TFPT scientific source excerpt Original repository path: experiments/theory-contracts/seam-positive-kernel-search-20261015/genesis_checks.py Original file SHA-256: fc1160300289b57659af1d10d21269b0c4ca3e2d9dcef9ba68872fe10df38d06 Inclusive original lines: 1-120 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | """Executable inference controls on existing TFPT source functions. 000002 | 000003 | These check explicitly named consequences, not whole origin hypotheses. 000004 | Analytic identities are recorded separately from finite precision replays. 000005 | """ 000006 | import argparse 000007 | import json 000008 | import mpmath as mp 000009 | 000010 | 000011 | def evaluate(check_id): 000012 | mp.mp.dps = 65 000013 | theta = lambda v, t: mp.jtheta(3, mp.pi*v, mp.exp(-mp.pi*t)) 000014 | theta0 = lambda t: theta(0, t) 000015 | close = lambda a, b: abs(a-b) < mp.mpf('1e-55') 000016 | if check_id == 'quillen-relative-normalization': 000017 | # Same geometry and reference on numerator/denominator: N(0,t)=1. 000018 | norm = lambda v, t: (theta(v, t)/theta0(t))**2 000019 | dv2 = mp.diff(lambda v: mp.log(norm(v, 1)), 0, 2) 000020 | dt = mp.diff(lambda t: mp.log(norm(0, t)), 1) 000021 | if not close(dt, 0) or not close(dv2, -2*mp.pi): 000022 | raise ArithmeticError('Original relative response replay failed') 000023 | facts = {'shape_derivative_log_N_at_zero_source': str(dt), 000024 | 'holonomy_second_derivative_log_N': str(dv2), 000025 | 'analytic_reason': 'N(0,t)=1 identically for the co-moving zero-source reference'} 000026 | claims = {'normalized_zero_source_has_shape_response': False, 000027 | 'normalized_charge_response_alone_fixes_absolute_replica_entropy': False} 000028 | scope = 'The given flat elliptic relative function; t variation is not an identified physical replica operation.' 000029 | elif check_id == 'theta-heat-shape-response': 000030 | dt = mp.diff(lambda t: mp.log(theta0(t)), 1) 000031 | ratio = mp.diff(lambda v: theta(v, 1), 0, 2)/theta0(1) 000032 | if not close(dt, -mp.mpf(1)/4) or not close(ratio/(4*mp.pi), dt): 000033 | raise ArithmeticError('Theta heat identity failed') 000034 | facts = {'theta_shape_log_derivative': str(dt), 000035 | 'theta_holonomy_second_derivative_ratio': str(ratio), 000036 | 'analytic_reason': 'Poisson Z(t)=t^-1/2 Z(1/t) and theta heat equation'} 000037 | claims = {'charge_curvature_fixes_theta_shape_derivative': True, 000038 | 'theta_shape_derivative_is_already_full_master_area_entropy': False} 000039 | scope = 'Unnormalized theta factor only; eta, metric, reference and sewing terms remain part of the actual determinant.' 000040 | elif check_id == 'doubled-source-counting': 000041 | beta = 4*mp.pi 000042 | def variance(a): 000043 | weights = [(q, mp.exp(-beta*(mp.mpf(q*q)/2+(a-mp.mpf(1)/2)*q))) for q in range(-16, 17)] 000044 | z = sum(w for q, w in weights) 000045 | mean = sum(q*w for q, w in weights)/z 000046 | return sum((q-mean)**2*w for q, w in weights)/z 000047 | variances = [variance(mp.mpf(1)/4), variance(mp.mpf(3)/4)] 000048 | etas = [mp.mpf(1)-2*a for a in (mp.mpf(1)/4, mp.mpf(3)/4)] 000049 | if not all(close(v, 1/(8*mp.pi)) for v in variances) or sum(etas) != 0: 000050 | raise ArithmeticError('Quarter source identities failed') 000051 | facts = {'quarter_variances': [str(v) for v in variances], 000052 | 'pair_variance': str(sum(variances)), 000053 | 'beta_times_each_variance': [str(beta*v) for v in variances], 000054 | 'eta_quarter_pair': [str(x) for x in etas], 'eta_sum': str(sum(etas)), 000055 | 'analytic_reason': 'Original quarter pair reduces to exp(-pi p^2); eta_a(0)=1-2a for n+a.'} 000056 | claims = {'two_quarter_blocks_are_two_faces': False, 000057 | 'nonzero_total_eta_is_needed_for_original_half_susceptibility': False, 000058 | 'quarter_pair_variance_equals_one_quarter_variance': False} 000059 | scope = 'Original independent quarter blocks on one marginal, not the two faces; eta statement is for the unweighted direct sum, not the whole physical master.' 