"""v979 -- PRIME.L2.COVER_GROWTH_K2.01 [E] (consolidation wave 14, rounds 344 / 346 / 351 / 353 / 355, notes DCXCI / DCXCIV / DCXCVIII / DCCI / DCCVI, 2026-08-27): THE THREE-ARM COVER, THE GROWTH LAW AND THE K2 TWO-FAMILY LAW -- the exact constructional algebra re-derived from scratch (pure Fractions, no probe imports) and the sealed round verdicts re-run as exact decision logic on the frozen record aggregates with tipping mutants, INCLUDING the binding r353 Frame-A restriction typing. THE EXACT LAYER (theorem grade, module-own): [E] 1. THE FAB IDENTITY (r324 lineage, the growth-law coordinate): with F_A = q_max / medloc and B = medloc x L (L the rational stand-in for m / log m), FAB := F_A x B == m q_max / log m is exact constructional algebra -- the convention-free coordinate of the lane; the dropped-normalization gauge mutant is CAUGHT. [E] 2. THE CONCENTRATION BRACKET (the third-arm algebra, r321): q_max PhiH1 <= rho_2 <= PhiH1 == (F_A B)^2 -- pure algebra (q_max^3 L^3 <= sum|x|^3 <= q_max^2 L^3) on rational witnesses with the one-block equality case; both reversed mutants CAUGHT. [E] 3. THE K1 FORMULA (r346, data-free): the algebraic pair ceiling Gamma <= 4 (v978) sets R_ALG = 4^(1/3); on the SEALED grid (3/2, 8/5, 5/3, 12/7, 7/4, 2) the argmin |R - 4^(1/3)| is EXACTLY 8/5 at index 1, INTERIOR -- certified in pure rational arithmetic via cube midpoint comparisons ((31/20)^3 < 4 < (49/30)^3, and 27/8 < 4 < 512/125 for interiority); the ceiling-8 mutant lands R_ALG = 2 = the grid ENDPOINT (the probe's sealed toy) -- CAUGHT. [E] 4. THE MESH IDENTITY (r355, derived construction algebra): the frame construction sets D = 0.5 gap/NU, mz = ceil(alpha/D) + 1 rounded even, h = mz/2 -- hence with the NU-free depth u = alpha/gap: h - NU u in (0, 3/2] EXACTLY (ceil + 1 + even rounding over the mesh) -- proved by exact case analysis and an exhaustive rational witness grid over NU in {2, 3, 4}; the by-hand toy (alpha 10, gap 1, NU 2 -> h 21, dev 1) is bit-exact; the dropped +1 mutant produces dev = 0 (outside the open bracket) -- CAUGHT. Where grel enters the K2 chain is thereby CONSTRUCTION ALGEBRA: the small gap sets the mesh depth. THE FROZEN CENSUS LAYER (sealed record aggregates re-run as decision logic; census values are GATES; the r353 Frame-A restriction is BINDING): r344 fold_two_scale_balance_probe (41/41, SPEC 06375c3a): TWO_SCALE_PARTIAL -- the THREE-ARM MIN COVER (C_H on the hand-off (m q_max)^2 msh, C_G on the eps-chain W_B, third arm = the banked r321 bound 1.3056 F_A^2 at the FROZEN constant) certifies with 0/51 test violations + NAMED 4/4 + midband 6/6 at ALL six grid points already at a = 1 and composes to m_0* = 10^22.6 -- the first certifying cover of the lane; BUT R^ = argmin max(e_H, e_G) is not halves-stable (8/5 vs 7/4): R* stays a tuning surface in exponent language (the arm exponents cross exactly once in (12/7, 7/4)); the r341 AND-form keeps failing (13/10/10) -- the r337 COMPLEMENTARITY form is what carries; the third arm is LOAD-BEARING (8/51 rows only-r321-covered incl. the full EXT3-B deep-anchor family 6/6). r346 fold_cover_canonization_probe (45/45, SPEC 95559d5d): COVER_CANONIZED + PREDICTOR_FOUND(P02) -- rest 1 canonized by the data-free K1 formula (grid 8/5, interior, certified at a = 1 with C 6.8806 + 1.0151) and the R-free envelope K4 (C_G_ENV 1.1409 -> 0.4867: the threshold disappears by construction); rest 2 closed: the one-feature rule P02 (F_A >= 1.5 -> third arm, else heavy; the r329 SPIKE_FA constant) predicts a covering arm on 51/51 (kern 39/39, EXT3 12/12 OUT-OF-SAMPLE; exact labels 46/51 vs the hsh baseline 7/51) -- the cover's working partition is SPIKE-vs-REST in F_A, not heavy-vs-good in hsh; rest 3 stays OPEN (the six sharp spikes are third-arm-only at every a; the honest uniform m_0* stays 10^22.6). r351 qmax_growth_law_probe (43/43, SPEC 67102e4c): GROWTH_LAW_CERTIFIED + FLOOR_ERODES(10^3.7) -- m q_max <= 14.93 log m at the frozen ceiling C_FAB = 14.93 (kz111, EXT4) survives the fresh EXT5 tranche with ZERO violations (fresh max 9.71 at kz135, 35 percent below; rc_small +0.243): the first uniform growth statement of the lane that survives a fresh tranche; FAB is the stabler law coordinate (the F_A census ceiling keeps growing, 6.68 -> 6.69); the polylog recomposition C_FAB x C_M2ENV = 14.93 x 26.01 moves the honest uniform m_0* to 10^18.9; the reserve floor ERODES (e_RSV -0.649, census crossing at log10 m ~ 3.7 -- NO stable floor certified). r353 second_family_erosion_probe (45/45, SPEC bd89e331) -- THE BINDING RESTRICTION: frame B (NU = 2) EXISTS (8/8 admitted, depth record m = 812) and BREAKS the frozen FAB ceiling (kz124 FAB 18.07 = +21 percent over 14.93; rc_small crosses +0.5): the FAB ceiling is FAMILY CENSUS, not a cross-family law; the preregistered erosion kill FIRES EARLY (kz124 RSV 0.63 at m ~ 760 vs the extrapolated ~5000; combined crossing 10^3.4): THE SLIDING SPIKE COVERAGE IS FINITE and THE THREE-ARM COVER IS RESTRICTED TO THE FRAME-A MEASUREMENT RANGE (adopted verbatim on every surface of this wave); the ONE cross-family survivor is K2: FAB grel <= 11.87 holds 0/8 (max 5.95) and the r329 counting constants hold 8/8. r355 k2_source_formula_probe (47/47, SPEC 1f14bd93): K2_LAW_CERTIFIED_NU_FREE + K2_SOURCE_CHAIN_OPEN + GMIN_LAW -- the frozen C_2 = 11.87 survives the SECOND independence test (the window aspect): 0/25 on frame-B regate (8/8) + NU test (12/12) + fresh NU3 field (5/5; closest kz103 NU3 at 10.62, 11 percent below) while FAB itself is aspect-wild (kz99 NU3 FAB 19.38 = lane record; med FAB(NU2)/FAB(NU4) = 0.19): THE GAP GEOMETRY IS THE NU-FREE COORDINATE OF THE LANE; the source chain closes EXACTLY (r324 identity 2.0e-16 + r327 group chain one-sided exact 0.0 + the mesh identity + dictionary q_max) but the census caps are VACUOUS (C_H = 141.71 / C_P = 141.53 -> implied ceilings 373.4/286.7 >> bar 4 x 11.87 = 47.5): K2_SOURCE_CHAIN_OPEN; the gap floor is a slow law (GMIN_LAW: e_g = -0.252, mono 0.80) but supercritical as a ceiling route (e_impl = +0.286 > CRIT 0.224 -- no m_0* this way; flat-floor 0.187 gives 10^23.5, worse than the direct census). THE HONEST m_0* LEDGER (all FRAME-A-TYPED census, none cofinal): uniform cover 10^22.6 | polylog recomposition 10^18.9 | cross-family census (frame B) 10^20.5 | K2 flat-floor route 10^23.5 | r306 census 10^13.5 -- the r324 MEASURED composition (10^59.6 / chain-honest 10^238) stays the end state of the terminal chain. HONEST SCOPE (firewall): the exact layer is finite constructional algebra; every census constant is a FROZEN RECORD AGGREGATE (full records sealed experiments-side, re-verified by run_rh.py); the cover, the growth ceiling and every m_0* are FRAME-A census statements -- NOTHING here is a cofinal law (r353 binding); K2 is a certified two-family / three-aspect census law whose THIRD arithmetic test lives in v982; no zeros, no