{"id": "c392", "title": "Held-Noah E source graph and its finite ladder components", "filename": "490d_C392_Held_Noah_E_Source_Graph_and_23_to_25_Edges_20260924.md", "role": "Research action", "step": 392, "sha256": "912a0a4eada82ce067fd03a951ad8759713061ef4207a175dbb60ee2d54a6034", "bytes": 4483, "origins": ["C01–C479/packets/C392/490d_C392_Held_Noah_E_Source_Graph_and_23_to_25_Edges_20260924.md"], "download": "/sources/912a0a4eada82ce067fd03a951ad8759713061ef4207a175dbb60ee2d54a6034.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Mirror / 529"], "excerpt": "490d C392 — Held-Noah E source graph and finite ladder components\n\n24 September 2026. Step 9 of 10 in the C384–C393 authorization.\n\nThe complete held-Noah E census has29 nontrivial coordinate edges, including the four retained double-E ladders and two source-qualified23→25 Noah edges. The census evaluates all373 distin", "content": "# 490d C392 — Held-Noah E source graph and finite ladder components\n\n24 September 2026. Step 9 of 10 in the C384–C393 authorization.\n\n**The complete held-Noah E census has29 nontrivial coordinate edges, including the four retained double-E ladders and two source-qualified23→25 Noah edges.** The census evaluates all373 distinct regular coordinates at each of the four selected Noah pivots:1492 exact-rational evaluations.\n\nAt each pivot, the expected source geometry appears:\n\n|Held Noah distance|Existing source comparison|\n|---|---|\n|460→500|Restored MT Noah birth→SP primary/LXX Cainan-OFF Shem birth|\n|598→650|SP/LXX next-Gear Flood→base MT Noah birth|\n|1058→1150→1250|Restored MT next-Gear Flood→base MT Shem birth→base MT same-Gear Flood|\n\nThese give16 edges across the four pivots. There are13 additional edges. Every endpoint retains its complete record indices and source labels in DATA.json; the extra gap families are:\n\n|Held pivot(s)|Distance conversion|Source-role comparison|\n|---|---|---|\n|3491,3493|805→875|MT Shem birth, Cainan/Terah context changes|\n|3491,3493|759→825|SP companion Noah death→SP primary/LXX Shem death, context and Gear changes|\n|3493,3708|1472→1600|MT Noah death across Cainan state and Gear|\n|3706,3708|1173→1275|MT Shem birth→MT preceding-Gear Flood start|\n|3706,3708|1035→1125|SP primary/LXX Noah death→Shem death, Terah state changes|\n|3706|621→675|SP/LXX G3 Flood start→MT G1 Noah birth|\n|3706,3708|23→25|SP primary/LXX Noah birth, one Gear backward|\n\nThe last family is particularly direct. At N3706, E sends3683→3681; at N3708 it sends3685→3683. The held Noah is in Cainan-OFF/Terah0/full4301. Both edge endpoints are in Cainan-ON/Terah60/full4300, with the input one Gear above the output. The source variant displacement is−215+130+60=−25; the input's existing next-Gear increment adds2, giving−23. E therefore expands the held-Noah distance23 to25. SP and LXX retain their separate source identities; no companion rail is used.\n\nThese two edges do not yet establish a P/J inverse, a Mirror lift, or a new axis. Their mixed-operator meaning is deliberately left for a subsequent authorized step.\n\nThe graph has25 maximal nontrivial paths. Its maximum length is two edges, and the only two-edge path at each pivot is the already retained1058→1150→1250 ladder. Every additional edge is isolated within this fixed-pivot E graph. Four fixed points at the held Noah centers are recorded separately. This rules out an extra longer E chain in the tested menu while preserving the newly found one-edge comparisons.\n\nThe census searches coordinate membership broadly; its extra edges often cross modes, branches, roles or Gears. They are finite labelled comparisons, not a single coherent biography or a newly prescribed chronology.\n\n## Verification and limits\n\n20 main checks and 16 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.\n\nThe graph is complete only at the four selected existing pivots in the frozen regular menu. Additional cross-context edges are not independent witnesses or adopted source instructions. Their mixed-operator interpretation has not been executed.\n\nMirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.\n\n## Decision after this result\n\n**C393, proposed and unexecuted:** Consolidate C384–C392 in C393, check the source census and affine identities using a separately written root method, replay the sealed packets, and publish the synthesis, checkpoint and recovery files. Leave C394 unexecuted.\n\nThe batch has a positive E/J source structure, explicit P/cumulative/mode limits, a source derivation of529 and a complete fixed-pivot E graph. A verified synthesis is the best final authorized step.\n"}