{
"status": "IMMUTABLE PREPARATION — source-bound proposals; no numbered root actions",
"scope": "C1132–C1431 bounded row-operation extension; reassess against the full Strategy every50 actions",
"source_bindings": {
"Strategy": {
"path": "/workspace/scratch/1b40da62dcbd/upload/490d_Unification_Research_Strategy_v0_2_20260906.md",
"sha256": "9c9aa357f5483b3af1dbb5f0025ee514fa28160576a037be03037aa49bf01476"
},
"C1131_technical_final": {
"path": "/workspace/scratch/1b40da62dcbd/c932_c1131/deliverables/490d_Chronological_Families_Technical_Companion_C1131_Final.md",
"sha256": "0c7bb554197b3e12751dea428d076ac7ba21f747e6c5ade643b2d4fe3e1e18e2"
},
"File18": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/38-File_18.Chronological_Data_Tables-20260919-141048-.md",
"sha256": "68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5"
},
"File51a": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/39-File_51a.Rounded_Scaffold_Mod5_Architecture.md",
"sha256": "d8aa38afb2a2df8f3bb57937f5d3dea897c286c034a1bee7398938d30e7bd77c"
},
"File52c_latest": {
"path": "/workspace/scratch/1b40da62dcbd/upload/File_52c.Rounded_Whole_Span_Inverse_Detailed_Study_Draft (2)(1).md",
"sha256": "a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530"
},
"File09": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/30-File_09.Cumulative_Architecture-9-.md",
"sha256": "45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e"
},
"File22": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/15-File_22.Cumulative_MT_Harmonics-20260906-202427-.md",
"sha256": "1c77fd504afbf59b20675980f1122b4f5618a1b8f389132f018d80f65f339894"
},
"Restart": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/32-Restart_Capsule-20260914-154034-.md",
"sha256": "746d59eb554ae807017d1ea4d815b2136933f3b1a07a73060354d9876bf8fc93"
},
"StateVocabulary": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/33-State_Vocabulary_Register-20260914-154034-.md",
"sha256": "fe626d19a545195e8e3ac6fb8b762c281529226a3821e632bd981fff81c90ad1"
},
"Procedures": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/25-Project_Procedures-20260908-220633-1-.md",
"sha256": "28962760304de60731fde6d89422e5ac9209c2fb18dc55b0f9bcceef0958fcfe"
},
"StyleGuide": {
"path": "/workspace/scratch/1b40da62dcbd/project_sources/26-490d_Repository_Style_Guide-20260908-220633-1-.md",
"sha256": "2e7993eac77ec119b27bfc9ace67e3d196d21d358a64c536a1dc8f60729e1abb"
},
"inherited_source_rows": {
"path": "/workspace/scratch/1b40da62dcbd/c732_c831/model/file18_rows.json",
"sha256": "37dd27bbe2eb9d0b7606d75620de499b0ab3493d7188ec814f4f443adb6af9b2"
},
"inherited_full_displacements": {
"path": "/workspace/scratch/1b40da62dcbd/c732_c831/model/tradition_displacement_profiles.json",
"sha256": "a30d1703e4ddaa7670451a1e32597fde8825da57aace1430526d3a8f688fb4f2"
},
"inherited_cap_packet": {
"path": "/workspace/scratch/1b40da62dcbd/c932_c1131/model/sp_cap_inputs.json",
"sha256": "553487c0680d71a577b3242d192ecf33a693607e4cc9ed944e5693ad9da0b2b4"
}
},
"source_control_summary": [
"The full456-line Strategy was read; its §3.2 regular-LXX777/cumulative753 sentence is superseded by current File18 §4A and current control hierarchy: main182/753 in both modes,571 calculated,188 nonoperative,777 appendix-only.",
"File18 SP Jared/Methuselah/Lamech847/720/653 are inclusive ledger counts; Lamech53 counted and52 completed are distinct. Ordinary compatibility claims exclude these rows unless explicitly retagged as formal ledger identities.",
"Remainders in the inherited File18 packet are calculated L-b, not independent quoted readings. Inverse recoverability using their rounded values must not be called independent source generation.",
"Cainan130/330/460 is native in LXX and a single source-admitted restoration in MT/SP. Absent row is not a zero-life person; no unlimited repeated switch.",
"No canonical edits, second decimal inversion, upstream Gear extension, new target tally, probability claim, or universal affine chronology map.",
"All proposal labels identify questions, not numbered root research actions. Algebraic predictions below are not reported as newly executed proofs."
],
"prior_results_to_reuse": [
"C733–C748: mode bridge, ordered full-field reconstruction and triangular inverse are established.",
"C750–C770:25-class rounding defect, complete residual fields, insertion neutrality and Actual recovery with residual are established.",
"C772–C788:finite source configuration, Terah triangle, Cainan support and matched birth-path transfer are established.",
"C953–C983:complete SP cap, local inverse, support interval, derivative and rounding comparison are established.",
"C984–C1007:Key allocation/calibration and affine-grid work is established and is not this proposal packet’s target."
