TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/stability-results.json
Original file SHA-256: e894f7531264fc5ab1b647922467c47c878d6c271c8e258f76ac4a7bfe7e24b7
Inclusive original lines: 1-145
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 | {
000002 |   "checks": [
000003 |     {
000004 |       "detail": "char(A0*) = lambda(lambda-1/3)(lambda-2/3) exactly",
000005 |       "id": "A0_SPECTRUM",
000006 |       "passed": true
000007 |     },
000008 |     {
000009 |       "detail": "V0,V1,V2 are exact eigenvectors for weights 0,1/3,2/3",
000010 |       "id": "A0_EIGENVECTORS",
000011 |       "passed": true
000012 |     },
000013 |     {
000014 |       "detail": "A_(k+1)=U A_k U^-1; this proves C4 covariance only",
000015 |       "id": "C4_FLAGS",
000016 |       "passed": true
000017 |     },
000018 |     {
000019 |       "detail": "sum A_k = diag(2,1,1)",
000020 |       "id": "RESIDUE_SUM",
000021 |       "passed": true
000022 |     },
000023 |     {
000024 |       "detail": "the four M_k generate irreducible A4 of order 12, not S4",
000025 |       "id": "FOUR_PUNCTURE_MONODROMY_IS_A4",
000026 |       "passed": true
000027 |     },
000028 |     {
000029 |       "detail": "adjoining the C4 covariance U extends A4 to the sign-twisted standard S4 representation",
000030 |       "id": "U_EXTENDS_A4_TO_S4",
000031 |       "passed": true
000032 |     },
000033 |     {
000034 |       "detail": "81 threshold patterns; all 31 with sum>=5 have rank 5; max sum=4",
000035 |       "id": "RANK1_DEG_MINUS2_81_PATTERNS",
000036 |       "passed": true
000037 |     },
000038 |     {
000039 |       "detail": "a degree -1 line lies in span(e2,e3) and has total weight at most 2/3",
000040 |       "id": "RANK1_DEG_MINUS1",
000041 |       "passed": true
000042 |     },
000043 |     {
000044 |       "detail": "81 upper-weight patterns; all 31 with sum<=3 have rank 4; min sum=4",
000045 |       "id": "RANK2_QUOTIENT_DEG_MINUS1_81_PATTERNS",
000046 |       "passed": true
000047 |     },
000048 |     {
000049 |       "detail": "the eight all-zero-weight equations have rank 7 in seven variables",
000050 |       "id": "RANK2_QUOTIENT_DEG_ZERO",
000051 |       "passed": true
000052 |     },
000053 |     {
000054 |       "detail": "all saturated rank-1 subbundles have pardeg<0 and all rank-2 quotients have pardeg>0",
000055 |       "id": "ALGEBRAIC_PARABOLIC_STABILITY",
000056 |       "passed": true
000057 |     },
000058 |     {
000059 |       "detail": "g=diag(w^2,w,w) leaves the exact residue -(2sqrt(2)/3)E12; pure BG shear is insufficient",
000060 |       "id": "INFINITY_DIAGONAL_SHEAR_AUDIT",
000061 |       "passed": true
000062 |     }
000063 |   ],
000064 |   "failures": [],
000065 |   "infinity_patch": {
000066 |     "affine_residue_sum": [
000067 |       2,
000068 |       1,
000069 |       1
000070 |     ],
000071 |     "consequence": "a further Levelt/Birkhoff lattice choice is required and may change the affine splitting frame",
000072 |     "finite_flags_unchanged_if_transition_valid": true,
000073 |     "negative_BG_transition": "g(w)=diag(w^2,w,w)",
000074 |     "pure_diagonal_shear_holomorphic": false,
000075 |     "remaining_residue": [
000076 |       [
000077 |         "0",
000078 |         "-2*sqrt(2)/3",
000079 |         "0"
000080 |       ],
000081 |       [
000082 |         "0",
000083 |         "0",
000084 |         "0"
000085 |       ],
000086 |       [
000087 |         "0",
000088 |         "0",
000089 |         "0"
000090 |       ]
000091 |     ]
000092 |   },
000093 |   "monodromy": {
000094 |     "covariance_character_distribution": {
000095 |       "-1": 9,
000096 |       "0": 8,
000097 |       "1": 6,
000098 |       "3": 1
000099 |     },
000100 |     "covariance_extension_group": "S4",
000101 |     "covariance_extension_group_order": 24,
000102 |     "four_puncture_character_distribution": {
000103 |       "-1": 3,
000104 |       "0": 8,
000105 |       "3": 1
000106 |     },
000107 |     "four_puncture_group": "A4",
000108 |     "four_puncture_group_order": 12,
000109 |     "kernel_cover": "degree 12 and genus 5 for the compactified four-puncture A4 kernel cover"
000110 |   },
000111 |   "rank1": {
000112 |     "bounds": {
000113 |       "degree_-1": "pardeg <= -1 + 2/3 = -1/3",
000114 |       "degree_-2": "pardeg <= -2 + 4/3 = -2/3",
000115 |       "degree_<=-3": "pardeg <= -3 + 8/3 = -1/3"
000116 |     },
000117 |     "degree_minus1_maximum_weight_units": 2,
000118 |     "degree_minus2_feasible_patterns": 46,
000119 |     "degree_minus2_patterns": 81,
000120 |     "maximum_weight_units": 4,
000121 |     "sum_at_least_5_full_rank": 31,
000122 |     "sum_at_least_5_patterns": 31
000123 |   },
000124 |   "rank2": {
000125 |     "bounds": {
000126 |       "quotient_degree_-1": "pardeg(Q) >= -1 + 4/3 = 1/3",
000127 |       "quotient_degree_-2": "pardeg(Q) = -2 + 8/3 = 2/3",
000128 |       "quotient_degree_0": "pardeg(Q) >= 1/3",
000129 |       "quotient_degree_>0": "pardeg(Q) > 0"
000130 |     },
000131 |     "degree_minus1_feasible_patterns": 34,
000132 |     "degree_minus1_quotient_patterns": 81,
000133 |     "degree_zero_all_weight_zero_matrix_rank": 7,
000134 |     "minimum_weight_units": 4,
000135 |     "sum_at_most_3_full_rank": 31,
000136 |     "sum_at_most_3_patterns": 31
000137 |   },
000138 |   "scope": {
000139 |     "not_proved": "identity of that affine flag object with the Deligne extension of the v115 ODE",
000140 |     "proved": "stability of the declared split parabolic object with the four raw rotated A0* flags",
000141 |     "symmetry": "C4 covariance exact; no D4 reflection linearization inferred",
000142 |     "v117_relation": "the four peripheral monodromies generate irreducible A4; U extends it to S4 and supplies the covariance data; A0* identification remains numerical"
000143 |   },
000144 |   "verdict": "PASS_SCOPED"
000145 | }