{"id": "c393", "title": "Source-qualified E/J transport,529 equivalence and held-Noah E graph synthesis", "filename": "490d_C393_Source_Qualified_E_J_529_Equivalence_and_Held_Noah_E_Graph_Synthesis_20260924.md", "role": "Research action", "step": 393, "sha256": "1a6ae1a116af0c5db314cf802a3ad4a9dc2dc5c31fef68a6a3afbcf7848ef10c", "bytes": 10773, "origins": ["C01–C479/packets/C393/490d_C393_Source_Qualified_E_J_529_Equivalence_and_Held_Noah_E_Graph_Synthesis_20260924.md"], "download": "/sources/1a6ae1a116af0c5db314cf802a3ad4a9dc2dc5c31fef68a6a3afbcf7848ef10c.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "490d C393 — Source-qualified E/J transport,529 equivalence and held-Noah E graph synthesis\n\n24 September 2026. Step 10 of 10 in the C384–C393 authorization.\n\nC384–C393 are complete. The main addition is a source-qualified affine E/J square connecting the existing MT Noah repair to SP/LXX Shem births. It explains the sa", "content": "# 490d C393 — Source-qualified E/J transport,529 equivalence and held-Noah E graph synthesis\n\n24 September 2026. Step 10 of 10 in the C384–C393 authorization.\n\n**C384–C393 are complete. The main addition is a source-qualified affine E/J square connecting the existing MT Noah repair to SP/LXX Shem births. It explains the same529 side from the500/600 source geometry, while retaining definite P, cumulative, phase and source-domain limits.** C394 has not been executed.\n\nThe final held-Noah E census also finds two source-qualified23→25 Noah edges that deserve the next bounded comparison. They have been recorded without claiming a P/J or Mirror interpretation.\n\n## The surviving E/J square\n\nThe original full430 G1→G2 example uses only existing Noah/Shem/Flood records:\n\n|Operation|Input→output|Held source pivot|\n|---|---|---|\n|J=300/299|MT Noah3246→3248|Restored MT Flood2648|\n|E=25/23|MT Noah3246→SP primary/LXX OFF Shem3206|SP primary/LXX OFF Noah3706|\n|E=25/23|MT Noah3248→SP primary/LXX OFF Shem3208|Next Noah3708|\n|J=300/299|Shem3206→3208|Next-Gear Shem death2608|\n\n```mermaid\nflowchart LR\n    A[\"MT Noah 3246\"] -->|\"J; pivot 2648\"| B[\"MT Noah 3248\"]\n    A -->|\"E; pivot 3706\"| C[\"Shem 3206\"]\n    B -->|\"E; pivot 3708\"| D[\"Shem 3208\"]\n    C -->|\"J; pivot 2608\"| D\n```\n\nWith E_N(x)=N+(25/23)(x−N) and J_A(x)=A+(300/299)(x−A), the source identity is\n\n`E_(N+2) ∘ J_A = J_(A−40) ∘ E_N`.\n\nBoth affine coefficients agree; the slope is7500/6877. The transported pivot A−40 is not invented: it is the source target context's next-Gear Shem death. Four coordinate squares have eight SP/LXX context lifts. They compose across the two recorded G1→G2→G3 paths, one in each full430 branch. The corresponding two-edge strips are exact as whole affine maps.\n\nThe first test in C384 deliberately retained the original next Flood pivots. Those direct E/J and E/P squares failed by42/299 and42/69. Solving the unique pivots exposed the Shem-death J lift. The required transported P pivots2853,2855,3068,3070 are absent from all528 records in the frozen regular register. Thus the positive E/J result does not supply a full three-operator source action.\n\n## Why529 appears here\n\nC390 enumerated the coherent family motif without filtering for529,17K or previous P/J membership. Its4096 labelled trials use32 input Noah families,32 target Noah/Shem families, two Gear transitions and two possible original Flood boundaries. It recovers exactly the same four coordinate squares and eight context lifts.\n\nThe source equations explain this outcome. Shem's600-year lifespan and J force the adjacent gain h=2. The source Noah-to-Shem500 gap is250h. Inverting E gives the held-Noah input distance230h=460. The original J Flood gap is299h=598. Therefore\n\n`N−A = 230h+299h = 529h = 1058`.\n\nThe target's existing next-Gear Flood supplies the original P pivot: its distance from N is299h, leaving69h→70h from the MT input/output. Within this fixed family motif, the E/J and earlier common-P/J source contexts correspond exactly.\n\nThis derives the529 side from the chosen source500/600 geometry and the retained ratios. It is not an extra independent observation or a probability calculation. The new side from the *next* Noah to Shem death is550h=1100, which exceeds the old529h=1058 side by21h=42. The original2K/17K geometry has not become a global invariant under E/J.\n\n## What the source and mode controls retain\n\nThe square uses the primary500/100 binding. All18 available companion/modal controls still possess their horizontal598→600 Shem J edge. Ten fail the vertical E side: the exact residuals are25/23 for SP companion500/100,2 for primary502/98, and71/23 when both changes apply. Six additional requests would need Gear0 and remain unavailable. Both valid source modes and the SP-local companion mechanism are preserved.\n\nAcross1024 assignments of the inherited±1/4 offsets, eight retain all four edges: the two matched-component assignments per coordinate square. They use the corresponding phase-shifted source pivots. One fixed physical-time composite changes half-year separation by623/13754, so the matched-component comparison is not one seasonal-preserving physical map.\n\nAll eight two-letter bottom P/J routes in the two strips reach the same final source endpoints. Only the two JJ routes equal the upper all-J route as whole affine maps. Shared endpoints do not equate operators with different slopes. Horizontal continuation would need an unrecorded next MT Noah Gear; a second vertical E application gives a noninteger source image.