490d C402 — Source reconstruction and warrant of the return-loop grammar
24 September 2026. Step 9 of 10 in the C394–C403 authorization.
Every source record used in the six coordinate loops reconstructs from the current tables and scoped variant rules. The new circuit grammar remains a derived mathematical comparison. The reviewed source passages establish the endpoints and scalar operators, but do not prescribe the newly assembled E/P/J circuits.
The direct reconstruction starts from the current G1 Noah baseline labels: MT2841, SP primary3491/companion3490, and native-Cainan LXX3621. File02 §6.2 and File18 §§2.2.1/3.2.1 supply these values. The three-Gear offsets are+0,+2,+4. The stated variant amounts are+215 for the branch, +60 for Terah, and+130 for regular Cainan, with tradition-specific handling.
| Source item | Bounded source support |
|---|---|
| MT Noah pair and950 lifespan | File02 §6.2; File18 §2.2.1 |
| SP primary/companion Noah stations | File18 §3.2.1, including the inclusive/harmonic primary-death qualification |
| MT/LXX/SP Flood start and close | File18 §3.1.4; each close is independently start−1 |
| Variant displacement215−130−60=25 | File18 §1.3 source variant field |
| LXX native Cainan versus theoretical removal | File18 §§1.3/1.6.2 |
| E25/23 and P70/69 | File46 L3 andL2, respectively |
| J598→600 | File02 §6.3, explicitly a gap conversion rather than a date transformation or Residue Protocol |
All52 labelled record slots across the12 source-context comparisons reconstruct exactly. This includes every held Noah, both moving Noah endpoints, each return J boundary and the four SP/LXX P-pivot record slots. Repeated slots and aliases are verification inventory, not additional witnesses.
LXX is reconstructed from its native Cainan-ON baseline. A moving LXX ON row receives no second Cainan insertion; the held LXX OFF row explicitly uses the admitted theoretical-removal comparison. MT/SP ON rows use restoration. These distinctions are preserved even where the resulting SP and LXX coordinates coincide.
The SP companion cases require Flood close because the companion Noah is599 center-units from the matching Flood start and600 from its close. The close remains an event boundary, not a companion Flood person-station. All Gear applications in this reconstruction stay within Noah/Shem/Flood.
The new source graph and its normal form arise by encoding held-pivot gap equalities as affine maps. Their exactness is an algebraic result about those comparisons. It does not turn File02's gap conversion into a general instruction to transform dates, or make the circuit words an attested ancient procedure. The reviewed passages do not establish that prescription; this bounded finding does not claim that every historical report or repository passage has been searched.
The source cards in DATA.json retain exact excerpts, section labels, line locations and hashes from File18, File02, File46 and the scoped Gear definition in File11. No repository file or canonical graph was changed.
Verification and limits
84 main checks and 19 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 warrant review is limited to the ten frozen source excerpts and stated dependencies. Mathematical/source compatibility is not proof of historical intention, a prescribed date action or independent corroboration.
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
C403, proposed and unexecuted: Consolidate C394–C402 in C403, verify the principal source census and path algebra with a separately written root method, replay the sealed packets, and publish the synthesis, checkpoint and recovery files. Leave C404 unexecuted.
The batch now has a finite source-loop domain, an exact reduced path grammar, proven global limitations and a direct source reconstruction. A verified synthesis and recovery checkpoint are the best final authorized step.