],
"recommended_first_selection": [
"OPX01",
"OPX02",
"OPX03",
"OPX05",
"OPX07",
"OPX08",
"OPX09",
"OPX11",
"OPX12",
"OPX13",
"OPX15"
],
"literal_source_row_packet": {
"MT": [
{
"name": "Adam",
"b_ledger": 130,
"L_ledger": 930,
"r_calculated": 800,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Seth",
"b_ledger": 105,
"L_ledger": 912,
"r_calculated": 807,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Enosh",
"b_ledger": 90,
"L_ledger": 905,
"r_calculated": 815,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Kenan",
"b_ledger": 70,
"L_ledger": 910,
"r_calculated": 840,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Mahalalel",
"b_ledger": 65,
"L_ledger": 895,
"r_calculated": 830,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Jared",
"b_ledger": 162,
"L_ledger": 962,
"r_calculated": 800,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Enoch",
"b_ledger": 65,
"L_ledger": 365,
"r_calculated": 300,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Methuselah",
"b_ledger": 187,
"L_ledger": 969,
"r_calculated": 782,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Lamech",
"b_ledger": 182,
"L_ledger": 777,
"r_calculated": 595,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Noah",
"b_ledger": 500,
"L_ledger": 950,
"r_calculated": 450,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": "Arphaxad-bound; source births differ by 502 despite b ledger 500. Boundary term +2."
},
{
"name": "Shem",
"b_ledger": 100,
"L_ledger": 600,
"r_calculated": 500,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Arphaxad",
"b_ledger": 35,
"L_ledger": 438,
"r_calculated": 403,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Shelah",
"b_ledger": 30,
"L_ledger": 433,
"r_calculated": 403,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Eber",
"b_ledger": 34,
"L_ledger": 464,
"r_calculated": 430,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Peleg",
"b_ledger": 30,
"L_ledger": 239,
"r_calculated": 209,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Reu",
"b_ledger": 32,
"L_ledger": 239,
"r_calculated": 207,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Serug",
"b_ledger": 30,
"L_ledger": 230,
"r_calculated": 200,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Nahor",
"b_ledger": 29,
"L_ledger": 148,
"r_calculated": 119,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Terah",
"b_ledger": 70,
"L_ledger": 205,
"r_calculated": 135,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
}
],
"SP": [
{
"name": "Adam",
"b_ledger": 130,
"L_ledger": 930,
"r_calculated": 800,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Seth",
"b_ledger": 105,
"L_ledger": 912,
"r_calculated": 807,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Enosh",
"b_ledger": 90,
"L_ledger": 905,
"r_calculated": 815,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Kenan",
"b_ledger": 70,
"L_ledger": 910,
"r_calculated": 840,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Mahalalel",
"b_ledger": 65,
"L_ledger": 895,
"r_calculated": 830,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Jared",
"b_ledger": 62,
"L_ledger": 847,
"r_calculated": 785,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": "inclusive; do not replace by simple birth-death difference",
"following_Shem_binding": null
},
{
"name": "Enoch",
"b_ledger": 65,
"L_ledger": 365,
"r_calculated": 300,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Methuselah",
"b_ledger": 67,
"L_ledger": 720,
"r_calculated": 653,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": "inclusive; do not replace by simple birth-death difference",
"following_Shem_binding": null
},
{
"name": "Lamech",
"b_ledger": 53,
"L_ledger": 653,
"r_calculated": 600,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": 52,
"L_counting": "inclusive; do not replace by simple birth-death difference",
"following_Shem_binding": null
},
{
"name": "Noah",
"b_ledger": 500,
"L_ledger": 950,
"r_calculated": 450,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": "Arphaxad-bound; source births differ by 502 despite b ledger 500. Boundary term +2."
},
{
"name": "Shem",
"b_ledger": 100,
"L_ledger": 600,
"r_calculated": 500,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Arphaxad",
"b_ledger": 135,
"L_ledger": 438,
"r_calculated": 303,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Shelah",
"b_ledger": 130,
"L_ledger": 433,
"r_calculated": 303,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Eber",
"b_ledger": 134,
"L_ledger": 404,
"r_calculated": 270,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Peleg",
"b_ledger": 130,
"L_ledger": 239,
"r_calculated": 109,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Reu",
"b_ledger": 132,
"L_ledger": 239,
"r_calculated": 107,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Serug",
"b_ledger": 130,
"L_ledger": 230,
"r_calculated": 100,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Nahor",
"b_ledger": 79,
"L_ledger": 148,
"r_calculated": 69,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Terah",
"b_ledger": 70,
"L_ledger": 145,
"r_calculated": 75,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
}
],
"LXX": [
{
"name": "Adam",
"b_ledger": 230,
"L_ledger": 930,
"r_calculated": 700,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Seth",
"b_ledger": 205,
"L_ledger": 912,
"r_calculated": 707,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Enosh",
"b_ledger": 190,
"L_ledger": 905,
"r_calculated": 715,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Kenan",
"b_ledger": 170,
"L_ledger": 910,
"r_calculated": 740,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Mahalalel",
"b_ledger": 165,
"L_ledger": 895,
"r_calculated": 730,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Jared",
"b_ledger": 162,
"L_ledger": 962,
"r_calculated": 800,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Enoch",
"b_ledger": 165,
"L_ledger": 365,
"r_calculated": 200,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Methuselah",
"b_ledger": 187,
"L_ledger": 969,
"r_calculated": 782,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Lamech",
"b_ledger": 182,
"L_ledger": 753,
"r_calculated": 571,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Noah",
"b_ledger": 500,
"L_ledger": 950,
"r_calculated": 450,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": "Arphaxad-bound; source births differ by 502 despite b ledger 500. Boundary term +2."