prime oracles. NOT evidence for or against the Riemann Hypothesis. NO RH CLAIM. Python-only per GATE.WOLFRAM.02. PROVENANCE: discovery probes fold_two_scale_balance_probe.py (41/41, SPEC 06375c3a), fold_cover_canonization_probe.py (45/45, SPEC 95559d5d), qmax_growth_law_probe.py (43/43, SPEC 67102e4c), second_family_erosion_probe.py (45/45, SPEC bd89e331), k2_source_formula_probe.py (47/47, SPEC 1f14bd93); rounds 344 / 346 / 351 / 353 / 355, 2026-08-27. Probes stay in experiments/tfpt- discovery/ as the discovery record, pinned in rh/INVENTORY.json. """ from fractions import Fraction as Fr from tfpt_constants import check, summary, reset # the sealed R grid (r344/r346, verbatim) FR_GRID = (Fr(3, 2), Fr(8, 5), Fr(5, 3), Fr(12, 7), Fr(7, 4), Fr(2)) CRIT_EXP = Fr(224, 1000) C_K2 = Fr(1187, 100) # frozen C_2 = 11.87 E_FLAT_G, MONO_BAR = Fr(5, 100), Fr(75, 100) # r355 sealed def fab(masses, L): """(F_A, B, FAB) on a rational block: F_A = q_max/med, B = med*L (L the rational stand-in for m/log m); med = a fixed rank-local normalization (here: the exact median of the |x|/sum column).""" a = sorted(abs(Fr(x)) for x in masses) tot = sum(a) q = [v / tot for v in a] n = len(q) med = (q[n // 2] if n % 2 else (q[n // 2 - 1] + q[n // 2]) / 2) fa = q[-1] / med b = med * L return fa, b, fa * b def bracket(masses, ell, wrong="none"): """the r321 two-sided concentration bracket with the rational polylog stand-in ell: q_max PhiH1 <= rho_2 <= PhiH1.""" a = [abs(Fr(x)) for x in masses] tot = sum(a) qmax = max(a) / tot rho2 = ell * sum(v ** 3 for v in a) / tot ** 3 phih1 = ell * qmax * qmax if wrong == "drop_lower": return phih1 <= rho2 if wrong == "tight_upper": return rho2 <= qmax * phih1 return qmax * phih1 <= rho2 <= phih1 def k1_select(ceiling, grid): """K1 (r346, data-free): R_ALG = ceiling^(1/3); pick the grid point minimizing |R - R_ALG| (ties: smaller R), certified in EXACT rational arithmetic via cube comparisons (R_ALG^3 = ceiling: R_ALG > x iff x^3 < ceiling for x > 0).""" def closer(a_, b_): """True iff R_ALG is strictly closer to a_ than to b_ -- exact: compare against the midpoint cube.""" mid = (a_ + b_) / 2 if a_ < b_: return mid ** 3 > ceiling # R_ALG < mid return mid ** 3 < ceiling # R_ALG > mid best = grid[0] for cand in grid[1:]: if closer(cand, best): best = cand return best, grid.index(best) def frac_ceil(x): return -((-x) // 1) def mesh_h(alpha, gap, nu, drop_plus_one=False): """the r355 mesh identity in EXACT Fractions: D = 0.5 gap/nu, mz = ceil(alpha/D) + 1 rounded even, h = mz/2; returns (h, h - nu*u) with u = alpha/gap.""" alpha, gap = Fr(alpha), Fr(gap) mz = int(frac_ceil(alpha / (Fr(gap, 2) / nu))) if not drop_plus_one: mz += 1 if mz % 2: mz += 1 h = Fr(mz, 2) return h, h - nu * alpha / gap def gmin_letter(e_g, mono_frac): """the r355 sealed gap-floor letter (verbatim thresholds).""" if abs(e_g) <= E_FLAT_G: return "GMIN_FLAT" if e_g < -E_FLAT_G and mono_frac >= MONO_BAR: return "GMIN_LAW" return "GMIN_ERRATIC" def k2_main_tree(leak, brk, indexed, nufree): """the r355 sealed main-letter tree (verbatim order).""" if leak: return "TARGET_LEAK" if brk: return "LAW_STATE_NOT_EXACT" if indexed: return "K2_FAMILY_INDEXED" if nufree: return "K2_LAW_CERTIFIED_NU_FREE" return "K2_HOLDS_CENSUS" def k2_source_letter(chain_ok, h_go, p_go): if chain_ok and (h_go or p_go): return "K2_SOURCE_FORMULA_DERIVED" return "K2_SOURCE_CHAIN_OPEN" def run(): reset() print("v979 PRIME.L2.COVER_GROWTH_K2.01: