Euler Signal Bridge

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1 {
2   "schema_version": 1,
3   "claim_id": "EulerSignalBridge-FIR-2026-10-09",
4   "repository": {
5     "commit": "standalone script; no Git repository",
6     "dirty": true
7   },
8   "command": "python verify_bridge.py",
9   "environment": {
10     "software": [
11       "Python 3.12.14",
12       "NumPy 2.3.5",
13       "Matplotlib 3.10.8"
14     ],
15     "hardware": "Linux x86_64; CPU only"
16   },
17   "mathematics": {
18     "assertion_tested": "FIR stencil equals finite binomial-coordinate transfer; successive affine transfers compose; prime residual coefficients are integral.",
19     "coefficient_domain": "Python arbitrary-precision integers for all arithmetic checks; float64 only for illustrative frequency curves",
20     "conventions": "Signed Euler EGF sech(t); a(n)=E_(2n); advance shift S a(n)=a(n+1); Delta=S-I.",
21     "inputs": [
22       "Signed Euler sequence through E_94",
23       "deterministic alternating cubic integer signal",
24       "affine transfer polynomial rows"
25     ],
26     "bounds": {
27       "sample_count": 48,
28       "transfer_M": [
29         1,
30         5
31       ],
32       "phase_s": "0 <= s < M",
33       "difference_k": [
34         0,
35         6
36       ],
37       "composition_M_N": [
38         1,
39         3
40       ],
41       "composition_order": [
42         0,
43         4
44       ],
45       "primes": [
46         2,
47         3,
48         5,
49         7,
50         11
51       ]
52     },
53     "non_claims": [
54       "No Fourier transform of the Euler sequence",
55       "No universal Euler congruence follows from finite checks",
56       "No novelty claim for the FIR or binomial identities",
57       "No Lean build performed"
58     ]
59   },
60   "randomness": {
61     "used": false,
62     "generator": "none",
63     "seed": null
64   },
65   "run": {
66     "started_at": "2026-10-09T01:58:32.687088+00:00",
67     "runtime_seconds": 0.23854584200307727,
68     "exit_status": 0
69   },
70   "outputs": [
71     {
72       "path": "exact_results.json",
73       "sha256": "a5ae2204454aa4a1a2e1ab83415ba8a8a93cde6db6a0367833351902ad07dd6c"
74     },
75     {
76       "path": "Komorebi_Euler_Signal_Bridge.png",
77       "sha256": "c7b9e72a4c444f296831850f4ba97b58aae2860277ca091a5824c2803c95d0d4"
78     }
79   ],
80   "checks": [
81     "direct sample stencil versus independently expanded polynomial rows",
82     "exact composition coefficient comparison",
83     "small hand-computable Euler controls",
84     "prime coefficient divisibility"
85   ],
86   "result": "PASS: 395 exact finite assertions plus initial-value controls.",
87   "residual_risks": [
88     "A version 1 manifest records limited execution provenance; the script hash is separately supplied.",
89     "Full-branch valuation bounds require a separate mathematical argument."
90   ]
91 }

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