},
{
"name": "Shem",
"b_ledger": 100,
"L_ledger": 600,
"r_calculated": 500,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Arphaxad",
"b_ledger": 135,
"L_ledger": 465,
"r_calculated": 330,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Cainan2",
"b_ledger": 130,
"L_ledger": 460,
"r_calculated": 330,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Shelah",
"b_ledger": 130,
"L_ledger": 460,
"r_calculated": 330,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Eber",
"b_ledger": 134,
"L_ledger": 504,
"r_calculated": 370,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Peleg",
"b_ledger": 130,
"L_ledger": 339,
"r_calculated": 209,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Reu",
"b_ledger": 132,
"L_ledger": 339,
"r_calculated": 207,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Serug",
"b_ledger": 130,
"L_ledger": 330,
"r_calculated": 200,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Nahor",
"b_ledger": 79,
"L_ledger": 208,
"r_calculated": 129,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
},
{
"name": "Terah",
"b_ledger": 70,
"L_ledger": 205,
"r_calculated": 135,
"r_status": "derived L_ledger minus b_ledger; not an independently quoted remainder",
"b_completed_primary": null,
"L_counting": null,
"following_Shem_binding": null
}
]
},
"ordinary_rounding_domain": {
"MT": 19,
"LXX_native": 20,
"SP": 16,
"excluded_SP_inclusive": [
"Jared",
"Methuselah",
"Lamech"
],
"total": 55
},
"inherited_regression_targets": {
"names": [
"Adam",
"Seth",
"Enosh",
"Kenan",
"Mahalalel",
"Jared",
"Enoch",
"Methuselah",
"Lamech",
"Noah",
"Shem",
"Arphaxad",
"Shelah",
"Eber",
"Peleg",
"Reu",
"Serug",
"Nahor",
"Terah",
"Abraham"
],
"profiles": {
"LXX": {
"R": [
1380,
1280,
1180,
1080,
980,
880,
880,
780,
780,
780,
780,
780,
550,
450,
350,
250,
150,
50,
0,
0
],
"C_lower": [
890,
890,
890,
890,
890,
890,
890,
890,
890,
914,
914,
914,
427,
400,
360,
260,
160,
60,
0,
0
],
"G": [
-490,
-390,
-290,
-190,
-90,
10,
10,
110,
110,
134,
134,
134,
-123,
-50,
10,
10,
10,
10,
0,
0
]
},
"SP": {
"R": [
300,
300,
300,
300,
300,
300,
400,
400,
520,
650,
650,
650,
550,
450,
350,
250,
150,
50,
0,
0
],
"C_lower": [
-608,
-608,
-608,
-608,
-608,
-608,
-493,
-493,
-244,
-120,
-120,
-120,
-120,
-120,
-60,
-60,
-60,
-60,
-60,
0
],
"G": [
-908,
-908,
-908,
-908,
-908,
-908,
-893,
-893,
-764,
-770,
-770,
-770,
-670,
-570,
-410,
-310,
-210,
-110,
-60,
0
]
}
}
},
"proposals": [
{
"id": "OPX01",
"title": "A unique two-generator row normal form",
"priority": "foundation",
"question": "Can all compatible source-row changes be classified by lifespan-preserving repartition and remainder-preserving extension, while boundary conventions stay separate?",
"domain_and_retained_premises": [
"Ordinary compatible row (b,r,L) with L=b+r. Remainders calculated from File18 are labelled calculated, not independent readings.",
"Set b_eff=b+kappa. kappa is a source binding/count correction, not an editable biography component. Treat SP inclusive capped rows as tagged ledger rows, outside the ordinary-biography assertion."
],
"exact_predictions": {
"basis": [
"R=(1,-1,0)",
"S=(1,0,1)"
],
"normal_form": "Delta(b,r,L)=alpha R+beta S; beta=Delta L; alpha=Delta b-Delta L=-Delta r",
"regular_edge_change": "Delta b_eff=alpha+beta+Delta kappa",
"cumulative_edge_change": "Delta L=beta",
"bridge_generator_change": "Delta(L-b_eff)=-alpha-Delta kappa",
"admissibility": "Each intermediate row must retain its source status and any required nonnegative components; algebra does not authorize a variant."
},
"proof_route": [
"Solve the compatible plane Delta L=Delta b+Delta r in the primitive integer basis R,S.",
"Compose formal moves by addition of (alpha,beta); separate algebraic composition from the finite source-admitted operation graph."
],
"complete_family_test": "Produce one complete labelled row classification on MT19, native LXX20 and SP19 source rows, marking the three SP inclusive exceptions and every binding correction. Do not replace these rows by an unlabelled 2D vector.",
"sources": [
"Strategy §§3.2,5B,5F",
"File18 §§2.1.3–2.2,3.1–3.2,4.1–4.2,4A",
"File51a §3.4"
],
"inherited_results_not_to_repeat": [
"C733–C748 already prove the mode bridge and boundary recovery.",
"C779–C786 already prove the Terah triangle and its projections."
],
"what_this_adds": "Provides a constructive operation vocabulary for the complete received rows. The coordinate change alone is not an information reduction; reduction must come from source-controlled support/equality constraints tested next.",
"counterexample_or_limit": "A remainder derived as L-b cannot be counted as a third independent datum. SP Lamech nominal53/inclusive653 and effective52 are different tags, not competing inputs to one ordinary row.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX02",
"title": "A five-parameter LXX change model",
"priority": "high",
"question": "Does the complete received MT→LXX shared-row comparison lie in one explicitly supported rank-five family, plus the separate native Cainan insertion?",
"domain_and_retained_premises": [
"Nineteen shared named rows, selected main LXX182/753, and unchanged shared Noah binding; native Cainan remains separate.",
"Masks are selected from already explored source patterns, not fitted to an unseen holdout."
