{ "step": "C373", "completed_steps": [ "C364", "C365", "C366", "C367", "C368", "C369", "C370", "C371", "C372", "C373" ], "predecessor_summaries": [ { "step": "C364", "title": "Cumulative counterpart of the joined 460/598 comparison", "main_result": "Six joined cumulative candidates require unsourced+40/+42 endpoints. The32-member register has no500 or1100 interval. Existing458+600=1058 repairs remain sourced; Cainan stays460.", "checks": 30, "source_checks": 17 }, { "step": "C365", "title": "Cumulative and regular Noah 460-490-460 biography rectangles", "main_result": "Eight cumulative Cainan-state950 rectangles and three primary regular SP/restored-MT950 rectangles share460/490/460. Native Noah7300–7293 is source-derived consistently from two dependencies. Twenty-four shape matches do not adopt an axis or select annual/Gear coupling.", "checks": 45, "source_checks": 17 }, { "step": "C366", "title": "Noah biography rectangles under retained source ancestry", "main_result": "The four complete C287 rows match950 state rectangles only with OFF indexj=k-e. Primary460/490 and companion459/491 are sourced, but center reversals differ by row and require opposite phases; same-phase lifts fail.", "checks": 63, "source_checks": 15 }, { "step": "C367", "title": "Fixed19K transport of the native cumulative Noah lifespan", "main_result": "All four complete C287 rows admit native cumulative Noah birth/death → reflected SP Noah death/birth under the existing19K translation, preserving950 and same-phase ancestry. No OFF-Noah internal member reaches restored-MT Noah birth; the required index lies30/31 beyondk.", "checks": 54, "source_checks": 16 }, { "step": "C368", "title": "Noah19K and joined-map selector intersection", "main_result": "Six C319 controls admit fixed19K native Noah950 transport; four admit the regular joined source map. Their intersection is22:i3/i5. The19K condition is equivalent to the existing cumulative2K condition, so no independent coupling prescription is established.", "checks": 44, "source_checks": 17 }, { "step": "C369", "title": "Two-state Noah lifespan bridge matrix modulo529", "main_result": "The sixteen source950 routes have bridge matrix19K-m d. Primaryd460 gives529 remainders69/138; companiond459 gives70/140. One19K translation does not cover all states, and the companion gap retains its annual-index ancestry.", "checks": 70, "source_checks": 15 }, { "step": "C370", "title": "Source lift of P138-to140 and the598-to600 repair", "main_result": "At existing Flood pivots 460 apart, P maps 138→140 and J maps 598→600 to the same sourced two-year repair. Six cumulative rows pass, including all four complete C287 rows; regular primary i3/i5 pass and companion i2/i4 fail exactly. This recovers the prior 458+600 repairs without changing the original 2K/17K outer endpoints.", "checks": 31, "source_checks": 19 }, { "step": "C371", "title": "Uniqueness and controls of the paired P/J repair", "main_result": "The two anchored gap maps agree uniquely at x=13D/10, output30D/23; D460 gives598→600 and138→140. All twenty C319 controls leave joint source matches22:i3/i5. Companion start/close mixing can rescue P alone but not agreement. Twelve same-offset components pass; fixed-center pivot maps fail the inherited offsets.", "checks": 93, "source_checks": 17 }, { "step": "C372", "title": "Primitive integer grammar of the paired P/J repair", "main_result": "Equal integer P/J gains have family69m→70m and299m→300m, pivot separation230m. When the first sourced segment equals the separation, the side is529m. Actual source separation460 fixesm2 and recovers138→140,598→600 and2K1058 with458+600 repair. Integer inputs alone do not suffice; companion controls fail equal gain.", "checks": 26, "source_checks": 19 } ], "predecessor_main_checks": 456, "predecessor_authentication_checks": 152, "predecessor_sealed_audit_totals": { "packets": 9, "manifest_payloads": 233, "certificate_bindings": 108, "predecessor_links": 9, "frozen_source_payloads": 116, "main_output_comparisons": 18, "root_secondary_output_comparisons": 0, "successful_publications": 27 }, "root_second_method_checks": 341, "reading_index_summary": "C364–C373 complete. The cumulative joined460/598→500/600 proposal has no source internal or terminal member in its frozen menu. Existing cumulative and regular Noah950 biographies instead share460/490/460 source shapes; companion shapes require the explicit annual-member shift j=k−1 and retain459/491/459. Fixed19K carries the native cumulative Noah lifespan to the reflected SP lifespan with birth/death roles exchanged and same-offset components preserved, but does not carry the OFF interior. The full bridge matrix has primary remainders69/138 and companion70/140 after division by529. At actual Flood pivots460 apart, P70/69 on138→140 and J300/299 on598→600 reach the same existing two-year repair: all four complete cumulative rows and the two regular primary rows pass; companion regular rows fail. The full C319 comparison again leaves22:i3/i5. Equal integer gains have primitive family69m→70m,299m→300m,separation230m. When the sourced first segment equals that separation, the side is529m; the actual460 fixesm2 and recovers1058=2K. This is a conditional source-supported arithmetic explanation, not a textual rule coupling the ratios or a global map. No canonical or graph edits.", "restart_checkpoint": "Latest completed C373; C374 unexecuted and outside the completed authorization. Use the C373 compact kit as active packet, starting with synthesis/checkpoint; earlier archives are selective references. C370 supplies paired P/J endpoint records; C371 contains uniqueness, twenty-control, boundary and phase tests; C372 gives the primitive integer proof. Retain C367 native950 transport by19K with exchanged birth/death roles. C369 bridge matrices use d460 primary and d459 companion, the latter explicitly including annual-index ancestry;69/70 remainders are not calendar residues. For D460, anchored P and J agree uniquely at outer gap598 with output600 and inner138→140; same-offset component comparisons pass, fixed-center pivot maps do not carry both inherited phases. The equal-gain integer family has pivot230m and source-qualified side529m; no primitive230 source endpoint is adopted. The regular companion alternative SP start allows a P-only hit while J still misses; never merge event boundaries. Prior C353458+600 repairs and their2K/17K outer endpoints remain. Prior C363 regular joined460/598→500/600 and Shem-held squared-E1058→1250 remain separately qualified; the cumulative joined counterpart has no source500 or1100 span in the declared menu. C343 Noah-held1058→1150→1250 ladder remains retained. C287 completei2…5 and C319 slicei3…7 differ. Source500/100 and502/98 modes remain valid. K529,E25/23,P70/69; File02 gapJ300/299 is not ResidueProtocol. Global paired MirrorJanuaryAD1, local junctionJanuaryAD2, no civil yearzero. Regular GearsNoah/Shem/Flood only; SP minus-one person companions local; primary Noah death retains inclusive/harmonic qualification. No new source endpoints, phases, fitted anchors, global axes, upstream Gears, primers, canonical or graph edits. Corrected LXX8464 supplement remains awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. Original unprefixed reports, Engine reports and C-series remain distinct; the old incompleteSeptember17 ZIP differs from the later verified intact original. No independent witness count or source-prescribed selector follows from repeated algebra or coordinates.", "source_access": { "File_18": "actual bytes match retained SHA256", "File_09": "actual bytes match retained SHA256", "File_02_and_File_46": "actual bytes match C370 frozen sources", "C265": "checkpoint readable; certificate hash matches retained control" }, "new_independent_agent_review": false, "C374_executed": false, "canonical_or_graph_edits": false }