{"id": "c458", "title": "Source Equations for the Two 2K Interval Ladders", "filename": "490d_C458_Source_Basis_of_1058_1150_1250_Ladders_20260925.md", "role": "Research action", "step": 458, "sha256": "4db97619b0b6eaa0085e33339335bf5c6524c1738882a97fb5fa1ac0cc0dfb80", "bytes": 3280, "origins": ["C01–C479/packets/C458/490d_C458_Source_Basis_of_1058_1150_1250_Ladders_20260925.md"], "download": "/sources/4db97619b0b6eaa0085e33339335bf5c6524c1738882a97fb5fa1ac0cc0dfb80.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Calendar Keys", "Counts & NT", "Mirror / 529"], "excerpt": "490d C458 — Source Equations for the Two 2K Interval Ladders\n\n25 September 2026 UTC. Step 14 of 25, C445–C469.\n\nBoth admitted2K ladders resolve exactly into source terms. Their input gaps are350+650+60−2 and600+650−130−60−2, each1058. Both first output gaps are500+650=1150; the complete second output is600+650=1250. El", "content": "# 490d C458 — Source Equations for the Two 2K Interval Ladders\n\n25 September 2026 UTC. Step 14 of 25, C445–C469.\n\nBoth admitted2K ladders resolve exactly into source terms. Their input gaps are350+650+60−2 and600+650−130−60−2, each1058. Both first output gaps are500+650=1150; the complete second output is600+650=1250. Eleven required coordinates have16 retained source records.\n\n| Pair | Source binding | Gap |\n|---|---|---:|\n|1895,2953|MTNoah death G3/C0/T0/F0 to SP or LXX-OFF Flood start G2/C0/T1/F0|1058|\n|1745,2895|MTShem death to SP or LXX-OFF Flood start, bothG3/C0/T0/F0|1150|\n|2148,3206|MTShem death G2/C1/T1/F1 to SP-primary or LXX-OFF Shem birth G1/C0/T0/F1|1058|\n|2020,3170|MTShem death to SP or LXX-OFF Flood start, bothG3/C0/T1/F1|1150|\n|1956,3206|MTShem death to SP-primary or LXX-OFF Shem birth, bothG1/C0/T0/F1|1250|\n\nThe shared first pivot3620 is SP companion Noah birth G1/C1/T0/F0. The second pivot2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The SP primary death qualification remains inclusive/harmonic.\n\nThe signed23→25 units are−75 and−29 for the first seed,−64 and−18 for the second seed, then−32 and+18 for its continuation. Each endpoint equation is checked independently against the source-state formula. The final1250 interval combines the600-year Shem-birth/death separation with the650-year MT-to-SP/LXX-OFF offset; it is a direct sourced span.\n\nBoth1150 output pairs differ by the same275-year translation. The relationship between their1058 inputs is therefore worth resolving before the two examples are counted as separate structural findings.\n\n## Verification and scope\n\n26 calculation checks and 19 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.\n\nAll source labels remain distinct. The650 is the normalized MT-to-SP/LXX-OFF offset in this register, not a blanket native-LXX offset for every state.\n\nMirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.\n\n## Best next bounded step\n\n**C459, proposed and unexecuted:** Place every admitted fixed-pivot E input in its signed23-unit lattice and determine whether the two transported2K seeds are one translated four-point configuration, including the corresponding source-state translation.\n\nThe complete source equations suggest that the two first-stage ladders are translated rows of one configuration. The signed23-unit census can verify that relation and its uniqueness in the fixed menu.\n", "evidenceLinks": [{"id": "d-24203a4c3b282f9b", "title": "File 02"}]}