],
"exact_predictions": {
"parameters": {
"h": 50,
"lambda": -24,
"a": 27,
"e": 40,
"n": 60
},
"regular_delta": "2h on Adam,Seth,Enosh,Kenan,Mahalalel,Enoch,Arphaxad,Shelah,Eber,Peleg,Reu,Serug; h on Nahor; zero otherwise",
"life_delta": "lambda on Lamech; a on Arphaxad and Shelah; e on Eber; 2h on Peleg,Reu,Serug; n on Nahor; zero otherwise",
"predicted_rank": 5,
"inserted_row": [
130,
330,
460
],
"native_shared_heads": {
"Delta_regular_Creation": 1380,
"Delta_cumulative_Creation": 890
},
"leveled_OFF_heads": {
"Delta_regular_Creation": 1250,
"Delta_cumulative_Creation": 430
}
},
"proof_route": [
"Form the two-mode row design matrix from the frozen named masks, before evaluating any endpoint.",
"Establish rank five by the five distinct observation rows in OPX03, then regenerate complete boundaries using inherited U."
],
"complete_family_test": "Regenerate all shared regular/cumulative displacement coordinates, including every zero plateau, using the existing displacement artifact only as a comparison target. Keep native Cainan as an inserted node.",
"sources": [
"File18 §§2.1.3–2.2,4.1–4.2,4A,1.6",
"Strategy §§4.1,5B,6"
],
"inherited_results_not_to_repeat": [
"C739–C740 already give every displacement and its local support."
],
"what_this_adds": "A genuine rank reduction within a declared supported linear model: common centenary magnitude, equal Arphaxad/Shelah lifespan change and the three remainder-preserving post-Flood changes are constraints, not additional outputs.",
"counterexample_or_limit": "This compresses explored data; it does not derive100,27,40,60 or the masks historically. Count the masks, Cainan row and source choices in description cost. Reject any claim of whole-repository minimality.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX03",
"title": "A minimal observation basis for the LXX model",
"priority": "high",
"question": "Which five source measurements determine the entire supported LXX comparison, and which printed agreements are then dependent?",
"domain_and_retained_premises": [
"Hold the OPX02 masks and native insertion packet; keep terminal/frame metadata."
],
"exact_predictions": {
"observation_basis": [
"Delta b(Adam)=100 -> h=50",
"Delta L(Lamech)=-24 -> lambda=-24",
"Delta L(Arphaxad)=27 -> a=27",
"Delta L(Eber)=40 -> e=40",
"Delta L(Nahor)=60 -> n=60"
],
"expected_identification": "Five independent observations recover all five parameters; omitting any one leaves a nonzero formal direction.",
"predicted_source_checks": [
"Delta L(Shelah)=27",
"Delta b(Nahor)=50",
"Delta L(Peleg)=Delta L(Reu)=Delta L(Serug)=100",
"All six pre-Flood centenary rows preserve L."
]
},
"proof_route": [
"Exhibit the observation matrix and its exact inverse.",
"Remove each observation separately and identify its unmeasured named-row support without searching alternative source states."
],
"complete_family_test": "Compare the regenerated complete19-row two-measurement field and the inserted Cainan row with the frozen source table. Do not count each predicted coordinate as independent evidence.",
"sources": [
"File18 §§2,4,1.6",
"Strategy §§5D,6"
],
"inherited_results_not_to_repeat": [
"C746 composition consistency and C748 unitriangular recovery remain inherited."
],
"what_this_adds": "Separates a minimal measurement basis from its dependent whole-family consequences. This tests compression rather than redisplaying endpoint sums.",
"counterexample_or_limit": "The basis is conditionally minimal only inside OPX02. It is not an independent textual basis or evidence that five choices explain the source history.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX04",
"title": "Recovering local rows from partially observed two-mode fields",
"priority": "medium",
"question": "How much source information is lost when only selected Regular and Cumulative boundaries survive?",
"domain_and_retained_premises": [
"One fixed n-row order and fixed terminals; common block boundaries retained in both modes; ordinary compatible rows or explicitly typed ledger coordinates."
],
"exact_predictions": {
"full_fields": "The joint map (b,L)->(Ub,UL) has rank2n; r=L-b is dependent.",
"m_block_observations": "If only m disjoint block totals are retained in each mode, rank is2m and kernel dimension2(n-m).",
"null_moves": "Within a block, opposed transfers in b or L preserve the measured totals but change internal boundaries."
},
"proof_route": [
"Use the inherited invertibility of U rather than proving it again.",
"Apply the declared block-incidence matrix separately to b and L; exhibit source-labelled opposing transfers in its kernel."
],
"complete_family_test": "Test the actual source segment partitions already used in the native19/20-row fields; retain omitted internal names in metadata. Use the existing Eber73 counterexample as context, not a new result.",
"sources": [
"File18 native tables",
"Strategy §§5B,5D,5G"
],
"inherited_results_not_to_repeat": [
"C747 already gives one swapped-row counterexample.",
"C993 gives the universal conversion/coarsening criterion."
