{"id": "c394", "title": "Primitive E23-to25 edges: P/J and Mirror compatibility", "filename": "490d_C394_Primitive_E23_to25_P_J_and_Mirror_Compatibility_20260924.md", "role": "Research action", "step": 394, "sha256": "ccda6b601710c48ffc6e6242cc51ad8d3a2d8b9d619a6152d77cbef7daeda536", "bytes": 3547, "origins": ["C01–C479/packets/C394/490d_C394_Primitive_E23_to25_P_J_and_Mirror_Compatibility_20260924.md"], "download": "/sources/ccda6b601710c48ffc6e6242cc51ad8d3a2d8b9d619a6152d77cbef7daeda536.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Mirror / 529"], "excerpt": "490d C394 — Primitive E23→25 edges: P/J and Mirror compatibility\n\n24 September 2026. Step 1 of 10 in the C394–C403 authorization.\n\nBoth sourced E23→25 arrows have an existing J return arrow. Their P counterparts and reflected cumulative endpoints are absent from the frozen menus. This is a finite source endpoint loop, ", "content": "# 490d C394 — Primitive E23→25 edges: P/J and Mirror compatibility\n\n24 September 2026. Step 1 of 10 in the C394–C403 authorization.\n\n**Both sourced E23→25 arrows have an existing J return arrow. Their P counterparts and reflected cumulative endpoints are absent from the frozen menus.** This is a finite source endpoint loop, whose whole-map meaning is the next question.\n\n|Held E Noah|E source arrow|Existing reverse J arrow|J Flood pivot|\n|---|---|---|---:|\n|3706|3683→3681|3681→3683|3083|\n|3708|3685→3683|3683→3685|3085|\n\nThe E held Noah is Cainan-OFF/Terah0/full4301. The moving Noah endpoints and return Flood pivot are Cainan-ON/Terah60/full4300. The input E Noah is one Gear above the output. SP primary and LXX records are separate context lifts of the same coordinates. The source difference remains−215+130+60=−25, with the input Gear increment2 making−23.\n\nFor any proposed input u→v with gain h, the P pivot is uniquely u−69h and the J pivot uniquely u−299h. Both orientations were checked in the entire528-record regular register:\n\n|E held Noah|Forward P / J required pivots|Reverse P / J required pivots|\n|---|---|---|\n|3706|3821 /4281: both absent|3543 absent /3083 sourced|\n|3708|3823 /4283: both absent|3545 absent /3085 sourced|\n\nThe two sourced return pivots each have the correct SP/LXX Flood-start records at the next Gear in the endpoint context. They realize598→600 under J. None of these endpoint pairs belongs to the earlier *common* P/J graph; a J-only return does not contradict that exhaustive common-edge census.\n\nThe corresponding original17K corner exchanges send the held Noah to existing native cumulative Shem, but send both E endpoints and the return J Flood pivot to absent cumulative coordinates. The inherited opposite phase offsets do not rescue membership. No new cumulative date or diagnostic axis is adopted.\n\nC392 supplies the E edges and labels, C378 the earlier common-P/J graph, C379 the original source-corner exchanges, and C365 the48-record cumulative menu.\n\n## Verification and limits\n\n19 main checks and 18 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.\n\nThe absence checks are confined to the frozen regular/cumulative menus. Coordinate aliases are not independent witnesses. Whole-map inversion and biography preservation have not been inferred from endpoint return.\n\nMirror/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.\n\n## Decision after this result\n\n**C395, proposed and unexecuted:** Determine the exact affine maps around the two E/J source endpoint loops, including order, fixed points, matched phases and950-year Noah biography transport.\n\nC394 supplies a positive two-edge source loop. Its meaning must be separated from a claim that E and J are inverse maps or preserve an entire chronology.\n"}