{
"status": "PASS",
"verified_utc": "2026-09-29T01:32:57.436541+00:00",
"grouped_check_count": 274,
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"method": "Independent arithmetic digit reversal using integer divmod; exact fractions; research.digest-compatible canonical JSON hashes.",
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"pass": true,
"actual": 990,
"expected": 990
},
{
"name": "partition law alternate: SP_regular",
"pass": true,
"actual": -6300,
"expected": -6300
},
{
"name": "partition law refined: SP_regular",
"pass": true,
"actual": -1800,
"expected": -1800
},
{
"name": "partition law alternate: SP_cumulative",
"pass": true,
"actual": 0,
"expected": 0
},
{
"name": "partition law refined: SP_cumulative",
"pass": true,
"actual": 0,
"expected": 0
},
{
"name": "model/partition_law",
"pass": true,
"actual": {
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"dL": 0,
"dU": 0,
"alternate_change": 0,
"refined_change": 0
},
"MT_cumulative": {
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"dU": -990,
"alternate_change": 0,
"refined_change": 990
},
"LXX_regular": {
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"dU": -990,
"alternate_change": 0,
"refined_change": 990
},
"LXX_cumulative": {
"dL": 0,
"dU": -990,
"alternate_change": 990,
"refined_change": 990
},
"SP_regular": {
"dL": -4500,
"dU": 1800,
"alternate_change": -6300,
"refined_change": -1800
},
"SP_cumulative": {
"dL": 0,
"dU": 0,
"alternate_change": 0,
"refined_change": 0
}
},
"expected": {
"MT_regular": {
"dL": 0,
"dU": 0,
"alternate_change": 0,
"refined_change": 0
},
"MT_cumulative": {
"dL": -990,
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},
"LXX_regular": {
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"dU": -990,
"alternate_change": 0,
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},
"LXX_cumulative": {
"dL": 0,
"dU": -990,
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"refined_change": 990
},
"SP_regular": {
"dL": -4500,
"dU": 1800,
"alternate_change": -6300,
"refined_change": -1800
},
"SP_cumulative": {
"dL": 0,
"dU": 0,
"alternate_change": 0,
"refined_change": 0
}
}
},
{
"name": "model/partition_classes membership",
"pass": true,
"actual": {
"(0, 0)": [
"MT_regular",
"SP_cumulative"
],
"(-990, -990)": [
"LXX_regular",
"MT_cumulative"
],
"(0, -990)": [
"LXX_cumulative"
],
"(-4500, 1800)": [
"SP_regular"
]
},
"expected": {
"(0, 0)": [
"MT_regular",
"SP_cumulative"
],
"(-990, -990)": [
"LXX_regular",
"MT_cumulative"
],
"(0, -990)": [
"LXX_cumulative"
],
"(-4500, 1800)": [
"SP_regular"
]
}
},
{
"name": "model/full_node_displacements",
"pass": true,
"actual": {
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1406,
2456,
3056,
4106
],
"inverse_path": [
1406,
6416,
7016,
12026
],
"node_displacements": [
0,
3960,
3960,
7920
],
"retained_edge": 600
},
"LXX_regular": {
"source_path": [
1406,
3236,
3836,
5486
],
"inverse_path": [
1406,
5216,
5816,
11426
],
"node_displacements": [
0,
1980,
1980,
5940
],
"retained_edge": 600
},
"SP_regular": {
"source_path": [
1406,
3106,
3706,
4406
],
"inverse_path": [
1406,
8506,
9106,
9806
],
"node_displacements": [
0,
5400,
5400,
5400
],
"retained_edge": 600
},
"MT_cumulative": {
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1406,
4836,
5436,
14006
],
"inverse_path": [
1406,
4836,
5436,
13016
],
"node_displacements": [
0,
0,
0,
-990
],
"retained_edge": 600
},
"LXX_cumulative": {
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1406,
5746,
6346,
14896
],
"inverse_path": [
1406,
5746,
6346,
11926
],
"node_displacements": [
0,
0,
0,
-2970
],
"retained_edge": 600
},
"SP_cumulative": {
"source_path": [
1406,
4716,
5316,
13396
],
"inverse_path": [
1406,
2736,
3336,
11416
],
"node_displacements": [
0,
-1980,
-1980,
-1980
],
"retained_edge": 600
}
},
"expected": {
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1406,
2456,
3056,
4106
],
"inverse_path": [
1406,
6416,
7016,
12026
],
"node_displacements": [
0,
3960,
3960,
7920
],
"retained_edge": 600
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"MT_cumulative": {
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1406,
4836,
5436,
14006
],
"inverse_path": [
1406,
4836,
5436,
13016
],
"node_displacements": [
0,
0,
0,
-990
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"retained_edge": 600
},
"LXX_regular": {
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1406,
3236,
3836,
5486
],
"inverse_path": [
1406,
5216,
5816,
11426
],
"node_displacements": [
0,
1980,
1980,
5940
],
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"LXX_cumulative": {
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1406,
5746,
6346,
14896
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"inverse_path": [
1406,
5746,
6346,
11926
],
"node_displacements": [
0,
0,
0,
-2970
],
"retained_edge": 600
},
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1406,
3106,
3706,
4406
],
"inverse_path": [
1406,
8506,
9106,
9806
],
"node_displacements": [
0,
5400,
5400,
5400
],
"retained_edge": 600
},
"SP_cumulative": {
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1406,
4716,
5316,
13396
],
"inverse_path": [
1406,
2736,
3336,
11416
],
"node_displacements": [
0,
-1980,
-1980,
-1980
],
"retained_edge": 600
}
}
},
{
"name": "model/upper_branch_translations",
"pass": true,
"actual": {
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3960,
3960,
7920
],
"uniform": false
},
"LXX_regular": {
"upper_offsets": [
1980,
1980,
5940
],
"uniform": false
},
"SP_regular": {
"upper_offsets": [
5400,
5400,
5400
],
"uniform": true
},
"MT_cumulative": {
"upper_offsets": [
0,
0,
-990
],
"uniform": false
},
"LXX_cumulative": {
"upper_offsets": [
0,
0,
-2970
],
"uniform": false
},
"SP_cumulative": {
"upper_offsets": [
-1980,
-1980,
-1980
],
"uniform": true
}
},
"expected": {
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3960,
3960,
7920
],
"uniform": false
},
"MT_cumulative": {
"upper_offsets": [
0,
0,
-990
],
"uniform": false
},
"LXX_regular": {
"upper_offsets": [
1980,
1980,
5940
],
"uniform": false
},
"LXX_cumulative": {
"upper_offsets": [
0,
0,
-2970
],
"uniform": false
},
"SP_regular": {
"upper_offsets": [
5400,
5400,
5400
],
"uniform": true
},
"SP_cumulative": {
"upper_offsets": [
-1980,
-1980,
-1980
],
"uniform": true
}
}
},
{
"name": "model/MT_SP_cumulative_preservation",
"pass": true,
"actual": {
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120,
490
],
"inverse_legs_difference": [
2100,
-1490
],
"head_gaps": [
610,
610,
610
],
"intermediate_gaps": [
120,
2100
]
},
"expected": {
"source_legs_difference": [
120,
490
],
"inverse_legs_difference": [
2100,
-1490
],
"head_gaps": [
610,
610,
610
],
"intermediate_gaps": [
120,
2100
]
}
},
{
"name": "model/LXX_MT_cumulative",
"pass": true,
"actual": {
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"source_upper_gap": -20,
"inverse_lower_gap": 910,
"inverse_upper_gap": -2000,
"source_head_gap": 890,
"inverse_head_gap": -1090
},
"expected": {
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"source_upper_gap": -20,
"inverse_lower_gap": 910,
"inverse_upper_gap": -2000,
"source_head_gap": 890,
"inverse_head_gap": -1090
}
},
{
"name": "model/LXX_SP_cumulative",
"pass": true,
"actual": {
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"inverse_gap": -480,
"source_triangle": 1500,
"inverse_triangle": -480,
"extra_contraction": -1980
},
"expected": {
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"source_triangle": 1500,
"inverse_triangle": -480,
"extra_contraction": -1980
}
},
{
"name": "model/mode_interaction",
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"actual": {
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"SP_minus_LXX_cumulative": 480,
"difference_of_differences": 690,
"equivalent_mode_difference": 690
},
"expected": {
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"SP_minus_LXX_cumulative": 480,
"difference_of_differences": 690,
"equivalent_mode_difference": 690
}
},
{
"name": "source LXX Noah row",
"pass": true,
"actual": 3836,
"expected": 3836
},
{
"name": "source LXX Shem row",
"pass": true,
"actual": 3336,
"expected": 3336
},
{
"name": "source LXX original Noah to Shem",
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"actual": 500,
"expected": 500
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{
"name": "model/Shem_incidences",
"pass": true,
"actual": {
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2736,
3336,
11416
],
"SP_completed_path": [
6,
4106,
5436,
6036,
14116
],
"SP_inverse_Shem_at1406": 3336,
"LXX_regular_Shem": 3336,
"SP_completed_inverse_Flood": 5436,
"MT_cumulative_Shem": 5436,
"source_state": "nativeCainanON; common selectedTerah70 andRoundedMoses1526; strictcomparison omitsShem+2"
},
"expected": {
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2736,
3336,
11416
],
"SP_completed_path": [
6,
4106,
5436,
6036,
14116
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"SP_inverse_Shem_at1406": 3336,
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"SP_completed_inverse_Flood": 5436,
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"source_state": "nativeCainanON; common selectedTerah70 andRoundedMoses1526; strictcomparison omitsShem+2"
}
},
{
"name": "model/Covenant_path_scope",
"pass": true,
"actual": [
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"LXX": 6,
"Key_image": "-3582/23",
"SP": 6,
"matches": false
},
{
"role": "reversed_Conquest",
"LXX": 4106,
"Key_image": "98918/23",
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},
{
"role": "reversed_Flood",
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"Key_image": "194168/23",
"SP": 5436,
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},
{
"role": "head",
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"SP": 14116,
"matches": true
}
],
"expected": [
{
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"SP": 6,
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},
{
"role": "reversed_Conquest",
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"SP": 4106,
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{
"role": "reversed_Flood",
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"SP": 5436,
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},
{
"role": "head",
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"matches": true
}
]
},
{
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2700,
-190
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"target": 14116
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2700,
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},
{
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{
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{
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]
},
{
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{
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"expected": {
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}
},
{
"name": "C1432 cap plus accepted Fall",
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490
],
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]
},
{
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"paired_intervals": [
[
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],
[
14116,
4116
]
]
},
"expected": {
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"paired_intervals": [
