490d C435 — Complete Input Census for the Six Source-Derived Pivot Pairs
25 September 2026 UTC. Step 1 of 10, C435–C444.
All 2,238 comparisons of the six fixed C434 pivot pairs with373 existing input coordinates are complete. There are two complete coordinate paths, both for G1/Terah-base and pivots3620 then2756:
| Input → intermediate → output, BC | Effective gap from H3206 | Changes in BC coordinates | Interpretation |
|---|---|---|---|
| 2148→2020→1956 | 1058=2K | 128,64 | Previously authenticated forward path |
| 3206→3170→3206 | 0 | 36,−36 | Additional zero-net affine loop |
The loop first expands3620−3206=414 to450, reaching3170. The second pivot2756 is below the intermediate: the signed gap−414 expands to−450, returning3206. Both absolute gap expansions are18×23→18×25, but their directions differ. This is a sourced affine comparison, not two successive forward chronological durations.
The loop endpoints3206 have SP-primary and theoretical LXX-OFF Shem-birth labels at G1/C0/T0/F1. Intermediate3170 has SP and theoretical LXX-OFF Flood-start labels at G3/C0/T1/F1. These source identities need an explicit audit before the word “loop” is interpreted as a return to one labelled record.
| Reference Gear/Terah | First-leg sourced outputs | Integer final outputs | Sourced final outputs | Complete paths |
|---|---|---|---|---|
| G1/T0 | 8 | 2 | 2 | 2 |
| G2/T0 | 3 | 2 | 2 | 0 |
| G3/T0 | 2 | 1 | 1 | 0 |
| G1/T1 | 4 | 2 | 1 | 0 |
| G2/T1 | 3 | 2 | 1 | 0 |
| G3/T1 | 3 | 1 | 1 | 0 |
The ten integer final-output cases and all2,238 rational trials are retained in DATA.json. There are23 sourced first-leg outputs and eight sourced composed outputs; requiring both reduces the result to two paths. No coordinate was added, rounded or fitted.
The2K path has two Cartesian actual-pivot label assignments. The new coordinate loop has16 assignments when its start and end aliases are chosen independently. This is not yet16 returns to the same source record; that distinction is reserved for the next step. Effective-pivot aliases are not additional executed pivots.
The source domain is the frozen C286 register, authenticated through C434. C434’s source formula and corrected File_46 L3 ratio control the maps. Absence means absence from this528-label/373-coordinate domain only.
Verification and scope
2244 calculation checks and 18 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.
Finite frozen-domain result. Opposite signed gap directions and start/end aliases remain explicit; no global source-preserving action is established.
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.
Best next bounded step
C436, proposed and unexecuted: Audit the source states and label identity of the3206→3170→3206 loop; derive its36-year offset from the existing100,60 and Gear4-year difference, and distinguish mixed-direction affine closure from chronological succession.
The census adds one sourced loop. Its event roles, source aliases and direction must be resolved before broader structural claims.