490d C429 — Complete harmonic endpoints of all source 2K pairs
24 September 2026. Step 6 of10, C424–C433.
The complete104-trial inventory has 13 sourced E outputs and13 sourced E² outputs. No P or J output belongs to the integer-coordinate source menu. Only four squared-E cases have a sourced intermediate as well as a sourced endpoint.
| Family | Held upper coordinates | Sourced result |
|---|---|---|
| T1 primary Noah | 3491,3493,3706,3708 | Complete E then E ladders through MT Shem birth to MT Flood start |
| T1 companion Noah | 3490,3492,3705,3707 | E² endpoints; E intermediates absent |
| T1 Shem | 2991,2993,3206,3208 | E² endpoints at MT Shem death; E intermediates absent |
| T2 Flood | 2951,2953,3081,3083,3166,3168,3296,3298 | One E step to sourced MT Shem death |
| T3 Flood | 3298,3300 | One E step to sourced MT Shem death |
| T4 companion Noah | 3899 | E² endpoint2649; intermediate2749 absent |
T2 and T3 share the3298/2240 coordinate case, so their ten template entries give nine distinct Flood-held E arrows. Their outputs are1801,1803,1931,1933,2016,2018,2146,2148 and2150. Every input gap1058 becomes1150 under E, and each output is92 below its input.
The four complete ladders are3491:2433→2341→2241;3493:2435→2343→2243;3706:2648→2556→2456;3708:2650→2558→2458. These belong to the prior Noah-held ladder family; completeness here does not make them new discoveries. The other nine squared-E cases remain endpoint comparisons with absent intermediates.
Every output record label is retained, including aliases at2240 and2455. For example, the companion Noah3705 squared-E output2455 is both MT Flood close and SP-primary/LXX Shem death under different contexts. An endpoint coordinate does not choose one of those identities automatically.
P and J give nonintegral outputs because1058×70/69=3220/3 and1058×300/299=13800/13. These fixed-upper gap calculations are diagnostic comparisons; they do not grant all held source roles a prescribed operator or turn J into a calendar map.
The nine Flood-held E arrows are the most useful new positive result. Their source-context formula and the T2/T3 overlap now deserve a focused check, especially at the top available Gear.
Verification and scope
130 calculation checks and 15 source/predecessor authentication checks passed. A separate main replay is byte-identical. Root-agent analysis and replay; no new independent-agent review is claimed. Verification counts are not independent historical witnesses.
The inventory is fixed-upper gap scaling over existing source pairs. Sourced endpoints and complete source paths remain distinct from a protocol prescription; the four known complete Noah ladders are retained prior results.
Mirror/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.
Decision after this result
C430, proposed and unexecuted: Derive the source-context rule for the nine Flood-held E arrows. Test how T2 and T3 meet at2240 and whether their upper three-Gear strip preserves one input role or requires a qualified role change at its boundary.
The harmonic census exposed a coherent positive Flood-held family. Its source identity and finite Gear boundary are more informative to resolve next than treating nine coordinate arrows as unrelated matches.