# 490d C392 — Held-Noah E source graph and finite ladder components

24 September 2026. Step 9 of 10 in the C384–C393 authorization.

**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.

At each pivot, the expected source geometry appears:

|Held Noah distance|Existing source comparison|
|---|---|
|460→500|Restored MT Noah birth→SP primary/LXX Cainan-OFF Shem birth|
|598→650|SP/LXX next-Gear Flood→base MT Noah birth|
|1058→1150→1250|Restored MT next-Gear Flood→base MT Shem birth→base MT same-Gear Flood|

These 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:

|Held pivot(s)|Distance conversion|Source-role comparison|
|---|---|---|
|3491,3493|805→875|MT Shem birth, Cainan/Terah context changes|
|3491,3493|759→825|SP companion Noah death→SP primary/LXX Shem death, context and Gear changes|
|3493,3708|1472→1600|MT Noah death across Cainan state and Gear|
|3706,3708|1173→1275|MT Shem birth→MT preceding-Gear Flood start|
|3706,3708|1035→1125|SP primary/LXX Noah death→Shem death, Terah state changes|
|3706|621→675|SP/LXX G3 Flood start→MT G1 Noah birth|
|3706,3708|23→25|SP primary/LXX Noah birth, one Gear backward|

The 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.

These 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.

The 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.

The 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.

## Verification and limits

20 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.

The 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.

Mirror/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.

## Decision after this result

**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.

The 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.