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4106
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[
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]
}
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{
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"anchor_only": "324418/23",
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"expected": {
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{
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"target_gap": 40,
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"cumulative_output": 386,
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"expected": {
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}
},
{
"name": "model/paired_anchor_comparison",
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"actual": {
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"cumulative_result": "6698/23",
"difference": "1000/23",
"predicted_difference": "1000/23"
},
"LXX": {
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"difference": 0,
"predicted_difference": 0
},
"SP": {
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"cumulative_result": "7918/23",
"difference": 60,
"predicted_difference": 60
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},
"expected": {
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"difference": "1000/23",
"predicted_difference": "1000/23"
},
"LXX": {
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"difference": 0,
"predicted_difference": 0
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"SP": {
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"difference": 60,
"predicted_difference": 60
}
}
},
{
"name": "model/stage_Key_interaction",
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"actual": {
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"Covenant_two_stage_residual": "-5400/23",
"LXX_two_stage_regular_join": "14278/23",
"LXX_two_stage_cumulative_join": "14278/23",
"positive_stage_commutator": "5400/23"
},
"expected": {
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"Covenant_two_stage_residual": "-5400/23",
"LXX_two_stage_regular_join": "14278/23",
"LXX_two_stage_cumulative_join": "14278/23",
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}
},
{
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"actual": {
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"later_anchors": [
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6
]
}
},
"expected": {
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6
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}
}
},
{
"name": "source binding filenames unique",
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"actual": 15,
"expected": 15
},
{
"name": "evidence exists: File52c_latest.md",
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"actual": true,
"expected": true
},
{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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"actual": "## Local changes become complete chronological fields\n\nWrite an ordinary row as begetting age \\(b\\), remaining years \\(r\\), and lifespan \\(L=b+r\\). A compatible change has the form\n\n\\[\n(b,r,L)\\longmapsto(b+d,\\ r+e-d,\\ L+e).\n\\]\n\nHere \\(d\\) changes the birth interval and \\(e\\) changes lifespan. If \\(e=0\\), years move between the two parts of a life while its total stays fixed. If \\(e=d\\), remaining years stay fixed while both the begetting age and lifespan rise. These are different local mechanisms even when the same century appears.\n\n| Row and comparison | Begetting age | Remaining years | Lifespan | What the change preserves |\n|---|---:|---:|---:|---|\n| Adam, MT → LXX | 130 → 230 | 800 → 700 | 930 → 930 | Lifespan |\n| Peleg, MT → LXX | 30 → 130 | 209 → 209 | 239 → 339 | Remaining years |\n| Eber, MT → SP | 34 → 134 | 430 → 270 | 464 → 404 | Neither part nor lifespan; \\(d=100,e=-60\\) |\n| Cainan, native LXX insertion | 130 | 330 | 460 | Adds a named row with two distinct measures |\n\nThus Regular and Cumulative differences are not rival readings of a single change total. They select different components of the source rows. Adam’s change is visible to a Regular birth chain and invisible to a lifespan sum. Peleg’s change is visible to both. Cainan contributes 130 or 460 according to the declared measurement.\n\nSource basis: File18 selected rows; Strategy §3.2; C1162–C1189.\n\nOnce the row measure and terminal are fixed, ordered addition generates the entire field. If \\(w_j\\) are the selected intervals downstream of a boundary and \\(a\\) is the terminal,\n\n\\[\nX_i=a+\\sum_{j\\ge i}w_j.\n\\]\n\nThe difference between adjacent boundaries recovers the intervening interval. Consequently, a complete field records where changes occur; its head total records only their sum.\n\nThe current model reconstructs the changes in all nineteen shared MT/LXX genealogical rows. Five amplitudes summarize their located changes: the repeated century \\(u=100\\), Lamech’s lifespan change \\(-24\\), the Arphaxad/Shelah lifespan addition \\(27\\), Eber’s lifespan addition \\(40\\), and Nahor’s lifespan addition \\(60\\). The relation \\(40+60=100\\) reduces this description to four amplitudes if retained as a further source condition. The named rows on which each change acts remain necessary.\n\nOn the matched Cainan-OFF comparison, the Regular head difference is 1250 and the lifespan difference is 430. Native LXX Cainan contributes another 130 and 460, making 1380 and 890. The two measurements therefore change differently even though they share the same inserted person.\n\nThe century is a useful summary of paired source rows, not an extra independent input after those rows are given. This model explains the changes across a complete selected family. It does not derive every source age from the amplitudes or prove that the particular changes occurred in this historical order.\n\nSource basis: C1182–C1189; complete source-row packet and five-amplitude model.\n\n## The Regular kernel has two generators\n\nThe first generator is the **located sequence of row changes**. In the matched Cainan-OFF comparison, the complete MT/LXX Regular difference from Adam through Abraham is\n\n| Boundary | LXX minus MT |\n|---|---:|\n| Adam | 1250 |\n| Seth | 1150 |\n| Enosh | 1050 |\n| Kenan | 950 |\n| Mahalalel | 850 |\n| Jared | 750 |\n| Enoch | 750 |\n| Methuselah | 650 |\n| Lamech | 650 |\n| Noah | 650 |\n| Shem | 650 |\n| Arphaxad | 650 |\n| Shelah | 550 |\n| Eber | 450 |\n| Peleg | 350 |\n| Reu | 250 |\n| Serug | 150 |\n| Nahor | 50 |\n| Terah | 0 |\n| Abraham | 0 |\n\nThe steps record source changes at particular names. Six pre-Flood century changes account for the 600 difference between the Creation level 1250 and Noah level 650. Native Cainan adds 130 from Arphaxad upstream, retaining the native 1380/780 levels separately.\n\nThe second generator is the **finite field of source variants**. Let the Terah difference be \\(T=60\\), Cainan’s Regular interval \\(C=130\\), and the separately sourced Sojourn choice \\(S=215\\). Their eight combinations give:\n\n| Choice | Offset |\n|---|---:|\n| Base | 0 |\n| T | 60 |\n| C | 130 |\n| T+C | 190 |\n| S | 215 |\n| T+S | 275 |\n| C+S | 345 |\n| T+C+S | 405 |\n\nThe consecutive gaps are \\(60|70|60|25|60|70|60\\). The 70 and 25 are differences between combinations; they are not additional switches.\n\nThese structures meet in the Strategy’s fivefold formulas:\n\n\\[\n1250=5(C+2T),\\qquad650=5C.\n\\]\n\nThe row mechanism gives \\(12.5u\\) and \\(6.5u\\), where the observed century is \\(u=100\\). Requiring the fivefold form yields \\(C=1.3u\\) and \\(T=.6u\\). Thus the coefficient five expresses a calibration between two source mechanisms. It does not itself generate the patriarchal ages.\n\nSP supplies a further located comparison. Its post-Flood birth additions total 650; its pre-Flood shortening is \\(100+120+130=350\\) in the completed-year comparison, leaving 300. The Lamech contribution retains its nominal 129 plus the one-year boundary completion, counted once. These locations explain more than the identity \\(950\\pm300=1250,650\\): the latter is a useful description of the resulting pair, while the row model explains its construction.\n\nSource basis: File07 finite states; File18 source rows; C1253–C1264.\n\n## SP births constrain its lifespan field\n\nThe SP mechanism links the two chronological measurements directly. Reconstruct the ancestral births, measure each birth’s inclusive capacity to the Flood boundary, and cap the comparison lifespan at that capacity:\n\n\\[\nL'_i=\\min(L_i,c_i).\n\\]\n\nThe native SP capacities below use Noah’s 600-year interval plus the inclusive one. The lifespans compared are the selected MT baseline values.\n\n| Ancestor | Baseline life | SP capacity | Selected capped life | Reduction |\n|---|---:|---:|---:|---:|\n| Adam | 930 | 1307 | 930 | 0 |\n| Seth | 912 | 1177 | 912 | 0 |\n| Enosh | 905 | 1072 | 905 | 0 |\n| Kenan | 910 | 982 | 910 | 0 |\n| Mahalalel | 895 | 912 | 895 | 0 |\n| Jared | 962 | 847 | 847 | 115 |\n| Enoch | 365 | 785 | 365 | 0 |\n| Methuselah | 969 | 720 | 720 | 249 |\n| Lamech | 777 | 653 | 653 | 124 |\n\nOne rule reproduces the nine outputs, including the three reductions totaling \\(115+249+124=488\\). Shorter birth paths bring the Flood boundary inside those three baseline lives. Enoch illustrates why an earlier birth boundary does not automatically shorten every life: his baseline 365 remains below capacity.\n\nThe relation is especially transparent for Methuselah. In the MT comparison, \\(969=187+182+600\\). The SP birth changes remove \\(120+130\\), while the inclusive boundary restores one: \\(250-1=249\\). This produces the selected 720 without treating its reduction as an unrelated adjustment.\n\nEber and official SP Terah supply another 60 each after the Flood, making the total lifespan displacement \\(488+120=608\\). Ideal Terah 205 is a separate state from official Terah 145.\n\nThis is a conditional mechanism for the selected SP field: the birth ages, baseline lives and count convention are supplied. A capped result alone cannot recover how far its original life exceeded the boundary. That missing excess remains part of a reversible record, rather than becoming a newly generated source value.\n\nSource basis: File18 native rows; C1132–C1161.\n\nThe same located changes now supply the SP equal-gain rectangle. Starting with the selected standard MT frames and the initial 1446 Exodus reference, the source construction gives two radii:\n\n\\[\n\\begin{aligned}\nR&=(4114-1446)+650-350-215+7=2760,\\\\\nC&=(14004-1446)-488-120+10=11960.\n\\end{aligned}\n\\]\n\nThe Regular line retains the post-Flood additions, pre-Flood shortening, Sojourn choice and seven-year source opening. The Cumulative line retains the cap losses, post-Flood lifespan changes and ten-year source opening. Those openings and absolute frames remain source premises.\n\n| Mode | Source opening | Radius from 1446 | Appointed Key | Expanded radius | Resulting common anchor |\n|---|---:|---:|---:|---:|---:|\n| Regular | 4206 | 2760 | \\(70/69\\) | 2800 | 1406 |\n| Cumulative | 13406 | 11960 | \\(300/299\\) | 12000 | 1406 |\n\nDuring these Key expansions, the source openings 4206 and 13406 are held fixed; the lower comparison endpoint moves from 1446 to 1406. Both radii gain forty. Their difference stays 9200; Priestly expansion then gives \\(9200\\times25/23=10000\\).