490d C425 — The source equation behind the 708 plus 350 class
24 September 2026. Step 2 of10, C424–C433.
The unfiltered6912-pair census recovers exactly the16 C424 labels. Every hit has one source equation:
1058 =350 +650 +60 −2 =350 +708.
The350 is the same-context Flood-start/Noah-death role difference. The650 is the SP or CainanOFF-normalized LXX baseline relative to MT. Terah contributes+60; the upper Gear is one below the lower, contributing−2. Cainan and sojourn differences are both zero, and the lower record is an ordinary MT Noah-death station.
The census compares all72 Flood-start records with all96 Noah-death records, retaining tradition, person rail, both Cainan settings, both Terah settings, both sojourn settings and all three Gears. The source equation reproduces every one of their6912 actual differences, not just the hits.
The16 labels consist of two upper traditions × two common Cainan settings × two common sojourn settings × two adjacent-Gear placements. SP and LXX coincide numerically at the matched Cainan flag but retain different source identities and native/theoretical statuses. Their eight coordinate pairs are repetitions of one structural relation across that finite source menu.
This explains why primary/native same-role stations have708 rather than1058 separation. The extra350 comes from comparing different roles. It does not create a same-role2K profile or a new calendar operator. The next useful reduction is to ask whether the other C414 role classes admit an equally small set of source-context equations.
Verification and scope
6914 calculation checks and 13 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 scalar708 correspondence is derived from existing endpoints. Source-label multiplicity is not independent corroboration; LXX native Cainan and theoretical removal remain distinct.
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
C426, proposed and unexecuted: Express every one of the46 labelled C414 2K pairs as a standard role difference plus explicit tradition, variant, Gear and local companion terms. Determine the minimal observed context templates and any coordinate overlap between them.
The new class reduces to one source equation. Extending that accounting to the already frozen complete2K census can reveal a smaller common structure without adding another search domain.