000060 | elif check_id == 'variable-mark-completion': 000061 | # Candidate class, not a deduction of these Gram forms from P1. 000062 | from fractions import Fraction 000063 | import sympy as sp 000064 | from sympy.matrices.normalforms import hermite_normal_form 000065 | finite_replays = [] 000066 | for r in (1, 2, 3): 000067 | n, g = 4*r*r, 4*r*r+1 000068 | d = sp.zeros(g) 000069 | for j in range(g-1): 000070 | d[j, j], d[j+1, j] = 1, -1 000071 | d[g-2, g-1], d[g-1, g-1] = 1, 1 000072 | a = sp.zeros(n, n-1) 000073 | for j in range(n-1): 000074 | a[j, j], a[j+1, j] = 1, -1 000075 | base = sp.diag(d, a) 000076 | v = sp.Matrix([sp.Rational(1, 2)]*g + 000077 | [sp.Rational(r*(n-1), n)]+[sp.Rational(-r, n)]*(n-1)) 000078 | coordinates = base.gauss_jordan_solve(v)[0] 000079 | den = 4*r 000080 | integer_generators = (den*sp.eye(2*n)).row_join(den*coordinates) 000081 | if any(x.q != 1 for x in integer_generators): 000082 | raise ArithmeticError('Nonintegral presentation') 000083 | integer_generators = sp.Matrix(integer_generators.rows, integer_generators.cols, 000084 | [sp.Integer(x) for x in integer_generators]) 000085 | h = hermite_normal_form(integer_generators) 000086 | gram = h.T*(base.T*base)*h/den**2 000087 | if (gram.det() != 1 or any(x.q != 1 for x in gram) 000088 | or any(gram[j, j] % 2 for j in range(2*n))): 000089 | raise ArithmeticError('Lattice completion replay failed') 000090 | finite_replays.append({'marks': n, 'rank': 2*n, 'base': f'D{g}+A{n-1}', 000091 | 'glue_order': 4*r, 'generator_squared_norm': str((v.T*v)[0]), 000092 | 'gram_determinant': str(gram.det()), 'integral_even': True}) 000093 | facts = {'conditional_class': 'standard positive D_(n+1)+A_(n-1), complete even unimodular extension', 000094 | 'all_admissible_mark_counts': 'n=4*r^2, integer r>=1', 000095 | 'analytic_necessity': 'det(base)=4n must be a square; even unimodular rank 2n is divisible by8', 000096 | 'analytic_sufficiency': 'glue generator (spinor_D,r*lambda1_A) has order4r and norm2r^2, yielding index4r and determinant1 for every r', 000097 | 'finite_independent_hnf_replays': finite_replays, 000098 | 'minimal_marks': 4, 'minimal_rank': 8, 000099 | 'source_pairing_or_minimality_derived_from_P1': False, 000100 | 'primitive_family_projection_condition': 'A local glue element with primitive A_(n-1) discriminant projection has order divisible by n; n divides |H|=4r, while n=4r^2, so r=1.', 000101 | 'primitive_projection_selected_marks': 4, 000102 | 'primitive_local_charge_derived_from_P1': False} 000103 | claims = {'higher_rank_completion_forces_residual_discriminant_sectors': False, 000104 | 'local_complete_gluing_alone_selects_four_marks': False, 000105 | 'minimal_member_of_this_declared_class_has_four_marks': True, 000106 | 'primitive_family_projection_allows_higher_marks': False} 000107 | scope = 'An explicit candidate family with assumed standard pairing and even selfdual completion. Minimality is additional. No derivation of physical P1, spacetime, or all TFPT outputs.' 000108 | else: 000109 | raise ValueError('Unknown curated check ID') 000110 | return {'id': check_id, 'status': 'pass', 'facts': facts, 000111 | 'inference_claims': [{'id': k, 'holds': v} for k, v in claims.items()], 000112 | 'scope': scope, 'precision_digits': 65, 000113 | 'new_physical_proof': False, 'fundamental_solution': False} 000114 | 000115 | 000116 | if __name__ == '__main__': 000117 | parser = argparse.ArgumentParser(description=__doc__) 000118 | parser.add_argument('--check', required=True) 000119 | args = parser.parse_args() 000120 | print(json.dumps(evaluate(args.check), ensure_ascii=False, indent=2))