\n\nThe equal-gain condition is \\(R/69=C/299\\), or \\(3C=13R\\). Before the source openings, the radii are 2753 and 11950 and their balance is \\(3C-13R=61\\). Adding seven and ten changes that balance by \\(3(10)-13(7)=-61\\). This identifies precisely how the source packet closes the rectangle.\n\nThe advance is an explanation of where its two inputs come from. The equality of gains follows once those inputs and Keys are fixed; it is one connected family of consequences. The cap mechanism does not independently select the source openings or the Exodus anchor.\n\nSource basis: Strategy §4.3; Report IV; C1223–C1230.\n\n## Rounded rows form the Moses family\n\nThe Moses-centred construction uses the MT Terah-70, Cainan-OFF state, excludes the separate Shem +2 convention, and holds Moses at 1526 BC. It follows an ordered Regular chronological path. Its late edges include events as well as begetting ages: Jacob is 91 at Joseph’s birth, Joseph is 39 at Entry, and Entry precedes Moses by 350. Row rounding gives 90, 40 and 350, preserving their combined 480.\n\nThe complete path contains twenty-five nodes. Five named blocks expose its structure:\n\n| Segment | Exact sum | Sum of rounded rows | Exact minus Rounded |\n|---|---:|---:|---:|\n| Adam → Seth | 130 | 130 | 0 |\n| Seth → Enoch | 492 | 490 | 2 |\n| Enoch → Arphaxad | 1034 | 1030 | 4 |\n| Arphaxad → Reu | 129 | 130 | −1 |\n| Reu → Moses | 801 | 800 | 1 |\n| **Adam → Moses** | **2586** | **2580** | **6** |\n\nThe whole Rounded path gives \\(2580=6\\times430\\). Removing its first block gives Seth-to-Moses \\(2450=5\\times490\\); removing the next gives Enoch-to-Moses \\(1960=4\\times490\\). These are connected measurements of one reconstructed path.\n\nThe post-Flood partition is especially revealing: strict Actual \\(129+801\\) becomes Rounded \\(130+800\\), reproducing the two parts of Adam’s selected life while retaining the total 930. Eber, Reu and Nahor’s rounding residuals account for the internal shift, with the Jacob/Joseph residuals cancelling later. The relationship belongs to the selected path and its rounding rule.\n\nSource basis: File18, File51a and File52c; C1232–C1252.\n\nFor exact reconstruction, record both the nearest-five rounded value and its residual:\n\n\\[\nQ(x)=5\\left\\lfloor\\frac{x+2}{5}\\right\\rfloor,\\qquad \\rho(x)=x-Q(x).\n\\]\n\nFor an individual integer row, the residual lies between −2 and 2. Along a path, the residuals add. All twenty-five exact coordinates are recovered by adding the appropriate downstream residual sum to each Rounded coordinate.\n\nThe whole path’s accumulated residual is six. Therefore Rounded Creation 4106 plus six recovers strict Actual Creation 4112. Standard Actual 4114 additionally includes the separate Shem +2 convention. Rounding the exact total 2586 once would give 2585, not the row-rounded 2580; likewise rounding the exact 1034 block once gives 1035 rather than its row-rounded 1030. The construction’s order matters.\n\nThe 130 bridge also follows from the selected cycles: \\(6(430)-5(490)=130\\). It is not an independent selector of Moses. More generally, \\(430m-490n=130\\) has positive solutions \\(m=6+49k,n=5+43k\\) for nonnegative \\(k\\). The named source path supplies the actual selection.\n\nNative LXX extends the same construction with its own rows and Cainan. Its twenty-six-node Rounded path totals 3960 above Moses, placing Creation at 5486. The gap from MT is \\(600+650+130=1380\\). Its corresponding post-Flood blocks are 660 and 1050, compared with MT’s 130 and 800. On the selected SP post-Flood comparison the blocks are 530 and 1050. The transmitted SP 4411 does not by itself supply a newly reconstructed complete Rounded SP genealogical field. The accepted Fall construction introduced below now supplies the complete selected SP trunks, using 4406 Regular and 13396 Cumulative as their derived Fall heads.\n\nThis is the bridge to File52c. The complete MT path supplies Creation 4106 and Noah 3056. File52c separately provides Nativity 6, Conquest 1406 and Flood 2456. Their roles together determine the admitted original duration words. Arphaxad’s birth also occupies 2456 in the reconstructed path; equal coordinates do not merge that birth with the Flood event.\n\nSource basis: C1240–C1252, C1273–C1279.\n\n## Original duration words and the inverse backbone\n\nFile52c’s decimal operation reverses the significant digits of each original span while retaining its trailing-zero places. Thus 1650 becomes 5610, 1050 becomes 5010, and 1400 becomes 4100. A source-appointed partition is part of the operation: the regular 2700-year Creation-to-Conquest span, treated whole, produces 7200; its 1650+1050 partition produces 5610+5010=10620. The named Flood division therefore carries information that the total alone omits. [File52c §§1.2,3.3–3.4]\n\nWith Conquest 1406 BC held, the regular primary path gives\n\n\\[\n1406+5610+5010=12026.\n\\]\n\nThe cumulative primary path uses Creation 14006 and Flood 4836, giving 9170+3430. Its one-pass images are 7190+3430, also totaling 10620 and rebuilding 12026 BC. This convergence concerns the specified primary paths; their source breakpoints remain distinct. [File52c §3.3]\n\nA decimal-register calculation explains the two-component convergence. For two original spans, each ten times a three-digit core ending in a nonzero digit, a Regular total 2700 forces transformed total 10620. In that same register, a Cumulative total 12600 permits transformed totals 10620 or 11610; its actual 917 and 343 cores select the 10620 branch. The source supplies the named split. The technical companion retains the proof and the alternative branch. [C938–C947]\n\nThe continuation to 14726 BC supplies an additional original interval: Conquest 1406 to Nativity 6 is 1400 years, whose one-pass image is 4100. Moving the held anchor from 1406 to 6 and including this leg changes the rebuilt endpoint by 4100−1400=2700. Therefore 12026 becomes 14726. The explanation retains both the original tail and the anchor change. [File52c §3.4; C952]\n\nThe four admitted MT paths can be compared compactly. The divisions are listed outward from the held 6 BC anchor toward earlier source dates:\n\n| Source path after Nativity | Original spans | One-pass spans |\n|---|---|---|\n| Regular: Conquest–Flood–Creation | 1400 + 1050 + 1650 | 4100 + 5010 + 5610 |\n| Regular: Conquest–Noah–Creation | 1400 + 1650 + 1050 | 4100 + 5610 + 5010 |\n| Regular: Conquest–Flood–Noah–Creation | 1400 + 1050 + 600 + 1050 | 4100 + 5010 + 600 + 5010 |\n| Cumulative primary: Conquest–Flood–Creation | 1400 + 3430 + 9170 | 4100 + 3430 + 7190 |\n\nEvery MT row in this table totals 14720 and therefore ends at 14726 BC. The Noah alternatives preserve the regular result through their particular component relations. The new genealogy interface matches the first three original rows exactly and reuses their established images; the cumulative row retains its own source measurement. The first transformed leg ends at 4106 BC, numerically equal to original regular Creation, but it remains the generated endpoint of the Conquest leg. This preserves the distinction between a shared coordinate and a shared chronological role. [File52c §3.4; C1274–C1276]\n\nThe same 12026 anchor also divides the selected Actual Creation bridge. Its cumulative and regular completion endpoints are 14004 and 4114 BC, respectively. Their 9890-year separation splits into\n\n\\[\n14004-12026=1978,\\qquad 12026-4114=7912=4\\times 1978.\n\\]\n\nPriestly expansion by 25/23 gives 2150 and 8600, preserving 1:4 and totaling 10750. These expanded parts belong to the expanded total. The Rounded endpoints 14006/4106 instead divide into 1980+7920=9900, again 1:4. Both selected pairs satisfy\n\n\\[\n12026=\\frac{4C+R}{5},\n\\]\n\nwhere `C,R` are their cumulative and regular Creation coordinates. Moving Rounded→Actual changes them by −2 and +8, preserving the weighted value because `4(−2)+8=0`. The regular +8 combines the six-year row residual with the separate standard Shem +2 convention; selecting the cumulative completion endpoint supplies its −2. The matching weight is derived from these selected values. It expresses their compatibility without making the state selections disappear. [File52c §3.14; C932–C948]\n\nThe same division is visible in the original one-pass convergence. The regular span grows from 2700 to 10620, gaining 7920; the cumulative span falls from 12600 to 10620, losing 1980. The gain is four times the loss. Thus the weighted coordinate and the inverse construction express a shared relation among these source values. Once the inputs are fixed, the two descriptions belong to one connected calculation. The historical significance rests on why those particular intervals and their named divisions occur in the source family. [C937–C948]\n\nThe completed backbone also has a 9890-year interval to the Conquest-held cumulative Flood companion at 4836 BC: `14726−4836=9890=23×430`. The Flood companion retains the 1406 anchor and unchanged 3430 span; it is a separate anchored comparison from the completed Nativity-held path. Its interval matches the Actual Creation bridge in magnitude, while the original Rounded Creation gap stays 9900. The correspondence links declared measurements without replacing their endpoints or chronological roles. [File52c §3.6]\n\n",
"expected": "## Local changes become complete chronological fields\n\nWrite an ordinary row as begetting age \\(b\\), remaining years \\(r\\), and lifespan \\(L=b+r\\). A compatible change has the form\n\n\\[\n(b,r,L)\\longmapsto(b+d,\\ r+e-d,\\ L+e).\n\\]\n\nHere \\(d\\) changes the birth interval and \\(e\\) changes lifespan. If \\(e=0\\), years move between the two parts of a life while its total stays fixed. If \\(e=d\\), remaining years stay fixed while both the begetting age and lifespan rise. These are different local mechanisms even when the same century appears.\n\n| Row and comparison | Begetting age | Remaining years | Lifespan | What the change preserves |\n|---|---:|---:|---:|---|\n| Adam, MT → LXX | 130 → 230 | 800 → 700 | 930 → 930 | Lifespan |\n| Peleg, MT → LXX | 30 → 130 | 209 → 209 | 239 → 339 | Remaining years |\n| Eber, MT → SP | 34 → 134 | 430 → 270 | 464 → 404 | Neither part nor lifespan; \\(d=100,e=-60\\) |\n| Cainan, native LXX insertion | 130 | 330 | 460 | Adds a named row with two distinct measures |\n\nThus Regular and Cumulative differences are not rival readings of a single change total. They select different components of the source rows. Adam’s change is visible to a Regular birth chain and invisible to a lifespan sum. Peleg’s change is visible to both. Cainan contributes 130 or 460 according to the declared measurement.\n\nSource basis: File18 selected rows; Strategy §3.2; C1162–C1189.\n\nOnce the row measure and terminal are fixed, ordered addition generates the entire field. If \\(w_j\\) are the selected intervals downstream of a boundary and \\(a\\) is the terminal,\n\n\\[\nX_i=a+\\sum_{j\\ge i}w_j.