],
"what_this_adds": "Quantifies the reconstruction burden of each omitted boundary on the joint two-mode object.",
"counterexample_or_limit": "Generic rank assumes unconstrained row coordinates. Source equality constraints or nonnegative boundary cases can lower dimension; state them separately.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX05",
"title": "Insertion is identifiable only with its junction data",
"priority": "high",
"question": "Can a collapsed Arphaxad→Shelah comparison distinguish the native Cainan insertion from changes in the adjacent parent row?",
"domain_and_retained_premises": [
"Use the shared-node projection of the native LXX path, without creating a zero-life Cainan in MT/SP.",
"Allow the adjacent parent changes and inserted row measures to vary only in a formal identifiability diagnostic."
],
"exact_predictions": {
"observed_collapsed_difference": [
230,
487
],
"source_decomposition": {
"parent_change": [
100,
27
],
"Cainan_measure": [
130,
460
],
"Cainan_remaining": 330
},
"rank_statement": "The map (d_b,d_L,c_b,c_L)->(d_b+c_b,d_L+c_L) has rank2 and a2-dimensional kernel.",
"kernel_generators": [
"(1,0,-1,0)",
"(0,1,0,-1)"
],
"recovery": "Holding source Cainan130/460 recovers parent100/27; observing the named junction in both modes also separates both pairs."
},
"proof_route": [
"Present the block map before substituting values.",
"Explain why330 is a difference of the two supplied measures, not a third independent insertion constraint."
],
"complete_family_test": "Apply the same source-slot bookkeeping to the complete native LXX field and the explicitly admitted MT/SP restoration companions, retaining both upstream support and the inserted node.",
"sources": [
"File18 §1.6 and §§4.2,6B–6D",
"Strategy §3.2"
],
"inherited_results_not_to_repeat": [
"C740,C759,C774,C782 already establish insertion arithmetic and support."
],
"what_this_adds": "Adds a precise inverse criterion for topology after coarsening, instead of rechecking130/460 shifts.",
"counterexample_or_limit": "Two source means of measuring a row do not by themselves establish the historical act of insertion or omission. No repeated +130 permission follows.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX06",
"title": "Typed insertion/removal as a partial inverse",
"priority": "medium",
"question": "What metadata makes the admitted OFF↔ON Cainan operation a coherent partial inverse?",
"domain_and_retained_premises": [
"Exactly one declared Cainan slot; source payload130/330/460; finite OFF and ON states; native LXX starts ON."
],
"exact_predictions": {
"law": "Remove(Insert(X,payload,slot))=X on the declared OFF domain.",
"reverse_limit": "Insert(Remove(Y))=Y only when the removed named row, source payload and adjacency are retained.",
"forbidden_extension": "Insert is undefined on an already-ON state under the single-switch source policy."
},
"proof_route": [
"Write the domain/codomain and labels explicitly; distinguish deletion of a node from summing its weight into a neighbour.",
"Use the source switch as a finite partial action, not an integer translation group."
],
"complete_family_test": "Check the four admitted downstream placements and all corresponding retained common nodes, using existing source-state packets as fixed cases.",
"sources": [
"File18 §§1.3.1,1.6",
"Strategy §5E"
],
"inherited_results_not_to_repeat": [
"C772–C785 already regenerate the finite states."
],
"what_this_adds": "A composition law with retained source information, useful for a later categorical description without a universal date map.",
"counterexample_or_limit": "A coarsened chronology generally cannot recover a deleted identity. The formal inverse does not establish textual direction or an insertion history.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX07",
"title": "A rounding carry law for successive coarsenings",
"priority": "high",
"question": "Can all changes caused by merging source subdivisions be reconstructed from local rounding carries independent of merge order?",
"domain_and_retained_premises": [
"Positive integer resolved row counts; Q(x)=5 floor((x+2)/5); source order and chosen blocks held."
],
"exact_predictions": {
"carry": "kappa(x,y)=Q(x)+Q(y)-Q(x+y)",
"associativity_identity": "kappa(x,y)+kappa(x+y,z)=kappa(y,z)+kappa(x,y+z)",
"block_defect": "sum_i Q(x_i)-Q(sum_i x_i) is the sum of carries along any fixed binary merge tree.",
"Cainan_prediction": "For any integer x, kappa(x,130)=kappa(x,330)=kappa(x,460)=0."
},
"proof_route": [
"Cancel the four Q evaluations symbolically.",
"Separate tree-independent total carry from tree-dependent intermediate boundaries and source labels."
],
"complete_family_test": "Test every adjacent triple of the three frozen row-measure streams b,r,L on all compatible native rows, plus the single source Cainan merge. Predict the complete coarsening defect field; do not search arbitrary partitions for targets.",
"sources": [
"File51a §§3.4,16–17",
"File18 §1.6",
"Strategy §5F"
],
"inherited_results_not_to_repeat": [
"C752 already proves the25-class local defect.",
"C759 already proves Cainan residual neutrality.",
"C765,C769 already give full-field subdivision failures."
],
"what_this_adds": "Adds the composition law needed to combine local defects coherently across whole source paths.",
"counterexample_or_limit": "Zero total carry does not identify an intermediate path. Coarsening does not authorize removing source event names or applying one-pass digit reversal to a new total.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX08",
"title": "Exact inverse fibres of three rounded row measurements",
"priority": "high",
"question": "How much information do Q(b),Q(r),Q(L) jointly retain on a compatible source row?",
"domain_and_retained_premises": [
"Ordinary integer biographies L=b+r with rounded b and r both at least5; the55-row ordinary domain excludes SP Jared/Methuselah/Lamech inclusive ledger rows.",
"Calculated remainder provenance remains explicit."
