{
"status": "PASS",
"scope": "Bounded exact arithmetic and literal source-role checks for selected three-tradition relations; no source-total reconstruction rerun",
"grouped_assertions": 28,
"count_note": "One assertion per named relation/group; source-role checks and the scope counterexample are included, not counted as mathematical discoveries.",
"source_bindings": {
"six_spines": {
"path": "/workspace/scratch/1b40da62dcbd/three_tradition_bridge_20260928/prep/sources/spine_arithmetic_verification.json",
"sha256": "9c2c28cb244e82f0ae69104605d526c9a7b976d9b3f8d7a25bda64b96d9a8ca6",
"bytes": 21779
},
"cap_round": {
"path": "/workspace/scratch/1b40da62dcbd/three_tradition_bridge_20260928/prep/sources/cap_round_loss_identity.json",
"sha256": "238adb4d7804f3f7873b3ee15c3ac61e23e8c1f7b8bf0615c2b7b462b5c3cb14",
"bytes": 1794
},
"File52c": {
"path": "/workspace/scratch/1b40da62dcbd/three_tradition_bridge_20260928/prep/sources/File52c_latest.md",
"sha256": "a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530",
"bytes": 253860
},
"File00": {
"path": "/workspace/scratch/1b40da62dcbd/three_tradition_bridge_20260928/prep/sources/File00.md",
"sha256": "ed718a9e579978a90eefb377911933312de10a3eae1221e59758158b994de64e",
"bytes": 236437
},
"new_spine_study": {
"path": "/workspace/scratch/1b40da62dcbd/three_tradition_bridge_20260928/prep/sources/LXX_SP_Reversed_Spines.md",
"sha256": "3083e334c2834b5b53aa2acab6aa957c1e21bd28ccb404eb91ec2158d859acdb",
"bytes": 32805
}
},
"source_costs": [
"Accepted five-year SP Fall adjustment",
"Declared MT/LXX/SP Rounded source states and single-reversal paths",
"Conditional Covenant target1866=2081−215",
"MT4116 and LXX5496 actual Year-6 states distinct from Rounded states"
],
"limitations": [
"These relations are source-specific, not generic consequences of reversal.",
"The Key maps the selected heads; common first node4106 supplies an exact counterexample to mapping the entire field by the same affine operator.",
"No probability, historical-origin, held-out prediction or minimality claim."
],
"inverse_of_inverse_performed": false,
"results": [
{
"name": "selected source and generated coordinates",
"kind": "arithmetic relation",
"actual": [
14006,
2736,
13136,
14116,
1866
],
"expected": [
14006,
2736,
13136,
14116,
1866
],
"passed": true
},
{
"name": "SP cumulative inverse Flood from original source leg",
"kind": "arithmetic relation",
"actual": [
3310,
1330,
2736
],
"expected": [
3310,
1330,
2736
],
"passed": true
},
{
"name": "MT inverse Shem from one original whole span",
"kind": "arithmetic relation",
"actual": [
5436,
5430,
3450,
3456
],
"expected": [
5436,
5430,
3450,
3456
],
"passed": true
},
{
"name": "File52c explicitly registers inverse Shem and its 11270 pairing",
"kind": "source-role binding",
"actual": true,
"expected": true,
"passed": true
},
{
"name": "File00 explicitly registers actual LXX Year-6 state",
"kind": "source-role binding",
"actual": true,
"expected": true,
"passed": true
},
{
"name": "three selected 11270 pairs",
"kind": "arithmetic relation",
"actual": [
11270,
11270,
11270
],
"expected": [
11270,
11270,
11270
],
"passed": true
},
{
"name": "shared 490 coefficient",
"kind": "arithmetic relation",
"actual": [
11270,
11270
],
"expected": [
11270,
11270
],
"passed": true
},
{
"name": "720 translation joins MT inverse-Shem pair to new pair",
"kind": "arithmetic relation",
"actual": [
720,
720
],
"expected": [
720,
720
],
"passed": true
},
{
"name": "870 translation preserves full three-node partition",
"kind": "arithmetic relation",
"actual": [
870,
870,
870
],
