TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/older-paper-source-recovery-20261025/older-circle-heat-results.json
Original file SHA-256: 79230771f4a456dd2d0024515992f24acd0e91b1a630baafa1d419ab383518c9
Inclusive original lines: 1-56
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 |   "coefficient_degree_compared": 20,
000003 |   "first_difference": "5/4",
000004 |   "first_different_opening_degree": 4,
000005 |   "full_opening_coefficients_q1_to_q8": [
000006 |     "1",
000007 |     "5/4",
000008 |     "45/32",
000009 |     "355/128",
000010 |     "6515/2048",
000011 |     "38563/8192",
000012 |     "435385/65536",
000013 |     "2260355/262144"
000014 |   ],
000015 |   "log_bound_at_Q_one_half_r_one_third": "3/10",
000016 |   "original_admissible_sector_and_EM_parameter_identification": "OPEN",
000017 |   "physical_TFPT_completion_claimed": false,
000018 |   "positive_half_first_difference": "5/4",
000019 |   "positive_half_first_different_opening_degree": 6,
000020 |   "positive_half_opening_coefficients_q1_to_q8": [
000021 |     "1",
000022 |     "5/4",
000023 |     "45/32",
000024 |     "195/128",
000025 |     "3315/2048",
000026 |     "24163/8192",
000027 |     "218425/65536",
000028 |     "941475/262144"
000029 |   ],
000030 |   "positive_negative_factorization": "PASS",
000031 |   "quarters": [
000032 |     {
000033 |       "gap_label": 0,
000034 |       "positive_toeplitz_defect_label": 0,
000035 |       "twist": "1/4"
000036 |     },
000037 |     {
000038 |       "gap_label": -1,
000039 |       "positive_toeplitz_defect_label": 0,
000040 |       "twist": "3/4"
000041 |     }
000042 |   ],
000043 |   "rank_one_opening_coefficients_q1_to_q8": [
000044 |     "1",
000045 |     "5/4",
000046 |     "45/32",
000047 |     "195/128",
000048 |     "3315/2048",
000049 |     "13923/8192",
000050 |     "116025/65536",
000051 |     "480675/262144"
000052 |   ],
000053 |   "scope": "exact spectral signs, gap lines, formal coefficients and geometric tails",
000054 |   "trace_norm_tail_at_r_one_third": "1/2",
000055 |   "verdict": "PASS"
000056 | }