],
"exact_predictions": {
"parameterization": "b=B+u, r=R+v with u,v in{-2,-1,0,1,2}; B=Q(b),R=Q(r).",
"third_measurement": "D=Q(L)-B-R=Q(u+v), necessarily in{-5,0,5}.",
"fibre_cardinalities": {
"D=-5": 3,
"D=0": 19,
"D=5": 3
},
"whole_family_prediction": "The inherited six nonzero ordinary splitting-defect rows have three possible component pairs; the other49 ordinary rows have19, before further source data."
},
"proof_route": [
"Classify the25 balanced residue pairs against the third measurement; use inherited defect law without calling its recomputation new.",
"Return the finite inverse fibre for every named source row, not just a selected success."
],
"complete_family_test": "Output55 labelled inverse-fibre records: MT19, native LXX20, SP16 ordinary rows. Explicitly record the three excluded SP ledger rows and their counting tags.",
"sources": [
"File18 ordinary native rows; §§3.1.3,4A for exclusions/status",
"File51a §3.4",
"Strategy §5F"
],
"inherited_results_not_to_repeat": [
"C752–C753 classify forward defects; C770 gives Actual recovery when residuals are fully supplied."
],
"what_this_adds": "A constructive inverse description of what joint rounded measurements lose, rather than another rounding formula.",
"counterexample_or_limit": "These are formal compatible numerical candidates, not admitted biographies. Rounded r can itself be derived from b and L, so the information is not automatically independent source evidence.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX09",
"title": "When exact lifespan makes rounded parts decisive",
"priority": "highest",
"question": "Which compatible source rows are uniquely reconstructed from rounded b, rounded r and exact L, and which still require a source choice?",
"domain_and_retained_premises": [
"Same ordinary55-row domain as OPX08; exact L retained; no hidden use of actual b or r in the inverse algorithm."
],
"exact_predictions": {
"formula": "s=L-Q(b)-Q(r); with |s|<=4, exactly5-|s| balanced pairs satisfy u+v=s.",
"uniqueness": "Unique iff |s|=4, within the interior integer domain.",
"complete_unique_rows": {
"MT": [
"Methuselah",
"Reu"
],
"LXX": [
"Methuselah",
"Reu"
],
"SP_ordinary": [
"Reu"
]
},
"MT_Methuselah": "Qb185,Qr780,L969 -> s4 -> b187,r782",
"MT_Reu": "Qb30,Qr205,L239 -> s4 -> b32,r207",
"LXX_Lamech_counterexample": "Qb180,Qr570,L753 -> s3 -> (181,572) or(182,571). The restored source182 still selects the main calculated571 remainder.",
"Cainan_limit": "Qb130,Qr330,L460 leaves five compatible pairs; source130 is not derived from this packet alone."
},
"proof_route": [
"Solve the bounded line u+v=s in[-2,2]^2.",
"Apply the same inverse to every eligible source row and publish successes and unresolved fibres together."
],
"complete_family_test": "Freeze Qb,Qr,L first, hide actual b/r during reconstruction, then compare all55 outputs with literal source rows. Preserve the fact that this is explored-source recoverability, not an untouched holdout.",
"sources": [
"File18 §§2.1.3–2.2,4.1–4.2,4A",
"File51a §3.4,§§16–17",
"Strategy §§5B,5F,6"
],
"inherited_results_not_to_repeat": [
"C750,C753 already identify Methuselah/Reu forward splitting defects."
],
"what_this_adds": "A sharper information criterion: some exact source parts can be reconstructed conditionally, while an explicit nearby Lamech case remains ambiguous.",
"counterexample_or_limit": "Do not advertise this as historical generation of187 or32: rounded remainder is not an independently attested premise in the inherited File18 packet. No speculative candidate becomes a source variant.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX10",
"title": "From local rounded fibres to a complete genealogy inverse",
"priority": "high",
"question": "How do actual cumulative boundaries and selected actual regular boundaries constrain the remaining rounded-row fibres?",
"domain_and_retained_premises": [
"Fixed source order, count bindings and terminal; exact cumulative boundaries recover L through inherited adjacent differences; rounded b/r measurements retained."
],
"exact_predictions": {
"local_stage": "Use OPX09 independently on every compatible row after recovering exact L.",
"coupling_stage": "Each retained regular block span adds one exact equation on the corresponding candidate b values, with kappa fixed.",
"linear_rank_baseline": "Before finite residue bounds, m independent regular block constraints remove m directions from unresolved b coordinates.",
"failure_certificate": "Any two admissible residual assignments preserving all supplied block sums prove non-identification; do not repair by another endpoint."
},
"proof_route": [
"Use dynamic programming or exact bounded linear constraints on the declared residue domain only.",
"Distinguish a singleton fibre from a rank assertion: finite bounds can give uniqueness even when the rational map has a kernel."
],
"complete_family_test": "First use the fixed Adam–Noah block, then extend through Terah only after reassessment. Report each unresolved named coordinate and all source conditions used; avoid numerical tallies of unrelated endpoint matches.",
"sources": [
"File18 native blocks",
"File51a rounded tables",
"Strategy §§5B,5F,8"
],
"inherited_results_not_to_repeat": [
"C748 and C770 already supply the two reversible coordinate steps."