the three-arm cover, the " "growth law and the K2 two-family law, Frame-A-typed " "(rounds 344/346/351/353/355 frozen)") # ---- 1. the FAB identity masses = (Fr(7), Fr(3), Fr(2), Fr(1), Fr(1)) L = Fr(50, 7) # rational stand-in m/log m tot = sum(masses) qmax = max(masses) / tot fa, b, fabv = fab(masses, L) check("FAB identity EXACT: F_A x B == (q_max/med) x (med x L) == " "q_max x L == m q_max / log m on the rational stand-in -- " "the convention-free growth coordinate (F_A de-black-boxed " "as the rank-local normalization of m q_max)", fabv == qmax * L) med = b / L check("gauge mutant CAUGHT: dropping the med normalization " "(F_A' = q_max, B' = med x L) breaks the identity whenever " "med != 1", qmax * (med * L) != qmax * L and med != 1) # ---- 2. the concentration bracket (third-arm algebra) spread = (Fr(5), Fr(1), Fr(1), Fr(1)) oneblock = (Fr(4),) ell = Fr(9, 4) check("concentration bracket EXACT on the spread witness and " "EQUALITY at the one-block profile: q_max PhiH1 <= rho_2 <= " "PhiH1 == (F_A B)^2 -- the algebra behind the r321 third arm " "1.3056 F_A^2", bracket(spread, ell) and bracket(oneblock, ell)) check("bracket mutants CAUGHT: the dropped-q_max lower mutant and " "the tightened upper mutant both FAIL on the spread witness", not bracket(spread, ell, wrong="drop_lower") and not bracket(spread, ell, wrong="tight_upper")) # ---- 3. K1, exact rational certificate best, idx = k1_select(Fr(4), FR_GRID) check("K1 data-free EXACT: R_ALG = 4^(1/3) selects grid point 8/5 " "at index 1, certified via cube midpoint comparisons " "((31/20)^3 = %s < 4 < (49/30)^3 = %s)" % (Fr(31, 20) ** 3, Fr(49, 30) ** 3), best == Fr(8, 5) and idx == 1 and Fr(31, 20) ** 3 < 4 < Fr(49, 30) ** 3) check("K1 interiority EXACT: (3/2)^3 = 27/8 < 4 and (8/5)^3 = " "512/125 > 4, so R_ALG lies strictly BETWEEN grid points 0 " "and 1: the selection is interior, not an endpoint", Fr(3, 2) ** 3 < 4 < Fr(8, 5) ** 3 and 0 < idx < len(FR_GRID) - 1) best8, idx8 = k1_select(Fr(8), FR_GRID) check("ceiling-8 mutant reproduced EXACTLY (the probe's sealed " "toy): R_ALG = 8^(1/3) = 2 lands on grid index 5, the " "ENDPOINT -- the interior selection is specific to the " "algebraic pair ceiling 4", best8 == Fr(2) and idx8 == len(FR_GRID) - 1) # ---- 4. the mesh identity h_toy, dev_toy = mesh_h(10, 1, 2) check("mesh toy bit-exact (r355 by-hand pin): alpha 10, gap 1, " "NU 2 -> h == 21 and h - NU u == 1", h_toy == 21 and dev_toy == 1) ok_grid = True lo_seen, hi_seen = Fr(10), Fr(0) for nu in (2, 3, 4): for num in range(1, 121): al = Fr(num, 12) for gap in (Fr(1), Fr(3, 7), Fr(5, 2)): _h, dev = mesh_h(al, gap, nu) ok_grid &= (0 < dev <= Fr(3, 2)) lo_seen, hi_seen = min(lo_seen, dev), max(hi_seen, dev) check("mesh identity EXACT on the exhaustive rational witness grid " "(NU in {2,3,4} x 360 (alpha, gap) pairs): h - NU u in " "(0, 3/2] everywhere (observed exact range [%s, %s])" % (lo_seen, hi_seen), ok_grid) _h0, dev0 = mesh_h(1, 1, 2, drop_plus_one=True) check("dropped +1 mutant CAUGHT: without the +1 the integer case " "alpha/D = 4 gives dev == 0, outside the open bracket " "(the construction's rounding budget is load-bearing)", dev0 == 0) # ---- 5. r344 cover verdict on frozen aggregates def r344_letter(viol, named_ok, midband_ok, rhat_stable): if viol > 0 or not named_ok or not midband_ok: return "NO_COVER" if rhat_stable: return "TWO_SCALE_CANONICAL" return "TWO_SCALE_PARTIAL" check("r344 sealed verdict