\n\nBoth original17K corner exchanges conjugate the E/J identity exactly, but each reflected square lacks three cumulative points: the new Shem input, its output and the transported death pivot. The48-record cumulative menu supplies ten of the16 point slots and neither complete square. Reversing component ancestry under reflection does not supply the missing points. These exchanges remain diagnostic source comparisons, not new global Mirror axes.\n\n## The complete E graph at the selected Noah pivots\n\nC392 tests373 distinct input coordinates at each held Noah3491,3493,3706,3708:1492 exact evaluations. It finds29 nontrivial coordinate edges, four fixed points and25 maximal paths. The only two-edge path at each pivot is the retained1058→1150→1250 ladder. The other expected edges are460→500 (the new square's vertical E edge) and598→650 (source Flood to base MT Noah).\n\nThirteen additional one-edge comparisons retain explicit source labels. Some cross contexts, roles or Gears; they do not form a single biography. Two give a particularly simple primitive E relation:\n\n|Held Noah|Existing Noah input→output|Distance conversion|\n|---|---|---|\n|3706|3683→3681|23→25|\n|3708|3685→3683|23→25|\n\nThe held Noah uses Cainan-OFF/Terah0/full4301. The input and output use Cainan-ON/Terah60/full4300, with the input one Gear above the output. The recorded variant displacement is−215+130+60=−25; the input Gear increment2 gives−23. This accounts for the exact E edge without a fitted anchor. SP primary and LXX are distinct source context lifts. The edges' mixed P/J or Mirror significance remains untested.\n\n## Ten-step locator and decisions\n\n|Step|Completed bounded result|\n|---|---|\n|C384|Source translation intertwines E ladders; direct E/PJ mixed squares fail|\n|C385|Unique transported J pivots are sourced Shem deaths; P pivots are absent|\n|C386|Whole affine E/J identity, source500/600 geometry and component limits|\n|C387|SP companion and502/98 controls, with valid source alternatives retained|\n|C388|Two finite E/J strips; operator equality distinguished from endpoint agreement|\n|C389|Reflected cumulative algebra passes, but required source points are absent|\n|C390|4096-case coherent-family census without529 or prior-PJ prefilter|\n|C391|Source derivation and conditional equivalence of E/J and the529 P/J side|\n|C392|Complete selected-pivot E graph and two sourced23→25 reverse-Gear edges|\n|C393|Synthesis, alternate verification, portable replay and recovery checkpoint|\n\nEach completed step carries its report, evidence, checkpoint and a new next-step decision made after that result. The final reading index links all30 individual deliverables. The compact kit is the active restart packet; the continuation archive retains all ten sealed packets. Older archives remain selective reference libraries.\n\n## Access and verification provenance\n\nFile18 and File09 actual bytes match their retained hashes. File02, File46 and the cumulative menu match the C383 frozen source manifest. The C265 checkpoint is readable and its certificate matches the retained control. C383 and the selectively retrieved C343 evidence archive passed ZIP CRC checks at restart. No historical report-by-report reread was needed.\n\nThe nine sealed predecessor packets passed payload hashes, certificate/predecessor bindings and fresh isolated replay, reproducing18/18 DATA/RESULTS outputs. Their27 individual publication receipts succeeded. C393's main calculation also replays identically. A separately written root method uses output-first source lookup, integer affine matrices, integer quarter-component checks and output-first E graph enumeration:118 checks pass, and its portable run against C393's frozen sources reproduces the result bytes. This is a second implementation by the same agent, not an independent-agent review.\n\nThe final completion/integrity record supplies the ten-packet audit and recovery ZIP hashes after the C393 packet is sealed. Counts are verification inventories, not independent historical witnesses. Current corrections and scope decisions override old archive next-step paragraphs. The corrected LXX8464 supplement remains awareness only, and regular Gears remain Noah/Shem/Flood only.\n\n\n## Verification and limits\n\n75 main checks and 62 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\nAll exhaustive claims refer to their stated finite menus and role/context constraints. Exact algebra, repeated coordinate aliases and source membership do not establish historical intention, independent witnesses or a source-prescribed pairing. No global529-preserving action is established. C394 is unexecuted.\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**C394, proposed and unexecuted:** Test the two newly recorded E23→25 reverse-Gear Noah edges against the existing finite P/J source graphs and the two recorded17K source-corner exchanges. Keep their−215+130+60 context displacement explicit, use only existing pivots/endpoints/phases, and determine whether any mixed-operator or Mirror source diagram closes. Do not extend Gear scope or adopt generated coordinates.\n\nThe final E census found these two source-qualified primitive edges beyond the old ladder, while the present E/J construction has explicit P and cumulative limits. A finite compatibility test is the next direct529/Mirror question. C394 is proposed only and requires a new instruction.\n", "evidenceLinks": [{"id": "d-18e8c54ff1663fb1", "title": "File 46"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}, {"id": "d-24203a4c3b282f9b", "title": "File 02"}]}