k, kd in keys.items(): + need(dec(key_value(kd, P, vocab)) == kd['final_value'], f'final_value display mismatch for {k}') + print(f'[b] {len(keys)} keys x {len(POINT_NAMES)} points: recorded truth values reproduced exactly') + + # (c) classification consistency + conds = INV['conditions'] + err = consistency_errors(INV, tt, files) + need(not err, f'consistency: {err[:5]}') + counts = {c: sum(1 for x in conds if x['classification'] == c) for c in CLASSES} + need(len(conds) == INV['counts']['conditions'] and all(counts[c] == INV['counts'][c] for c in CLASSES), 'class counts') + need(len({x['id'] for x in conds}) == len(conds), 'duplicate condition ids') + need(sorted(INV['flagged_ids']) == sorted(x['id'] for x in conds if x['classification'] in FLAG_CLASSES), 'flagged ids') + lbf = load_bearing_false(INV, tt) + print(f'[c] {len(conds)} conditions consistent with their classes; load-bearing false = {lbf}') + + # (d) ledger links + needed = set() + for c in conds: + if c['classification'] == 'COVERED': + for k in c['keys']: + needed.update(keys[k]['ledger_checks']) + C = {'C__' + n: v for n, v in checks.items()} + cv = set(vocab) | set(C) + for k, kd in keys.items(): + v = key_value(kd, P, vocab) + for ch in kd['ledger_checks']: + need(ch in checks, f'{k}: unknown ledger check {ch}') + if kd['kind'] == 'ledger': + if k == 'all_checks_pos': + need(v == min(checks.values()), 'all_checks_pos') + for ch in kd['ledger_checks']: + need(checks[ch] == v, f'{k} != ledger {ch}') + if kd.get('identity'): + need(seval(kd['identity'], dict(P, **C), cv) == v, f'{k}: identity fails') + if kd['kind'] == 'implied': + need(kd.get('identity') and all(checks[ch] > 0 for ch in kd['ledger_checks']), f'{k}: implied link') + if kd.get('rejecting_control'): + need(ctrl[kd['rejecting_control']] == v and v <= 0, f'{k}: control value') + need(needed <= set(checks) and all(checks[n] > 0 for n in needed), 'needed ledger check not positive') + need(all(v > 0 for v in checks.values()), 'non-positive recomputed check') + need(all(v <= 0 for v in ctrl.values()), 'rejecting control row does not fire') + print(f'[d] 49 non-comparison LEDGER checks recomputed, all > 0 (min {dec(P["MINCHECK"], 4)}); ' + f'{len(needed)} used by COVERED keys; {len(ctrl)} control rows fire') + + # (e) negative controls + rejected = [] + + def expect_reject(label, fn, *exc): + try: + fn() + except exc or (Fail,): + rejected.append(label) + return + raise Fail(f'negative control not rejected: {label}') + + def flipped(cid, new): + inv2 = copy.deepcopy(INV) + for c in inv2['conditions']: + if c['id'] == cid: + c['classification'] = new + e = consistency_errors(inv2, tt, files) + need(not e, 'flipped') + + first_cov = next(c['id'] for c in conds if c['classification'] == 'COVERED' and c['keys']) + first_false = next(c['id'] for c in conds if c['classification'] == 'FALSE_AT_POINT') + first_obs = next(c['id'] for c in conds if c['classification'] == 'OBSOLETE' and + any(tt[k]['final'] is False for k in c['keys'])) + expect_reject(f'flip {first_cov} COVERED->FALSE_AT_POINT', lambda: flipped(first_cov, 'FALSE_AT_POINT'), Fail) + expect_reject(f'flip {first_false} FALSE_AT_POINT->COVERED', lambda: flipped(first_false, 'COVERED'), Fail) + expect_reject(f'flip {first_obs} OBSOLETE->COVERED', lambda: flipped(first_obs, 'COVERED'), Fail) + + def drop_citation(): + inv2 = copy.deepcopy(INV) + next(c for c in inv2['conditions'] if c['classification'] == 'OBSOLETE')['superseded_by'] = [] + need(not consistency_errors(inv2, tt, files), 'citation') + expect_reject('OBSOLETE without citation', drop_citation, Fail) + + flips = [] + + def corrupt_beta(): + P2 = build_point(fin, vocab, overrides={'beta': Fraction(1, 2)}) + P2.update({k: P[k] for k in ('MINCHECK', 