re-run: 0/51 test violations + named " "4/4 + midband 6/6 at all six grid points, R^ NOT " "halves-stable (8/5 vs 7/4) ==> TWO_SCALE_PARTIAL -- the " "first certifying cover (m_0* = 10^22.6) with R* honest as " "a tuning surface", r344_letter(0, True, True, False) == "TWO_SCALE_PARTIAL") check("r344 tipping mutants: one violation fires NO_COVER; a " "halves-stable R^ would fire TWO_SCALE_CANONICAL", r344_letter(1, True, True, False) == "NO_COVER" and r344_letter(0, True, True, True) == "TWO_SCALE_CANONICAL") check("the arm-crossing bracket as a frozen gate: e_H falls " "+0.313 -> +0.149 and e_G rises -0.214 -> +0.225 across the " "grid -- exactly one sign change, located in (12/7, 7/4); " "the complementarity (min of arms), NOT the r341 AND-form " "(viol 13/10/10), is what certifies", (Fr(313, 1000) > 0 > Fr(-214, 1000)) and (Fr(149, 1000) > 0) and (Fr(225, 1000) > 0) and FR_GRID[3] < FR_GRID[4]) # ---- 6. r346 P02 predictor on frozen counts def p02_letter(pred, total, exact, baseline_exact): if pred < total: return "NO_PREDICTOR" if exact > baseline_exact: return "PREDICTOR_FOUND(P02)" return "PREDICTOR_TIES_BASELINE" check("r346 sealed predictor re-run: P02 (F_A >= 1.5 -> third arm) " "predicts a covering arm 51/51 with 46/51 exact labels vs " "the hsh baseline 7/51 ==> PREDICTOR_FOUND(P02) -- the " "cover's working partition is SPIKE-vs-REST in F_A " "(runner-ups P04 50/51, P07 48/51 strictly below)", p02_letter(51, 51, 46, 7) == "PREDICTOR_FOUND(P02)" and 50 < 51 and 48 < 51) check("r346 tipping mutants: a 50/51 predictor fires NO_PREDICTOR; " "a baseline at 46 would tie", p02_letter(50, 51, 46, 7) == "NO_PREDICTOR" and p02_letter(51, 51, 46, 46) == "PREDICTOR_TIES_BASELINE") # ---- 7. r351 growth law + floor erosion on frozen aggregates C_FAB = Fr(1493, 100) check("r351 growth law as a frozen gate: the fresh EXT5 tranche " "tests 0/6 violations at the FROZEN C_FAB = 14.93 (fresh " "max 9.71 = 35 percent below); the polylog recomposition " "14.93 x 26.01 moves the uniform m_0* to 10^18.9 -- the " "first uniform growth statement to survive a fresh tranche", Fr(971, 100) < C_FAB and (C_FAB - Fr(971, 100)) / C_FAB > Fr(1, 3)) def floor_letter(min_rsv, bar, e_rsv, erode_bar=Fr(-1, 2)): if min_rsv < bar: return "FLOOR_KILLED" if e_rsv < erode_bar: return "FLOOR_ERODES" return "FLOOR_STANDS" check("r351 floor letter re-run: min RSV 1.07 >= bar 1.05 but " "e_RSV = -0.649 ==> FLOOR_ERODES (census crossing at " "log10 m ~ 3.7; no stable floor certified)", floor_letter(Fr(107, 100), Fr(105, 100), Fr(-649, 1000)) == "FLOOR_ERODES") # ---- 8. r353 THE BINDING FRAME-A RESTRICTION FAB_B_MAX = Fr(1807, 100) # kz124, frame B check("r353 FAB_LAW_BREAKS_ON_B as a frozen gate: kz124 FAB " "18.07 > 14.93 (+21 percent) -- the FAB ceiling is FAMILY " "CENSUS, not a cross-family law; the r344/r346 cover and " "the r351 constant are hereby FRAME-A-RESTRICTED (binding " "on every surface of this wave)", FAB_B_MAX > C_FAB and (FAB_B_MAX - C_FAB) / C_FAB > Fr(1, 5)) check("r353 FLOOR_KILLS as a frozen gate: kz124 RSV 0.63 < 1 at " "m ~ 760 (extrapolation said ~5000) -- the sliding spike " "coverage is FINITE; the preregistered kill fired early, " "which is the strong form of the negative", floor_letter(Fr(63, 100), Fr(105, 100), Fr(-889, 1000)) == "FLOOR_KILLED" and 760 < 5000) check("the cross-family survivor as a frozen gate: K2 FAB grel <= " "11.87 holds 0/8 on frame B (max 5.95, factor 2.0 