\n\\]\n\nThe difference between adjacent boundaries recovers the intervening interval. Consequently, a complete field records where changes occur; its head total records only their sum.\n\nThe current model reconstructs the changes in all nineteen shared MT/LXX genealogical rows. Five amplitudes summarize their located changes: the repeated century \\(u=100\\), Lamech’s lifespan change \\(-24\\), the Arphaxad/Shelah lifespan addition \\(27\\), Eber’s lifespan addition \\(40\\), and Nahor’s lifespan addition \\(60\\). The relation \\(40+60=100\\) reduces this description to four amplitudes if retained as a further source condition. The named rows on which each change acts remain necessary.\n\nOn the matched Cainan-OFF comparison, the Regular head difference is 1250 and the lifespan difference is 430. Native LXX Cainan contributes another 130 and 460, making 1380 and 890. The two measurements therefore change differently even though they share the same inserted person.\n\nThe century is a useful summary of paired source rows, not an extra independent input after those rows are given. This model explains the changes across a complete selected family. It does not derive every source age from the amplitudes or prove that the particular changes occurred in this historical order.\n\nSource basis: C1182–C1189; complete source-row packet and five-amplitude model.\n\n## The Regular kernel has two generators\n\nThe first generator is the **located sequence of row changes**. In the matched Cainan-OFF comparison, the complete MT/LXX Regular difference from Adam through Abraham is\n\n| Boundary | LXX minus MT |\n|---|---:|\n| Adam | 1250 |\n| Seth | 1150 |\n| Enosh | 1050 |\n| Kenan | 950 |\n| Mahalalel | 850 |\n| Jared | 750 |\n| Enoch | 750 |\n| Methuselah | 650 |\n| Lamech | 650 |\n| Noah | 650 |\n| Shem | 650 |\n| Arphaxad | 650 |\n| Shelah | 550 |\n| Eber | 450 |\n| Peleg | 350 |\n| Reu | 250 |\n| Serug | 150 |\n| Nahor | 50 |\n| Terah | 0 |\n| Abraham | 0 |\n\nThe steps record source changes at particular names. Six pre-Flood century changes account for the 600 difference between the Creation level 1250 and Noah level 650. Native Cainan adds 130 from Arphaxad upstream, retaining the native 1380/780 levels separately.\n\nThe second generator is the **finite field of source variants**. Let the Terah difference be \\(T=60\\), Cainan’s Regular interval \\(C=130\\), and the separately sourced Sojourn choice \\(S=215\\). Their eight combinations give:\n\n| Choice | Offset |\n|---|---:|\n| Base | 0 |\n| T | 60 |\n| C | 130 |\n| T+C | 190 |\n| S | 215 |\n| T+S | 275 |\n| C+S | 345 |\n| T+C+S | 405 |\n\nThe consecutive gaps are \\(60|70|60|25|60|70|60\\). The 70 and 25 are differences between combinations; they are not additional switches.\n\nThese structures meet in the Strategy’s fivefold formulas:\n\n\\[\n1250=5(C+2T),\\qquad650=5C.\n\\]\n\nThe row mechanism gives \\(12.5u\\) and \\(6.5u\\), where the observed century is \\(u=100\\). Requiring the fivefold form yields \\(C=1.3u\\) and \\(T=.6u\\). Thus the coefficient five expresses a calibration between two source mechanisms. It does not itself generate the patriarchal ages.\n\nSP supplies a further located comparison. Its post-Flood birth additions total 650; its pre-Flood shortening is \\(100+120+130=350\\) in the completed-year comparison, leaving 300. The Lamech contribution retains its nominal 129 plus the one-year boundary completion, counted once. These locations explain more than the identity \\(950\\pm300=1250,650\\): the latter is a useful description of the resulting pair, while the row model explains its construction.\n\nSource basis: File07 finite states; File18 source rows; C1253–C1264.\n\n## SP births constrain its lifespan field\n\nThe SP mechanism links the two chronological measurements directly. Reconstruct the ancestral births, measure each birth’s inclusive capacity to the Flood boundary, and cap the comparison lifespan at that capacity:\n\n\\[\nL'_i=\\min(L_i,c_i).\n\\]\n\nThe native SP capacities below use Noah’s 600-year interval plus the inclusive one. The lifespans compared are the selected MT baseline values.\n\n| Ancestor | Baseline life | SP capacity | Selected capped life | Reduction |\n|---|---:|---:|---:|---:|\n| Adam | 930 | 1307 | 930 | 0 |\n| Seth | 912 | 1177 | 912 | 0 |\n| Enosh | 905 | 1072 | 905 | 0 |\n| Kenan | 910 | 982 | 910 | 0 |\n| Mahalalel | 895 | 912 | 895 | 0 |\n| Jared | 962 | 847 | 847 | 115 |\n| Enoch | 365 | 785 | 365 | 0 |\n| Methuselah | 969 | 720 | 720 | 249 |\n| Lamech | 777 | 653 | 653 | 124 |\n\nOne rule reproduces the nine outputs, including the three reductions totaling \\(115+249+124=488\\). Shorter birth paths bring the Flood boundary inside those three baseline lives. Enoch illustrates why an earlier birth boundary does not automatically shorten every life: his baseline 365 remains below capacity.\n\nThe relation is especially transparent for Methuselah. In the MT comparison, \\(969=187+182+600\\). The SP birth changes remove \\(120+130\\), while the inclusive boundary restores one: \\(250-1=249\\). This produces the selected 720 without treating its reduction as an unrelated adjustment.\n\nEber and official SP Terah supply another 60 each after the Flood, making the total lifespan displacement \\(488+120=608\\). Ideal Terah 205 is a separate state from official Terah 145.\n\nThis is a conditional mechanism for the selected SP field: the birth ages, baseline lives and count convention are supplied. A capped result alone cannot recover how far its original life exceeded the boundary. That missing excess remains part of a reversible record, rather than becoming a newly generated source value.\n\nSource basis: File18 native rows; C1132–C1161.\n\nThe same located changes now supply the SP equal-gain rectangle. Starting with the selected standard MT frames and the initial 1446 Exodus reference, the source construction gives two radii:\n\n\\[\n\\begin{aligned}\nR&=(4114-1446)+650-350-215+7=2760,\\\\\nC&=(14004-1446)-488-120+10=11960.\n\\end{aligned}\n\\]\n\nThe Regular line retains the post-Flood additions, pre-Flood shortening, Sojourn choice and seven-year source opening. The Cumulative line retains the cap losses, post-Flood lifespan changes and ten-year source opening. Those openings and absolute frames remain source premises.\n\n| Mode | Source opening | Radius from 1446 | Appointed Key | Expanded radius | Resulting common anchor |\n|---|---:|---:|---:|---:|---:|\n| Regular | 4206 | 2760 | \\(70/69\\) | 2800 | 1406 |\n| Cumulative | 13406 | 11960 | \\(300/299\\) | 12000 | 1406 |\n\nDuring these Key expansions, the source openings 4206 and 13406 are held fixed; the lower comparison endpoint moves from 1446 to 1406. Both radii gain forty. Their difference stays 9200; Priestly expansion then gives \\(9200\\times25/23=10000\\).\n\nThe equal-gain condition is \\(R/69=C/299\\), or \\(3C=13R\\). Before the source openings, the radii are 2753 and 11950 and their balance is \\(3C-13R=61\\). Adding seven and ten changes that balance by \\(3(10)-13(7)=-61\\). This identifies precisely how the source packet closes the rectangle.\n\nThe advance is an explanation of where its two inputs come from. The equality of gains follows once those inputs and Keys are fixed; it is one connected family of consequences. The cap mechanism does not independently select the source openings or the Exodus anchor.\n\nSource basis: Strategy §4.3; Report IV; C1223–C1230.\n\n## Rounded rows form the Moses family\n\nThe Moses-centred construction uses the MT Terah-70, Cainan-OFF state, excludes the separate Shem +2 convention, and holds Moses at 1526 BC. It follows an ordered Regular chronological path. Its late edges include events as well as begetting ages: Jacob is 91 at Joseph’s birth, Joseph is 39 at Entry, and Entry precedes Moses by 350. Row rounding gives 90, 40 and 350, preserving their combined 480.\n\nThe complete path contains twenty-five nodes. Five named blocks expose its structure:\n\n| Segment | Exact sum | Sum of rounded rows | Exact minus Rounded |\n|---|---:|---:|---:|\n| Adam → Seth | 130 | 130 | 0 |\n| Seth → Enoch | 492 | 490 | 2 |\n| Enoch → Arphaxad | 1034 | 1030 | 4 |\n| Arphaxad → Reu | 129 | 130 | −1 |\n| Reu → Moses | 801 | 800 | 1 |\n| **Adam → Moses** | **2586** | **2580** | **6** |\n\nThe whole Rounded path gives \\(2580=6\\times430\\). Removing its first block gives Seth-to-Moses \\(2450=5\\times490\\); removing the next gives Enoch-to-Moses \\(1960=4\\times490\\). These are connected measurements of one reconstructed path.\n\nThe post-Flood partition is especially revealing: strict Actual \\(129+801\\) becomes Rounded \\(130+800\\), reproducing the two parts of Adam’s selected life while retaining the total 930. Eber, Reu and Nahor’s rounding residuals account for the internal shift, with the Jacob/Joseph residuals cancelling later. The relationship belongs to the selected path and its rounding rule.\n\nSource basis: File18, File51a and File52c; C1232–C1252.\n\nFor exact reconstruction, record both the nearest-five rounded value and its residual:\n\n\\[\nQ(x)=5\\left\\lfloor\\frac{x+2}{5}\\right\\rfloor,\\qquad \\rho(x)=x-Q(x).\n\\]\n\nFor an individual integer row, the residual lies between −2 and 2. Along a path, the residuals add. All twenty-five exact coordinates are recovered by adding the appropriate downstream residual sum to each Rounded coordinate.\n\nThe whole path’s accumulated residual is six. Therefore Rounded Creation 4106 plus six recovers strict Actual Creation 4112. Standard Actual 4114 additionally includes the separate Shem +2 convention. Rounding the exact total 2586 once would give 2585, not the row-rounded 2580; likewise rounding the exact 1034 block once gives 1035 rather than its row-rounded 1030. The construction’s order matters.\n\nThe 130 bridge also follows from the selected cycles: \\(6(430)-5(490)=130\\). It is not an independent selector of Moses. More generally, \\(430m-490n=130\\) has positive solutions \\(m=6+49k,n=5+43k\\) for nonnegative \\(k\\). The named source path supplies the actual selection.\n\nNative LXX extends the same construction with its own rows and Cainan. Its twenty-six-node Rounded path totals 3960 above Moses, placing Creation at 5486. The gap from MT is \\(600+650+130=1380\\). Its corresponding post-Flood blocks are 660 and 1050, compared with MT’s 130 and 800. On the selected SP post-Flood comparison the blocks are 530 and 1050. The transmitted SP 4411 does not by itself supply a newly reconstructed complete Rounded SP genealogical field. The accepted Fall construction introduced below now supplies the complete selected SP trunks, using 4406 Regular and 13396 Cumulative as their derived Fall heads.\n\nThis is the bridge to File52c. The complete MT path supplies Creation 4106 and Noah 3056. File52c separately provides Nativity 6, Conquest 1406 and Flood 2456. Their roles together determine the admitted original duration words. Arphaxad’s birth also occupies 2456 in the reconstructed path; equal coordinates do not merge that birth with the Flood event.\n\nSource basis: C1240–C1252, C1273–C1279.