"expected": [
870,
870,
870
],
"passed": true
},
{
"name": "three-node partitions on both sides of 870 translation",
"kind": "arithmetic relation",
"actual": [
[
11270,
1330,
12600
],
[
11270,
1330,
12600
]
],
"expected": [
[
11270,
1330,
12600
],
[
11270,
1330,
12600
]
],
"passed": true
},
{
"name": "existing cap loss changes under source rounding",
"kind": "arithmetic relation",
"actual": [
488,
[
115,
250,
120
],
485
],
"expected": [
488,
[
115,
250,
120
],
485
],
"passed": true
},
{
"name": "raw Creation then accepted Fall gives 490",
"kind": "arithmetic relation",
"actual": [
9170,
8685,
8680,
485,
490
],
"expected": [
9170,
8685,
8680,
485,
490
],
"passed": true
},
{
"name": "source coefficient is rounded cap loss plus accepted Fall adjustment",
"kind": "arithmetic relation",
"actual": 490,
"expected": 490,
"passed": true
},
{
"name": "same MT/SP contraction occurs on different legs",
"kind": "arithmetic relation",
"actual": [
[
0,
-1980
],
[
-1980,
0
]
],
"expected": [
[
0,
-1980
],
[
-1980,
0
]
],
"passed": true
},
{
"name": "MT-SP cumulative head gap survives both inverse constructions",
"kind": "arithmetic relation",
"actual": [
610,
610,
610
],
"expected": [
610,
610,
610
],
"passed": true
},
{
"name": "LXX fixed segment doubles to SP fixed segment",
"kind": "arithmetic relation",
"actual": 8680,
"expected": 8680,
"passed": true
},
{
"name": "head separation uses two copies of same coefficient",
"kind": "arithmetic relation",
"actual": 980,
"expected": 980,
"passed": true
},
{
"name": "Key25/23 held at selected Covenant reaches SP inverse head",
"kind": "arithmetic relation",
"actual": 14116,
"expected": 14116,
"passed": true
},
{
"name": "reciprocal Key23/25 returns LXX inverse head",
"kind": "arithmetic relation",
"actual": 13136,
"expected": 13136,
"passed": true
},
{
"name": "fixed Key and generated heads recover Covenant pivot",
"kind": "arithmetic relation",
"actual": 1866,
"expected": 1866,
"passed": true
},
{
"name": "70-fold covenant measures of same Key relation",
"kind": "arithmetic relation",
"actual": [
11270,
12250,
980
],
"expected": [
11270,
12250,
980
],
"passed": true
},
{
"name": "common first node is not mapped to itself",
"kind": "scope counterexample",
"actual": [
"98918/23",
false
],
"expected": [
"98918/23",
false
],
"passed": true
},
{
"name": "common first node really belongs to both complete paths",
"kind": "scope binding",
"actual": [
4106,
4106
],
"expected": [
4106,
4106
],
"passed": true
},
{
"name": "Actual-Year-6 to SP-inverse target ladder",
"kind": "arithmetic relation",
"actual": [
1380,
1380
],
"expected": [
1380,
1380
],
"passed": true
},
{
"name": "reflection about actual MT Year-6 exchanges selected LXX and SP nodes",
"kind": "arithmetic relation",
"actual": [
2736,
5496,
4116
],
"expected": [
2736,
5496,
4116
],
"passed": true
},
{
"name": "MT14006 distances along declared target ladder",
"kind": "arithmetic relation",
"actual": [
8510,
9890,
11270
],
"expected": [
8510,
9890,
11270
],
"passed": true
},
{
"name": "rounded Creation separation agrees with ladder step",
"kind": "arithmetic relation",
"actual": 1380,
"expected": 1380,
"passed": true
},
{
"name": "existing SP/MT 9890 translated interval",
"kind": "arithmetic relation",
"actual": [
9890,
9890
],
"expected": [
9890,
9890
],
"passed": true
}
]
}
Evidence
bridge algebra verification.json
Linked sources and evidence
Edition and provenance
bridge_algebra_verification.json
SHA-256 1621b9280c9df1a1607027257cca56cd2a9282e75ab5b6e3f6f2b9dd9f864e70
C480–C1634/Research_Cycles/C1432/bridge_algebra_verification.json