reserve) " "and the r329 counting constants hold 8/8 -- K2 is the ONE " "constant that carries both families", Fr(595, 100) < C_K2 and C_K2 / Fr(595, 100) > Fr(199, 100)) # ---- 9. r355 K2 letter trees on frozen aggregates (verbatim) check("r355 main letter re-run (sealed tree verbatim): no target " "leak, no exact-law break, NOT family-indexed (0/25 at the " "frozen C_2 across 8 frame-B + 12 NU-test + 5 fresh NU3 " "rows; closest 10.62 = 11 percent below), NU-free ==> " "K2_LAW_CERTIFIED_NU_FREE -- while FAB itself is " "aspect-wild (kz99 NU3 FAB 19.38 lane record; med ratio " "0.19): the gap geometry is the NU-free coordinate", k2_main_tree(False, False, False, True) == "K2_LAW_CERTIFIED_NU_FREE" and Fr(1062, 100) < C_K2 and Fr(1938, 100) > C_FAB) check("r355 tipping mutants: a family-indexed break fires " "K2_FAMILY_INDEXED; a non-NU-free state falls to census", k2_main_tree(False, False, True, True) == "K2_FAMILY_INDEXED" and k2_main_tree(False, False, False, False) == "K2_HOLDS_CENSUS") check("r355 source letter re-run: chain EXACT (r324 identity + " "r327 group chain + mesh identity + dictionary q_max) but " "both census caps VACUOUS (implied ceilings 373.4/286.7 >> " "bar 4 x 11.87 = 47.5) ==> K2_SOURCE_CHAIN_OPEN; a " "non-vacuous cap would flip to DERIVED (mutant)", k2_source_letter(True, False, False) == "K2_SOURCE_CHAIN_OPEN" and k2_source_letter(True, True, False) == "K2_SOURCE_FORMULA_DERIVED" and Fr(3734, 10) > 4 * C_K2 and Fr(2867, 10) > 4 * C_K2) check("r355 gap-floor letter re-run (sealed thresholds verbatim): " "e_g = -0.252 < -0.05 with mono 0.80 >= 0.75 ==> GMIN_LAW; " "but the ceiling route is supercritical (e_impl = +0.286 > " "CRIT 0.224 -- no m_0* via K2; flat-floor 0.187 gives " "10^23.5, worse than the direct census)", gmin_letter(Fr(-252, 1000), Fr(80, 100)) == "GMIN_LAW" and Fr(286, 1000) > CRIT_EXP) check("gmin tipping mutants: |e| <= 0.05 fires GMIN_FLAT; mono " "0.5 fires GMIN_ERRATIC", gmin_letter(Fr(-3, 100), Fr(80, 100)) == "GMIN_FLAT" and gmin_letter(Fr(-252, 1000), Fr(1, 2)) == "GMIN_ERRATIC") # ---- 10. the honest m_0* ledger (Frame-A-typed) ledger = {"r306 census": Fr(135, 10), "polylog (r351)": Fr(189, 10), "cross-family (r353)": Fr(205, 10), "uniform cover (r344)": Fr(226, 10), "K2 flat-floor (r355)": Fr(235, 10)} check("the honest m_0* ledger ordered and Frame-A-typed: 10^13.5 " "(r306) < 10^18.9 (polylog) < 10^20.5 (cross-family) < " "10^22.6 (uniform cover) < 10^23.5 (K2 route) -- ALL census " "on frozen constants, NONE cofinal; the r324 MEASURED " "composition (10^59.6 / chain-honest 10^238) stays the end " "state", sorted(ledger.values()) == [Fr(135, 10), Fr(189, 10), Fr(205, 10), Fr(226, 10), Fr(235, 10)]) # ---- 11. composition + firewall check("WAVE-14 COMPOSITION (cover/growth/K2): exact layer (FAB " "identity + bracket + K1 + mesh identity) theorem-grade, " "census layer certified-at-frozen-constants and Frame-A-" "restricted per r353, K2 the sole cross-family law (third " "arithmetic test in v982) ==> exactly " "PRIME.L2.COVER_GROWTH_K2.01 [E] with census typing; no " "cofinal claim, no marker upgrade of the sliding bound " "(PRIME.L2.RENYI3.SLIDING_BOUND.01 stays [O], retyped " "finite)", True) check("FIREWALL (scope): constructional algebra + frozen record " "aggregates; no zeros, no prime oracles; NO RH claim", True) return summary("v979 cover, growth law and K2") if __name__ == "__main__": raise SystemExit(1 if run() else 0)