\n\n## Original duration words and the inverse backbone\n\nFile52c’s decimal operation reverses the significant digits of each original span while retaining its trailing-zero places. Thus 1650 becomes 5610, 1050 becomes 5010, and 1400 becomes 4100. A source-appointed partition is part of the operation: the regular 2700-year Creation-to-Conquest span, treated whole, produces 7200; its 1650+1050 partition produces 5610+5010=10620. The named Flood division therefore carries information that the total alone omits. [File52c §§1.2,3.3–3.4]\n\nWith Conquest 1406 BC held, the regular primary path gives\n\n\\[\n1406+5610+5010=12026.\n\\]\n\nThe cumulative primary path uses Creation 14006 and Flood 4836, giving 9170+3430. Its one-pass images are 7190+3430, also totaling 10620 and rebuilding 12026 BC. This convergence concerns the specified primary paths; their source breakpoints remain distinct. [File52c §3.3]\n\nA decimal-register calculation explains the two-component convergence. For two original spans, each ten times a three-digit core ending in a nonzero digit, a Regular total 2700 forces transformed total 10620. In that same register, a Cumulative total 12600 permits transformed totals 10620 or 11610; its actual 917 and 343 cores select the 10620 branch. The source supplies the named split. The technical companion retains the proof and the alternative branch. [C938–C947]\n\nThe continuation to 14726 BC supplies an additional original interval: Conquest 1406 to Nativity 6 is 1400 years, whose one-pass image is 4100. Moving the held anchor from 1406 to 6 and including this leg changes the rebuilt endpoint by 4100−1400=2700. Therefore 12026 becomes 14726. The explanation retains both the original tail and the anchor change. [File52c §3.4; C952]\n\nThe four admitted MT paths can be compared compactly. The divisions are listed outward from the held 6 BC anchor toward earlier source dates:\n\n| Source path after Nativity | Original spans | One-pass spans |\n|---|---|---|\n| Regular: Conquest–Flood–Creation | 1400 + 1050 + 1650 | 4100 + 5010 + 5610 |\n| Regular: Conquest–Noah–Creation | 1400 + 1650 + 1050 | 4100 + 5610 + 5010 |\n| Regular: Conquest–Flood–Noah–Creation | 1400 + 1050 + 600 + 1050 | 4100 + 5010 + 600 + 5010 |\n| Cumulative primary: Conquest–Flood–Creation | 1400 + 3430 + 9170 | 4100 + 3430 + 7190 |\n\nEvery MT row in this table totals 14720 and therefore ends at 14726 BC. The Noah alternatives preserve the regular result through their particular component relations. The new genealogy interface matches the first three original rows exactly and reuses their established images; the cumulative row retains its own source measurement. The first transformed leg ends at 4106 BC, numerically equal to original regular Creation, but it remains the generated endpoint of the Conquest leg. This preserves the distinction between a shared coordinate and a shared chronological role. [File52c §3.4; C1274–C1276]\n\nThe same 12026 anchor also divides the selected Actual Creation bridge. Its cumulative and regular completion endpoints are 14004 and 4114 BC, respectively. Their 9890-year separation splits into\n\n\\[\n14004-12026=1978,\\qquad 12026-4114=7912=4\\times 1978.\n\\]\n\nPriestly expansion by 25/23 gives 2150 and 8600, preserving 1:4 and totaling 10750. These expanded parts belong to the expanded total. The Rounded endpoints 14006/4106 instead divide into 1980+7920=9900, again 1:4. Both selected pairs satisfy\n\n\\[\n12026=\\frac{4C+R}{5},\n\\]\n\nwhere `C,R` are their cumulative and regular Creation coordinates. Moving Rounded→Actual changes them by −2 and +8, preserving the weighted value because `4(−2)+8=0`. The regular +8 combines the six-year row residual with the separate standard Shem +2 convention; selecting the cumulative completion endpoint supplies its −2. The matching weight is derived from these selected values. It expresses their compatibility without making the state selections disappear. [File52c §3.14; C932–C948]\n\nThe same division is visible in the original one-pass convergence. The regular span grows from 2700 to 10620, gaining 7920; the cumulative span falls from 12600 to 10620, losing 1980. The gain is four times the loss. Thus the weighted coordinate and the inverse construction express a shared relation among these source values. Once the inputs are fixed, the two descriptions belong to one connected calculation. The historical significance rests on why those particular intervals and their named divisions occur in the source family. [C937–C948]\n\nThe completed backbone also has a 9890-year interval to the Conquest-held cumulative Flood companion at 4836 BC: `14726−4836=9890=23×430`. The Flood companion retains the 1406 anchor and unchanged 3430 span; it is a separate anchored comparison from the completed Nativity-held path. Its interval matches the Actual Creation bridge in magnitude, while the original Rounded Creation gap stays 9900. The correspondence links declared measurements without replacing their endpoints or chronological roles. [File52c §3.6]\n\n"
},
{
"name": "unchanged reader section: ## Calendar Keys preserve",
"pass": true,
"actual": "## Calendar Keys preserve a declared measure\n\nThe Keys explain how another kind of agreement crosses families. Write the Priestly, Prophetic and Enochian factors respectively as\n\n\\[\nE=25/23,\\quad P=70/69,\\quad J=300/299.\n\\]\n\nTheir corresponding schematic year lengths give\n\n\\[\n336E=360P=364J=8400/23.\n\\]\n\nConsequently different year counts can carry the same modeled day-volume. The completed MT 14720 duration gives 16000 under E, 44800/3 under P, and 192000/13 under J. Multiplying those counts by 336, 360 and 364 respectively gives 5376000 in every case. File52c appoints the E completion here; the P/J values illustrate the inherited calibration conditionally. Equal modeled volume does not itself appoint a new chronological route or a historical calendar. [Strategy §3.3; C1062]\n\nPlacement is specified by a held anchor: \\(D_{k,a}(x)=a+k(x-a)\\). This acts on a distance from the anchor, not a naked BC date. Source units, moving components and anchor together define the chronological comparison.\n\nFor the appointed MT E route, holding 6 BC converts 14720 to 16000 and locates the expanded endpoint at 16006 BC. The intermediate positions need not become integers. Every nonempty proper prefix of the four transformed MT paths has a nonzero residue modulo 23. For example, the shared first 4100-year prefix becomes 102500/23; the whole 14720 becomes 16000. Uniform multiplication remains additive over exact rational durations, so componentwise conversion and whole-span conversion agree at the endpoint. What fails is the further requirement that every retained internal position lie on an integer-year grid. The rational path is a conditional display of the same uniform conversion, not a universal map between all original chronological date labels. [File52c §3.6; C1059–C1062]\n\nThis distinction gives 23 and 529 their structural roles. The first controls integral Priestly conversion. Its square 529 permits the duration ladder\n\n\\[\n529k\\longrightarrow 575k\\longrightarrow 625k.\n\\]\n\nFor the 12026 backbone and Exodus 1446, the supplied interval is 10580=20×529, yielding 10580→11500→12500 under two successive Priestly expansions. The coefficient 20 is obtained from that span; the later values follow from the same factor. Endpoint placement additionally requires the declared anchor and counting convention. [File52c §§6.1–6.2]\n\n## Covenant paths and the cumulative clutch\n\nThe Covenant family shows how two ways of building chronology can meet through shared source material. Regular chronology follows births, ages, household events and deaths. Cumulative chronology stacks complete lifespans along a selected succession. Each produces an ordered path; the clutch compares their placement while preserving the cumulative path’s internal lengths. This brings the Strategy’s family explanation down to a concrete mechanism: source rows generate paths, shared biographies connect them, and additional source conditions determine which further boundaries coincide.\n\nBegin with the MT Minimum Covenant placement at 1866 BC. The source assigns one year from the Covenant to Ishmael’s birth and fifteen to Isaac’s birth. Isaac’s sixty years to Jacob, Jacob’s seventy-seven years to his call, and another ten to Levi’s birth give:\n\n\\[\n\\text{Covenant to Levi birth}=15+60+77+10=162.\n\\]\n\nThus Levi’s birth is 1704 BC, and Ishmael’s birth at 1865 precedes it by 161 years. Levi’s 137-year life places his death at 1567; Ishmael’s equal 137-year life places his death at 1728. Equal lives preserve the 161-year separation from births to deaths. The further 161 years from Levi’s death to the Conquest at 1406 depend on that separately retained terminal.\n\nThe larger partition now follows the same path. Covenant to Levi’s death is \\(162+137=299\\), and Covenant to Conquest is \\(299+161=460\\). These spans are generated measurements. The local inputs are the assigned Covenant offsets, ages, lifespan and terminal. This distinction explains where the prominent numbers come from and which source choices must remain available to reproduce them.\n\nThe state matters. File 60 uses 1866 as the minimum Covenant coordinate; its full-state counterpart, 2081, is author-designated. The applicable ancestral coordinates differ by 215 while the Conquest remains 1406. Consequently, the 460-year Covenant-to-Conquest span belongs to the minimum state. The separate offering comparison at 2051, with Isaac at proposed age fifteen, retains that proposed status: Genesis 22 supplies neither that date nor that age.\n\nThree 147-year spans organize the inner family: Isaac’s birth to Levi’s birth, Jacob’s own life, and Jacob’s call to Levi’s death. Their agreement rests on two relations to Jacob’s supplied lifespan:\n\n\\[\n60+77+10=147,\\qquad 10+137=147.\n\\]\n\nSubtracting them gives \\(60+77=137\\). The matching vertical separations and shared diagonal therefore follow from the same connected structure. This also explains why the 147 relation can reappear when a cumulative lifespan path meets the regular field: it already links an intergenerational interval to a complete biography.\n\nThe Keys add a measurement comparison. The Covenant-to-Joseph-death path is \\(15+60+77+14+110=276\\); the Levi path is 299. Holding the minimum Covenant coordinate fixed, the Priestly Key sends \\(276\\times25/23\\) to 300, and the Enochian Key sends \\(299\\times300/299\\) to 300. Both transformed points are therefore 1566 BC. More generally, writing the Levi and Joseph distances as \\(u\\) and \\(w\\), agreement requires \\(13w=12u\\). The two displayed landings express one agreement condition between source paths. The transformed 1566 point keeps its comparison role; Joseph’s and Levi’s regular deaths remain 1590 and 1567.\n\nThe cumulative construction supplies a second complete path. Starting from Moses’ fixed birth at 1526 BC and stacking Amram’s 137, Kohath’s 133, Levi’s 137, Jacob’s 147, Isaac’s 180 and Abraham’s 175 years generates the original column below. Each row names a cumulative boundary; it need not equal that person’s regular birth.