],
"what_this_adds": "Constructively joins complete-path information to bounded local recovery and states exactly what an extra source boundary contributes.",
"counterexample_or_limit": "A complete actual regular field already contains all begetting intervals, making the inverse tautological. Use a declared proper subset of boundaries and count every retained rounded remainder premise.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX11",
"title": "Lifting admitted row moves to rounded-plus-residual coordinates",
"priority": "high",
"question": "Can row transformations compose exactly on the recoverable rounded representation, including changes not divisible by5?",
"domain_and_retained_premises": [
"Encode positive integer x by y=Q(x),rho=x-Q(x) in{-2,-1,0,1,2}. A shift d is used only where source authorization exists; formal controls remain marked diagnostics."
],
"exact_predictions": {
"carry": "c(rho,d)=5 floor((rho+d+2)/5)",
"lift": "T_d(y,rho)=(y+c(rho,d),rho+d-c(rho,d))",
"composition": "c(rho,d1+d2)=c(rho,d1)+c(rho+d1-c(rho,d1),d2)",
"rounding_only_limit": "Dropping rho prevents a well-defined induced action for arbitrary d; shifts divisible by5 descend without that extra state."
},
"proof_route": [
"Recover x=y+rho and transport ordinary addition through this bijection.",
"Prove the carry composition law; do not reinterpret the auxiliary signed carry argument as a dated count."
],
"complete_family_test": "Apply to the complete source-local changes in OPX01, checking all three measurement streams and their fixed count bindings. Existing source multiples-of-five are regression cases; actual nonmultiple lifespan changes provide the discriminating cases.",
"sources": [
"File51a §§3.4,16–17",
"File18 main lifespan changes",
"Strategy §§5C,5F,5G"
],
"inherited_results_not_to_repeat": [
"C760 proves equivariance for multiples of5; C770 proves recovery with the residual."
],
"what_this_adds": "Supplies a coherent composition law on the richer retained object, rather than declaring rounding an affine group action.",
"counterexample_or_limit": "The lossless augmented representation does not reduce source information by itself. It does not open shifts or variant compositions absent from source controls.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX12",
"title": "Rank of the full birth-plus-cap observation map",
"priority": "highest",
"question": "Exactly which baseline information is absent after the whole birth field and all nine capped lives are observed?",
"domain_and_retained_premises": [
"N and k fixed; nine completed begettings b and nine baseline lives L variable; three strictly active cap rows S={Jared,Methuselah,Lamech}; no threshold ties.",
"B=N1+Ub and y=min(L,Ub+k1), with all source tags retained."
],
"exact_predictions": {
"Jacobian": "[[U,0],[A U,I-A]], A=diag(1_S)",
"rank": 15,
"domain_dimension": 18,
"kernel_dimension": 3,
"kernel": "Birth observations force db=0; only dL on the three clipped rows remains invisible.",
"inverse_fibre": "Each uncapped baseline is fixed by y; clipped baselines are independently bounded below by their capacities."
},
"proof_route": [
"Use inherited invertibility of U and eliminate db from the joint observation map.",
"State the strict-support domain and inequality fibre rather than treating a derivative rank as a global inverse theorem."
],
"complete_family_test": "Bind all nine printed births/capacities/outputs in the existing cap packet, demonstrate all15 independent observable directions, and keep the three named losses explicit.",
"sources": [
"File18 §§3.1,3.1.3",
"Strategy §§5B,5D,5G"
],
"inherited_results_not_to_repeat": [
"C968 already gives rowwise inverse conditions; C971 gives a different late-variable constraint packet; C974 gives the begetting response at fixed baseline."
],
"what_this_adds": "One whole-family information theorem identifies precisely the three missing source quantities after both observed representations are retained.",
"counterexample_or_limit": "The result does not explain the original962/969/777 or establish MT priority. At a threshold the differential formula changes; a closed inverse fibre remains the safer global statement.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX13",
"title": "What additional source measurements recover the lost excesses?",
"priority": "high",
"question": "Which additional independent source measurements would close the three-dimensional cap information gap?",
"domain_and_retained_premises": [
"The OPX12 observation packet; let z_J,z_M,z_L be the nonnegative lost baseline excesses. Add only source-supported measurements."
],
"exact_predictions": {
"one_total": "Holding the inherited total reduction488 imposes z_J+z_M+z_L=488 and raises local rank15 to16, leaving two directions.",
"two_more_rows": "Two independently supplied named excesses or baseline lives plus that total identify the third, provided the measurements are independent.",
"inherited_solution": [
115,
249,
124
]
},
"proof_route": [
"Build the three-column source-measurement incidence matrix and compute its rank before inserting source values.",
"For any proposed extra relationship, test whether it is merely a rearrangement of the already-held cap equations."
],
"complete_family_test": "Assess source support for the entire three-row excess vector together; coordinate with the source-choice investigation. Do not enumerate arbitrary triples as chronological alternatives.",
"sources": [
"File18 §3.1.3 and baseline tables",
"Strategy §§5D,6,8"
],
"inherited_results_not_to_repeat": [
"C957 gives488; C969 shows that even an ancestral multiset does not restore every row identity."
],
"what_this_adds": "Makes the next source research burden exact: at most three independent named measurements are missing, and a known sum supplies only one.",
"counterexample_or_limit": "The total488 is already calculated from the retained baseline packet. It cannot become independent evidence when that same packet is what the inverse is meant to reconstruct.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX14",
"title": "A finite cap response across support changes",
"priority": "medium",
"question": "Can the local derivative be extended to a single exact finite-response law without authorizing new source states?",
"domain_and_retained_premises": [
"Fixed baseline L and k; formal begetting change db; capacities shift by v=U db; all resulting count conditions checked."