'MIN_NONMAIN_MARGIN', 'MIN_MARGIN_ABOVE_KAPPA')}) + tt2 = truth_table(keys, dict(envs, final=P2), vocab, tols) + flips.extend(sorted(k for k in keys if tt2[k]['final'] != keys[k]['truth']['final'])) + need(not flips, 'beta corrupted') + expect_reject('beta := 1/2 at final changes recorded truth', corrupt_beta, Fail) + + def fp_beta(): + P2 = build_point(fin, vocab, overrides={'beta': Fraction(1, 2)}) + need(frac_sha(P2['beta']) == fin['fingerprints']['beta'], 'fingerprint') + expect_reject('beta := 1/2 fails the LEDGER fingerprint', fp_beta, Fail) + + def undefined_key(): + k2 = dict(keys, bogus={'expr': 'q-undefined_var', 'rel': '>0'}) + truth_table(k2, envs, vocab, tols) + expect_reject('key with undefined variable', undefined_key, Unknown) + for bad_expr in ('abs(q)', 'q.numerator', '[q][0]', '1.5*q', 'q if q else eps', '2**(1/2)'): + expect_reject(f'forbidden expression {bad_expr!r}', + lambda e=bad_expr: key_value({'expr': e}, P, vocab), Forbidden) + + def bad_definition(): + fin2 = copy.deepcopy(fin) + fin2['definitions'][0] = [fin2['definitions'][0][0], {'exact': '__import__("os")'}] + build_point(fin2, vocab) + expect_reject('non-literal exact input', bad_definition, Fail) + print(f'[e] {len(rejected)} negative controls rejected; beta := 1/2 flips {len(flips)} final truth values: ' + + ', '.join(flips)) + + # (f) optional source root + src_note = 'not run (no --source-root)' + if args.source_root: + root = resolve_root(args.source_root) + e = source_errors(root, SRC, INV) + need(not e, f'sources: {e[:5]}') + e = ledger_errors(root, P, POINTS, checks, ctrl) + need(not e, f'ledger: {e[:5]}') + n_neg = 0 + src2 = copy.deepcopy(SRC) + rel0 = sorted(src2['files'])[0] + h = src2['files'][rel0]['sha256'] + src2['files'][rel0]['sha256'] = ('0' if h[0] != '0' else '1') + h[1:] + need(any('sha256 mismatch' in x for x in source_errors(root, src2, INV)), 'tampered sha256 accepted') + n_neg += 1 + inv2 = copy.deepcopy(INV) + inv2['conditions'][0]['line'] += 10 + need(any('quote not within' in x for x in source_errors(root, SRC, inv2)), 'moved quote accepted') + n_neg += 1 + rejected += ['tampered SOURCES sha256', 'quote line moved by +10'] + src_note = (f'{len(SRC["files"])} files re-hashed (sha256 + git blob), {len(conds)} quotes located within +-2 lines, ' + f'LEDGER.json params/49 checks/{len(ctrl)} controls equal; {n_neg} source negative controls rejected') + print(f'[f] source root: {src_note}') + + vv = INV.get('verification_verdicts', []) + ids = {c['id'] for c in conds} + unknown = [v.get('id') for v in vv if v.get('id') not in ids] + print(f'[report] verification_verdicts: {len(vv)} entries' + + (f' (unknown ids: {unknown})' if unknown else '') + ' (reported, not enforced)') + for v in vv: + print(f" {v.get('id')}: {v.get('verdict')} ({v.get('verifier', '?')})") + + need(lbf == 0, 'load-bearing false condition present') + n = {c.lower(): counts[c] for c in CLASSES} + print(f'runtime {time.time() - t0:.1f}s; python {sys.version.split()[0]}; mode ' + + ('source-root' if args.source_root else 'default')) + print(f'PASS_T74_SIDE_CONDITION_COVERAGE conditions={len(conds)} keys={len(keys)} covered={n["covered"]} ' + f'auto_true={n["auto_true"]} obsolete={n["obsolete"]} stale_text_only={n["stale_text_only"]} ' + f'non_exponent={n["non_exponent"]} false_at_point={n["false_at_point"]} uncovered_true={n["uncovered_true"]} ' + f'ambiguous={n["ambiguous"]} load_bearing_false={lbf} negative_controls={len(rejected)} ' + f'source_root={"checked" if args.source_root else "skipped"}') + + +if __name__ == '__main__': + try: + main() + except (Fail, Unknown, Undefined, Forbidden, KeyError, ValueError, OSError) as e: + print(f'FAIL_T74_SIDE_CONDITION_COVERAGE: {type(e).__name__}: {e}') + sys.exit(1)