\n\n| Cumulative boundary | Original Nisan | Half-clutch | Full clutch |\n|---|---:|---:|---:|\n| Abraham | 2435 | 2428 | 2421 |\n| Isaac | 2260 | 2253 | 2246 |\n| Jacob | 2080 | 2073 | 2066 |\n| Levi | 1933 | 1926 | 1919 |\n| Kohath | 1796 | 1789 | 1782 |\n| Amram | 1663 | 1656 | 1649 |\n| Moses-side interface | 1526 | 1519 | 1512 |\n\nThe fourteen-year clutch is derived before generating the other columns. In the full regular state, Levi is born at 1919 and dies at 1782; Moses is born at 1526 and reaches the Exodus at 1446. For the maximum-envelope calculation, each successor is assumed to begin when the preceding life ends. Levi, Kohath, Amram and Moses’ eighty years to Exodus then supply \\(137+133+137+80=487\\) years. Regular elapsed chronology supplies \\(1919-1446=473\\). Their difference is fourteen.\n\nThe reason the first join works becomes clearer algebraically. Let \\(B,D\\) be regular Levi birth and death, \\(M\\) Moses’ birth, \\(e\\) Exodus, and \\(L,K,A\\) the three Levitical lifespans. Since \\(B-D=L\\), the clutch is\n\n\\[\nd=[L+K+A+(M-e)]-(B-e)=M+K+A-D.\n\\]\n\nBut \\(M+K+A\\) is cumulative Kohath. Subtracting \\(d\\) therefore places that boundary at regular Levi’s death by construction: \\(1796-14=1782\\). The adjacent join follows because both paths use Levi’s same 137-year life: cumulative Levi becomes \\(1933-14=1919\\), regular Levi’s birth. These two joins reveal how the comparison is built.\n\nThe next join requires the earlier 147 relation. Cumulative Jacob lies one Jacob lifespan before cumulative Levi. After translation it becomes \\(2080-14=2066\\), regular Isaac’s birth, precisely because regular Isaac-to-Levi also measures 147. The cumulative and Covenant families thus meet through an identifiable shared source condition. Once this condition is retained, the resulting coincidence follows across the two constructions.\n\nThe half-clutch is the exact midpoint: subtract seven instead of fourteen. Moving every boundary by either amount preserves all six lifespan blocks. Moving just one end temporarily changes its block; moving the other end by the same amount restores the original length in its new position. The last row records interfaces measured from Moses’ fixed birth. Its 1519 and 1512 values do not relocate that birth.\n\nPhase completes the field. The exact Aaron/Tishri branch adds 3.5 to every entry of the Nisan table, using the same Nisan-derived clutch. Thus original cumulative Levi is 1936.5 on that branch; the separate whole-year display is 1936. Keeping one clutch preserves the phase difference across all columns. Recalculating a different full clutch to force the same regular landing would erase that difference and produce a different comparison.\n\nThe complete field contains seven rows, two phases and three clutch positions: forty-two coordinates generated by the same path, shift and phase. The technical companion gives both phase tables and their exact dependency count.\n\nIn the coupled construction, even the row positions and clutch are generated: lifespans and Moses’ anchor build the cumulative path; regular Levi’s death determines its translation. The common register therefore retains the source inputs, operations and required joins while recording the conspicuous gaps as consequences. This explains a complete family of agreements and identifies the source information each agreement uses. The arithmetic establishes those dependencies; the chronology’s historical premises and theological interpretation retain their own evidentiary roles.\n\nSource basis: Files60–62; inherited Covenant dependency proofs; C1311 and C1319.\n\n## Counts extend ordered measurement\n\nThe counted families extend the same construction already visible in the genealogies. A source supplies labelled items, an order and a measure. Accumulation builds a path; selected observations may recover its inputs; grouping may preserve some information while losing other information. Animal counts, ritual categories and named generations therefore belong within the common grammar. What crosses each interface must remain explicit: a count carries its category, a generation carries its name and slot, and a chronological comparison carries its source state and placement.\n\nEsau’s gift provides a complete reconstruction example. Its nine printed counts belong to female and male goats, sheep and cattle, the female camel block, and female and male donkeys. The declared male-first clean order gives cumulative counts 20, 40, 50, 250, 450 and 490. The female register gives 200, 400, 430, 470 and 490. Together these observations recover eight animal counts. Male donkeys occur in neither register, so their count remains undetermined until the grand total of 550 supplies the missing information. The recovered count is 10. Unnumbered camel young introduce no additional numerical input. (File 58 §§13.1–13.4; C1009–C1010.)\n\nNine selected measurements already recover the whole list: the six clean cumulative counts, the third and fifth female counts, and the grand total. Recovery uses exact integer additions and subtractions. This is the same accumulation-and-difference procedure used for chronological intervals, now applied to category-labelled counts. It gives another complete description of nine numerical inputs; it does not generate them from fewer independent values. A value such as 430 also retains its role: connecting that female cumulative count to a chronological span requires the separately supplied dates. (File 58 §§13.2–13.4; C1011–C1013.)\n\nThe Numbers-only Tishri 1–22 ledger, in the Enochian fixed-week state with three Sabbaths, shows how additional source conditions can complete a reconstruction. Its seven categories are daily offerings, Sabbaths, New Moon, Trumpets, Atonement, seven-day Sukkot and Eighth Day. Their four species totals—75 bulls, 18 rams, 176 lambs and 11 goats—sum to 280, but do not determine the category allocation by themselves. Retaining the source’s category templates, including Sukkot’s 70:14:98:7 species vector, leaves seven amplitudes to determine. The four totals, equal amplitudes for Trumpets, Atonement and Eighth Day, and the daily contribution of 44 lambs then recover every category. The numerical templates remain part of the source cost. (File 58 §§2.2–3.2; C1014–C1015.)\n\nThe daily Sukkot sequence makes that dependence concrete. Seven totals summing to 189 and decreasing by one must be 30, 29, 28, 27, 26, 25 and 24. With 17 nonbull animals on each day, the bull counts are 13 through 7. The total alone does not select that sequence: the decrement and daily allocation supply information. This is how source rules explain a whole pattern without treating each resulting number as an independent observation. (File 58 §7.1; C1016.)\n\n## NT slots and source chronology\n\nThe NT family replaces animal counts with named generation slots. Its 70-year measure and 6 BC hinge supply a schematic coordinate field. Relative positions, duration and placement remain distinguishable. The Key comparisons send Enoch’s radius one slot outward to Jared under the Prophetic factor and six slots outward to Adam under the Priestly factor. Their equations are proportional, so they fix the radius at 69 slots without independently determining the slot duration. The supplied 2450-year span across 35 slots fixes 70 years, giving a radius of 4830. The existing co-registrations retain the 6 BC birth hinge; this is conditional reconstruction of the supplied display. (File 43 §§2.1–2.3,3.4; File 54 §6, §§8.6,13.2; C1019–C1022.)\n\nThe latest comparison carries this fixed NT field across all 22 shared Adam–Jacob names in the native MT, SP and LXX birth tables. Each tradition keeps its supplied frame and count conventions. The result exposes a complete ten-name stretch with identical SP and LXX births, although their lifespan measurements differ:\n\n| Name | Shared birth, BC | SP lifespan | LXX lifespan |\n|---|---:|---:|---:|\n| Shelah | 2756 | 433 | 460 |\n| Eber | 2626 | 404 | 504 |\n| Peleg | 2492 | 239 | 339 |\n| Reu | 2362 | 239 | 339 |\n| Serug | 2230 | 230 | 330 |\n| Nahor | 2100 | 148 | 208 |\n| Terah | 2021 | 145 | 205 |\n| Abraham | 1951 | 175 | 175 |\n| Isaac | 1851 | 180 | 180 |\n| Jacob | 1791 | 147 | 147 |\n\nAt each of these ten names, SP and LXX give the same NT-to-birth difference. Seven lifespans nevertheless differ: 27, four contributions of 100, and two of 60, totaling 547. Regular birth comparison cannot detect those differences; the Cumulative source-row measure can. The agreement therefore identifies a shared measurement of the sources while leaving their other measurements distinct. This transfers the already established source differences into the NT display without supplying a new generating rule. (File 18 §§3.2–3.3,4.2–4.3; C1266–C1269.)\n\nNative LXX Cainan clarifies what the named slots retain. Its Arphaxad–Cainan–Shelah birth intervals are 135 and 130 years, while the corresponding NT intervals are 70 and 70. The successive comparison values consequently change by 65 and 60. Omitting Cainan from the shared-name table leaves a two-slot NT interval of 140; it must not be mistaken for one generation. The source person, insertion position and biographical measure remain distinct from the carrier width. (File 18 §4.2; File 43 §3.4; C1267,C1270.)\n\nThe Rounded head interface is similarly role-specific. LXX 5486, NT Adam 5256 and MT 4106 give the established 230|1150 division. Since the LXX Adam-to-Seth interval is 230, NT Adam shares a coordinate with Rounded LXX Seth. That does not identify their roles or produce a universal conversion of the full genealogy. No Moses or clutch coordinates are imported into this NT field. (File 54 §§2.1–2.2,8.1A; C1271–C1272.)\n\nToledot adds the distinction between counting and grouping. Eleven formula occurrences form ten major sections because Esau occupies occurrences 9 and 10 within one section. Terah, occurrence 6, has five occurrences on each side but five earlier and four later sections. Giving the Esau section weight two preserves the eleven-occurrence measure and Terah’s balance. It does not preserve every operation on the original list. Reflection pairs positions 9 and 10 with 3 and 2—Noah and Adam, still separate sections—so the grouped Esau section has no single reflected image. (File 70 Appendix B.1; C1023–C1028.)\n\nThe primary NT path supplies the positive grouping example. Its 77 seventy-year intervals divide into eleven complete 490-year blocks. Reflection reverses their order and preserves all twelve block boundaries. The separately displayed AD 65–135 extension remains outside that primary path. Together, these families show what a chronological interface must carry: labels and order for recovery, source conditions for allocation, measures for comparison, and compatible grouping for symmetry. Those retained structures explain both exact agreements and the information an agreement leaves unresolved. (File 43 §3.4; File 54 §8.6; C1029.)\n\n",