],
"exact_predictions": {
"formula": "Delta y=(L-c)_+-(L-c-v)_+, componentwise; c=Ub+k1.",
"piecewise_reduction": "Inside one strict support region this reduces to A v, recovering C974; threshold crossings are handled by the same positive-part formula.",
"source_limit": "Source-admitted frame translations have v=0 when Noah/Flood move together and preserve all capacities."
},
"proof_route": [
"Write min(L,c)=L-(L-c)_+ and subtract.",
"Use a bounded, predeclared diagnostic crossing at a source threshold only to demonstrate the derivative domain; do not invent a historical switch."
],
"complete_family_test": "Evaluate the full nine-row response for every existing source-qualified counting path; reserve unsupported threshold changes as algebraic negative controls only.",
"sources": [
"File18 §§3.1,3.1.3",
"Strategy §§5B,5E"
],
"inherited_results_not_to_repeat": [
"C962 gives the fixed support interval; C974–C977 give local response and frame/count invariance."
],
"what_this_adds": "A global piecewise formula makes the earlier local model composable across mathematical regions and exposes exactly when its simpler derivative ceases to apply.",
"counterexample_or_limit": "This is a mathematical extension of the comparison model, not a wider chronology domain. It should be lower priority than identifying source-supported excess constraints.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX15",
"title": "Joint cap-loss and rounding-residual bookkeeping",
"priority": "high",
"question": "Can the information lost by capping and rounding be separated in one complete reconstruction identity?",
"domain_and_retained_premises": [
"Fixed capacity c, original L, capped y=min(L,c), loss z=L-y; epsilon(x)=Q(x)-x, with the existing nearest-five policy."
],
"exact_predictions": {
"identity": "Q(L)-Q(y)=z+epsilon(L)-epsilon(y)",
"exact_reconstruction": "L=Q(y)-epsilon(y)+z",
"source_changed_rows": {
"actual_losses": [
115,
249,
124
],
"rounded_losses": [
115,
250,
120
],
"rounded_minus_actual": [
0,
1,
-4
]
},
"whole_field": "Apply U to each retained vector; the source total488 becomes485 after separately rounding the baseline and capped lives, with no new endpoint parameter."
},
"proof_route": [
"Derive the identity by substitution; distinguish loss z from a rounding residual.",
"Combine OPX12 fibre information with this equality to state which metadata restores L and which merely reproduces Q(L)."
],
"complete_family_test": "Produce all nine zero/nonzero rows, not just the three changed examples, and their complete cumulative suffix responses. Treat numerical values as inherited regression targets.",
"sources": [
"File18 §3.1.3",
"File51a rounding policy",
"Strategy §§5F–5G"
],
"inherited_results_not_to_repeat": [
"C981 already explains the0,-1,+4 comparison-residual support and -608→-605 consequence."
],
"what_this_adds": "A single loss-register interface connects two irreversible operations while identifying the additional information needed to invert their composite.",
"counterexample_or_limit": "Recording every lost quantity makes a map reversible by bookkeeping but does not compress or explain those quantities. Do not count the rounded loss identity as independent corroboration.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
},
{
"id": "OPX16",
"title": "A source-costed reconstruction ledger for the combined row grammar",
"priority": "synthesis",
"question": "Which proposed reductions explain new structure, and which merely re-encode source inputs?",
"domain_and_retained_premises": [
"Freeze the selected proposals and their full input packets before root execution. Use Strategy §§5B–G and6 at each50-action reassessment."
],
"exact_predictions": {
"ledger_columns": [
"source input and provenance",
"formal operation and exact domain",
"full generated field",
"independent equation count conditional on held values",
"unrecovered source information",
"counterexample",
"description cost including masks and exceptions"
],
"expected_distinctions": [
"OPX01 and lossless residual encoding are coordinate changes, not reductions.",
"OPX02/03 reduce a declared supported family to five parameters, conditional on its masks.",
"OPX09 can give singleton bounded inverse fibres without an independent historical derivation.",
"OPX12/13 locate missing baseline data without generating it."
]
},
"proof_route": [
"Assess each completed result against the full Strategy, not only its nearest mathematical formula.",
"Stop branches that repeat an inherited scalar identity without reducing source burden, transferring a rule, or identifying a genuine failure."
],
"complete_family_test": "Publish one integrated row-operation diagram and complete reconstruction ledger, with native/leveled states and inclusive/ordinary rows still separate.",
"sources": [
"Strategy entirety, especially §§1,5,6,8–9",
"C1131 final technical companion"
],
"inherited_results_not_to_repeat": [
"The C1131 operation inventory and source-cost cautions remain the baseline."
],
"what_this_adds": "Keeps the cycle aimed at explaining how families connect and what remains source-supplied, rather than accumulating endpoint observations.",
"counterexample_or_limit": "No unique smallest grammar, statistical rarity, or historical sequence follows merely from exact algebra or a successful finite reconstruction.",
"status": "Proposal and exact prediction; no numbered execution or new verification claimed"
}
],
"execution_status": "No new numerical family reconstruction or proof was executed while preparing this packet; expected algebraic results await independently bound root execution."
}
Evidence
operator extension proposals.json
Linked sources and evidence
Edition and provenance
operator_extension_proposals.json
SHA-256 1421aa3dbef2f870ef256672b2abd931a3562dc997a22a606507ce3e6c58ec5e
C480–C1634/Research_Cycles/C1132_C1431_Recovered/prep/operator_extension_proposals.json