"expected": "## Calendar Keys preserve a declared measure\n\nThe Keys explain how another kind of agreement crosses families. Write the Priestly, Prophetic and Enochian factors respectively as\n\n\\[\nE=25/23,\\quad P=70/69,\\quad J=300/299.\n\\]\n\nTheir corresponding schematic year lengths give\n\n\\[\n336E=360P=364J=8400/23.\n\\]\n\nConsequently different year counts can carry the same modeled day-volume. The completed MT 14720 duration gives 16000 under E, 44800/3 under P, and 192000/13 under J. Multiplying those counts by 336, 360 and 364 respectively gives 5376000 in every case. File52c appoints the E completion here; the P/J values illustrate the inherited calibration conditionally. Equal modeled volume does not itself appoint a new chronological route or a historical calendar. [Strategy §3.3; C1062]\n\nPlacement is specified by a held anchor: \\(D_{k,a}(x)=a+k(x-a)\\). This acts on a distance from the anchor, not a naked BC date. Source units, moving components and anchor together define the chronological comparison.\n\nFor the appointed MT E route, holding 6 BC converts 14720 to 16000 and locates the expanded endpoint at 16006 BC. The intermediate positions need not become integers. Every nonempty proper prefix of the four transformed MT paths has a nonzero residue modulo 23. For example, the shared first 4100-year prefix becomes 102500/23; the whole 14720 becomes 16000. Uniform multiplication remains additive over exact rational durations, so componentwise conversion and whole-span conversion agree at the endpoint. What fails is the further requirement that every retained internal position lie on an integer-year grid. The rational path is a conditional display of the same uniform conversion, not a universal map between all original chronological date labels. [File52c §3.6; C1059–C1062]\n\nThis distinction gives 23 and 529 their structural roles. The first controls integral Priestly conversion. Its square 529 permits the duration ladder\n\n\\[\n529k\\longrightarrow 575k\\longrightarrow 625k.\n\\]\n\nFor the 12026 backbone and Exodus 1446, the supplied interval is 10580=20×529, yielding 10580→11500→12500 under two successive Priestly expansions. The coefficient 20 is obtained from that span; the later values follow from the same factor. Endpoint placement additionally requires the declared anchor and counting convention. [File52c §§6.1–6.2]\n\n## Covenant paths and the cumulative clutch\n\nThe Covenant family shows how two ways of building chronology can meet through shared source material. Regular chronology follows births, ages, household events and deaths. Cumulative chronology stacks complete lifespans along a selected succession. Each produces an ordered path; the clutch compares their placement while preserving the cumulative path’s internal lengths. This brings the Strategy’s family explanation down to a concrete mechanism: source rows generate paths, shared biographies connect them, and additional source conditions determine which further boundaries coincide.\n\nBegin with the MT Minimum Covenant placement at 1866 BC. The source assigns one year from the Covenant to Ishmael’s birth and fifteen to Isaac’s birth. Isaac’s sixty years to Jacob, Jacob’s seventy-seven years to his call, and another ten to Levi’s birth give:\n\n\\[\n\\text{Covenant to Levi birth}=15+60+77+10=162.\n\\]\n\nThus Levi’s birth is 1704 BC, and Ishmael’s birth at 1865 precedes it by 161 years. Levi’s 137-year life places his death at 1567; Ishmael’s equal 137-year life places his death at 1728. Equal lives preserve the 161-year separation from births to deaths. The further 161 years from Levi’s death to the Conquest at 1406 depend on that separately retained terminal.\n\nThe larger partition now follows the same path. Covenant to Levi’s death is \\(162+137=299\\), and Covenant to Conquest is \\(299+161=460\\). These spans are generated measurements. The local inputs are the assigned Covenant offsets, ages, lifespan and terminal. This distinction explains where the prominent numbers come from and which source choices must remain available to reproduce them.\n\nThe state matters. File 60 uses 1866 as the minimum Covenant coordinate; its full-state counterpart, 2081, is author-designated. The applicable ancestral coordinates differ by 215 while the Conquest remains 1406. Consequently, the 460-year Covenant-to-Conquest span belongs to the minimum state. The separate offering comparison at 2051, with Isaac at proposed age fifteen, retains that proposed status: Genesis 22 supplies neither that date nor that age.\n\nThree 147-year spans organize the inner family: Isaac’s birth to Levi’s birth, Jacob’s own life, and Jacob’s call to Levi’s death. Their agreement rests on two relations to Jacob’s supplied lifespan:\n\n\\[\n60+77+10=147,\\qquad 10+137=147.\n\\]\n\nSubtracting them gives \\(60+77=137\\). The matching vertical separations and shared diagonal therefore follow from the same connected structure. This also explains why the 147 relation can reappear when a cumulative lifespan path meets the regular field: it already links an intergenerational interval to a complete biography.\n\nThe Keys add a measurement comparison. The Covenant-to-Joseph-death path is \\(15+60+77+14+110=276\\); the Levi path is 299. Holding the minimum Covenant coordinate fixed, the Priestly Key sends \\(276\\times25/23\\) to 300, and the Enochian Key sends \\(299\\times300/299\\) to 300. Both transformed points are therefore 1566 BC. More generally, writing the Levi and Joseph distances as \\(u\\) and \\(w\\), agreement requires \\(13w=12u\\). The two displayed landings express one agreement condition between source paths. The transformed 1566 point keeps its comparison role; Joseph’s and Levi’s regular deaths remain 1590 and 1567.\n\nThe cumulative construction supplies a second complete path. Starting from Moses’ fixed birth at 1526 BC and stacking Amram’s 137, Kohath’s 133, Levi’s 137, Jacob’s 147, Isaac’s 180 and Abraham’s 175 years generates the original column below. Each row names a cumulative boundary; it need not equal that person’s regular birth.\n\n| Cumulative boundary | Original Nisan | Half-clutch | Full clutch |\n|---|---:|---:|---:|\n| Abraham | 2435 | 2428 | 2421 |\n| Isaac | 2260 | 2253 | 2246 |\n| Jacob | 2080 | 2073 | 2066 |\n| Levi | 1933 | 1926 | 1919 |\n| Kohath | 1796 | 1789 | 1782 |\n| Amram | 1663 | 1656 | 1649 |\n| Moses-side interface | 1526 | 1519 | 1512 |\n\nThe fourteen-year clutch is derived before generating the other columns. In the full regular state, Levi is born at 1919 and dies at 1782; Moses is born at 1526 and reaches the Exodus at 1446. For the maximum-envelope calculation, each successor is assumed to begin when the preceding life ends. Levi, Kohath, Amram and Moses’ eighty years to Exodus then supply \\(137+133+137+80=487\\) years. Regular elapsed chronology supplies \\(1919-1446=473\\). Their difference is fourteen.\n\nThe reason the first join works becomes clearer algebraically. Let \\(B,D\\) be regular Levi birth and death, \\(M\\) Moses’ birth, \\(e\\) Exodus, and \\(L,K,A\\) the three Levitical lifespans. Since \\(B-D=L\\), the clutch is\n\n\\[\nd=[L+K+A+(M-e)]-(B-e)=M+K+A-D.\n\\]\n\nBut \\(M+K+A\\) is cumulative Kohath. Subtracting \\(d\\) therefore places that boundary at regular Levi’s death by construction: \\(1796-14=1782\\). The adjacent join follows because both paths use Levi’s same 137-year life: cumulative Levi becomes \\(1933-14=1919\\), regular Levi’s birth. These two joins reveal how the comparison is built.\n\nThe next join requires the earlier 147 relation. Cumulative Jacob lies one Jacob lifespan before cumulative Levi. After translation it becomes \\(2080-14=2066\\), regular Isaac’s birth, precisely because regular Isaac-to-Levi also measures 147. The cumulative and Covenant families thus meet through an identifiable shared source condition. Once this condition is retained, the resulting coincidence follows across the two constructions.\n\nThe half-clutch is the exact midpoint: subtract seven instead of fourteen. Moving every boundary by either amount preserves all six lifespan blocks. Moving just one end temporarily changes its block; moving the other end by the same amount restores the original length in its new position. The last row records interfaces measured from Moses’ fixed birth. Its 1519 and 1512 values do not relocate that birth.\n\nPhase completes the field. The exact Aaron/Tishri branch adds 3.5 to every entry of the Nisan table, using the same Nisan-derived clutch. Thus original cumulative Levi is 1936.5 on that branch; the separate whole-year display is 1936. Keeping one clutch preserves the phase difference across all columns. Recalculating a different full clutch to force the same regular landing would erase that difference and produce a different comparison.\n\nThe complete field contains seven rows, two phases and three clutch positions: forty-two coordinates generated by the same path, shift and phase. The technical companion gives both phase tables and their exact dependency count.\n\nIn the coupled construction, even the row positions and clutch are generated: lifespans and Moses’ anchor build the cumulative path; regular Levi’s death determines its translation. The common register therefore retains the source inputs, operations and required joins while recording the conspicuous gaps as consequences. This explains a complete family of agreements and identifies the source information each agreement uses. The arithmetic establishes those dependencies; the chronology’s historical premises and theological interpretation retain their own evidentiary roles.\n\nSource basis: Files60–62; inherited Covenant dependency proofs; C1311 and C1319.\n\n## Counts extend ordered measurement\n\nThe counted families extend the same construction already visible in the genealogies. A source supplies labelled items, an order and a measure. Accumulation builds a path; selected observations may recover its inputs; grouping may preserve some information while losing other information. Animal counts, ritual categories and named generations therefore belong within the common grammar. What crosses each interface must remain explicit: a count carries its category, a generation carries its name and slot, and a chronological comparison carries its source state and placement.\n\nEsau’s gift provides a complete reconstruction example. Its nine printed counts belong to female and male goats, sheep and cattle, the female camel block, and female and male donkeys. The declared male-first clean order gives cumulative counts 20, 40, 50, 250, 450 and 490. The female register gives 200, 400, 430, 470 and 490. Together these observations recover eight animal counts. Male donkeys occur in neither register, so their count remains undetermined until the grand total of 550 supplies the missing information. The recovered count is 10. Unnumbered camel young introduce no additional numerical input. (File 58 §§13.1–13.4; C1009–C1010.)\n\nNine selected measurements already recover the whole list: the six clean cumulative counts, the third and fifth female counts, and the grand total. Recovery uses exact integer additions and subtractions. This is the same accumulation-and-difference procedure used for chronological intervals, now applied to category-labelled counts. It gives another complete description of nine numerical inputs; it does not generate them from fewer independent values. A value such as 430 also retains its role: connecting that female cumulative count to a chronological span requires the separately supplied dates. (File 58 §§13.2–13.4; C1011–C1013.)\n\nThe Numbers-only Tishri 1–22 ledger, in the Enochian fixed-week state with three Sabbaths, shows how additional source conditions can complete a reconstruction. Its seven categories are daily offerings, Sabbaths, New Moon, Trumpets, Atonement, seven-day Sukkot and Eighth Day. Their four species totals—75 bulls, 18 rams, 176 lambs and 11 goats—sum to 280, but do not determine the category allocation by themselves. Retaining the source’s category templates, including Sukkot’s 70:14:98:7 species vector, leaves seven amplitudes to determine. The four totals, equal amplitudes for Trumpets, Atonement and Eighth Day, and the daily contribution of 44 lambs then recover every category. The numerical templates remain part of the source cost. (File 58 §§2.2–3.2; C1014–C1015.)\n\nThe daily Sukkot sequence makes that dependence concrete. Seven totals summing to 189 and decreasing by one must be 30, 29, 28, 27, 26, 25 and 24. With 17 nonbull animals on each day, the bull counts are 13 through 7. The total alone does not select that sequence: the decrement and daily allocation supply information. This is how source rules explain a whole pattern without treating each resulting number as an independent observation. (File 58 §7.1; C1016.)\n\n## NT slots and source chronology\n\nThe NT family replaces animal counts with named generation slots. Its 70-year measure and 6 BC hinge supply a schematic coordinate field. Relative positions, duration and placement remain distinguishable. The Key comparisons send Enoch’s radius one slot outward to Jared under the Prophetic factor and six slots outward to Adam under the Priestly factor. Their equations are proportional, so they fix the radius at 69 slots without independently determining the slot duration. The supplied 2450-year span across 35 slots fixes 70 years, giving a radius of 4830. The existing co-registrations retain the 6 BC birth hinge; this is conditional reconstruction of the supplied display. (File 43 §§2.1–2.3,3.4; File 54 §6, §§8.6,13.2; C1019–C1022.)\n\nThe latest comparison carries this fixed NT field across all 22 shared Adam–Jacob names in the native MT, SP and LXX birth tables. Each tradition keeps its supplied frame and count conventions. The result exposes a complete ten-name stretch with identical SP and LXX births, although their lifespan measurements differ:\n\n| Name | Shared birth, BC | SP lifespan | LXX lifespan |\n|---|---:|---:|---:|\n| Shelah | 2756 | 433 | 460 |\n| Eber | 2626 | 404 | 504 |\n| Peleg | 2492 | 239 | 339 |\n| Reu | 2362 | 239 | 339 |\n| Serug | 2230 | 230 | 330 |\n| Nahor | 2100 | 148 | 208 |\n| Terah | 2021 | 145 | 205 |\n| Abraham | 1951 | 175 | 175 |\n| Isaac | 1851 | 180 | 180 |\n| Jacob | 1791 | 147 | 147 |\n\nAt each of these ten names, SP and LXX give the same NT-to-birth difference. Seven lifespans nevertheless differ: 27, four contributions of 100, and two of 60, totaling 547. Regular birth comparison cannot detect those differences; the Cumulative source-row measure can. The agreement therefore identifies a shared measurement of the sources while leaving their other measurements distinct. This transfers the already established source differences into the NT display without supplying a new generating rule. (File 18 §§3.2–3.3,4.2–4.3; C1266–C1269.)\n\nNative LXX Cainan clarifies what the named slots retain. Its Arphaxad–Cainan–Shelah birth intervals are 135 and 130 years, while the corresponding NT intervals are 70 and 70. The successive comparison values consequently change by 65 and 60. Omitting Cainan from the shared-name table leaves a two-slot NT interval of 140; it must not be mistaken for one generation. The source person, insertion position and biographical measure remain distinct from the carrier width. (File 18 §4.2; File 43 §3.4; C1267,C1270.)\n\nThe Rounded head interface is similarly role-specific. LXX 5486, NT Adam 5256 and MT 4106 give the established 230|1150 division. Since the LXX Adam-to-Seth interval is 230, NT Adam shares a coordinate with Rounded LXX Seth. That does not identify their roles or produce a universal conversion of the full genealogy. No Moses or clutch coordinates are imported into this NT field. (File 54 §§2.1–2.2,8.1A; C1271–C1272.)\n\nToledot adds the distinction between counting and grouping. Eleven formula occurrences form ten major sections because Esau occupies occurrences 9 and 10 within one section. Terah, occurrence 6, has five occurrences on each side but five earlier and four later sections. Giving the Esau section weight two preserves the eleven-occurrence measure and Terah’s balance. It does not preserve every operation on the original list. Reflection pairs positions 9 and 10 with 3 and 2—Noah and Adam, still separate sections—so the grouped Esau section has no single reflected image. (File 70 Appendix B.1; C1023–C1028.)\n\nThe primary NT path supplies the positive grouping example. Its 77 seventy-year intervals divide into eleven complete 490-year blocks. Reflection reverses their order and preserves all twelve block boundaries. The separately displayed AD 65–135 extension remains outside that primary path. Together, these families show what a chronological interface must carry: labels and order for recovery, source conditions for allocation, measures for comparison, and compatible grouping for symmetry. Those retained structures explain both exact agreements and the information an agreement leaves unresolved. (File 43 §3.4; File 54 §8.6; C1029.)\n\n"
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{
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},
{
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1473,
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],
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1473,
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]
},
{
"name": "C1473 content hash",
"pass": true,
"actual": "11241b9a598e3b24e38cf282043dc01f3e366b90a782dd0a29caeb80a5f41ff4",
"expected": "11241b9a598e3b24e38cf282043dc01f3e366b90a782dd0a29caeb80a5f41ff4"
},
{
"name": "C1473 completed and reassessed",
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"actual": true,
"expected": true
},
{
"name": "C1474 number and predecessor",
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1474,
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],
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1474,
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]
},
{
"name": "C1474 content hash",
"pass": true,
"actual": "178a72c8ceaec3202c1c74be704a6293407531fe13bc1530ec2d81764f3d1fdb",
"expected": "178a72c8ceaec3202c1c74be704a6293407531fe13bc1530ec2d81764f3d1fdb"
},
{
"name": "C1474 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1475 number and predecessor",
"pass": true,
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1475,
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],
"expected": [
1475,
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]
},
{
"name": "C1475 content hash",
"pass": true,
"actual": "611dfee82a462e2c731534c904b3c940d29159db1063d21e19495941bf0acbfb",
"expected": "611dfee82a462e2c731534c904b3c940d29159db1063d21e19495941bf0acbfb"
},
{
"name": "C1475 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1476 number and predecessor",
"pass": true,
"actual": [
1476,
"611dfee82a462e2c731534c904b3c940d29159db1063d21e19495941bf0acbfb"
],
"expected": [
1476,
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]
},
{
"name": "C1476 content hash",
"pass": true,
"actual": "7806f816e5ad76d942b6254a66ea1b807411f9fd50d17ae0429bc59964f3477b",
"expected": "7806f816e5ad76d942b6254a66ea1b807411f9fd50d17ae0429bc59964f3477b"
},
{
"name": "C1476 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1477 number and predecessor",
"pass": true,
"actual": [
1477,
"7806f816e5ad76d942b6254a66ea1b807411f9fd50d17ae0429bc59964f3477b"
],
"expected": [
1477,
"7806f816e5ad76d942b6254a66ea1b807411f9fd50d17ae0429bc59964f3477b"
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},
{
"name": "C1477 content hash",
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"expected": "5164c224ec28a79b52c3066f249eec40a65ea204b61754616b23653339a0ec83"
},
{
"name": "C1477 completed and reassessed",
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"actual": true,
"expected": true
},
{
"name": "C1478 number and predecessor",
"pass": true,
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1478,
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],
"expected": [
1478,
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]
},
{
"name": "C1478 content hash",
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"expected": "cdce25368d3253b8d8066f3867faf67fae909892fd98ef58b3042d2057b937eb"
},
{
"name": "C1478 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1479 number and predecessor",
"pass": true,
"actual": [
1479,
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],
"expected": [
1479,
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]
},
{
"name": "C1479 content hash",
"pass": true,
"actual": "63a25015a57211c30dab598e1b7f66eeb7f5e2df16d31d173c65cdccfff4d998",
"expected": "63a25015a57211c30dab598e1b7f66eeb7f5e2df16d31d173c65cdccfff4d998"
},
{
"name": "C1479 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1480 number and predecessor",
"pass": true,
"actual": [
1480,
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"expected": [
1480,
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]
},
{
"name": "C1480 content hash",
"pass": true,
"actual": "b75a1f0445f4fa21bd995faa92275f67dee8e8089cd9ed985e69d63d5db99102",
"expected": "b75a1f0445f4fa21bd995faa92275f67dee8e8089cd9ed985e69d63d5db99102"
},
{
"name": "C1480 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1481 number and predecessor",
"pass": true,
"actual": [
1481,
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"expected": [
1481,
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]
},
{
"name": "C1481 content hash",
"pass": true,
"actual": "9226a941264f633c23fa2c1f9409fb9b10f2707c79c31c966eccbfaea619f56d",
"expected": "9226a941264f633c23fa2c1f9409fb9b10f2707c79c31c966eccbfaea619f56d"
},
{
"name": "C1481 completed and reassessed",
"pass": true,
"actual": true,
"expected": true
},
{
"name": "C1482 number and predecessor",
"pass": true,
"actual": [
1482,
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1482,
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]
},
{
"name": "C1482 content hash",
"pass": true,
"actual": "63a2c1e00d6bd151dbc8c279f358e52735901cb21b6bdf2f97b533ad0b2d0623",
"expected": "63a2c1e00d6bd151dbc8c279f358e52735901cb21b6bdf2f97b533ad0b2d0623"
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{
"name": "C1482 completed and reassessed",
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"actual": true,
"expected": true
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{
"name": "no pending research record",
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"actual": false,
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}
]
}
Evidence
verification.json
Linked sources and evidence
Edition and provenance
verification.json
SHA-256 34befa6b0f2fb182f1eaf44e87a11e7f32ac4e407e93c58645c0de7791c8e271
C480–C1634/Research_Cycles/C1433_C1482/model/verification.json