{ "step": "C413", "completed_steps": [ "C404", "C405", "C406", "C407", "C408", "C409", "C410", "C411", "C412", "C413" ], "predecessor_summaries": [ { "step": "C404", "title": "Noah-to-Shem transport of the three-point return graph", "main_result": "The existing E charts transport the six Noah graph arrows exactly, but only the two J arrows have sourced Shem pivots. Required E pivots3016/3018 and P pivots2853/2855 are absent. Of402 finite paths, only identities,J,J,JJ retain all primitive sources; no nonempty closed path survives.", "checks": 430, "source_checks": 19 }, { "step": "C405", "title": "Source-qualified 500-year translation of Noah return loops to Shem", "main_result": "Translation by−500 carries all12 labelled/six coordinate Noah E/J loops and both complete E/P/J graphs to existing Shem births/deaths. All52 source slots match. The complete Shem graphs join at2533, with vertices2531,2533,2535; all402 path maps are exactly conjugate with unchanged slopes.", "checks": 545, "source_checks": 18 }, { "step": "C406", "title": "Independent coherent-family census of Shem return loops", "main_result": "All2048 direct Shem-family trials yield12 labelled/six coordinate E/J loops and exactly two complete E/P/J loops, equal to the−500 image of the Noah census. No loops fall outside that correspondence. Source600 and Gear2 force J; the context difference215−130−60=25 supplies E.", "checks": 28, "source_checks": 15 }, { "step": "C407", "title": "500 and 502 source bindings and the finite Gear boundary", "main_result": "The500 binding admits all12 labelled/six coordinate loops and both E/P/J graphs. The502 binding admits six labelled/three coordinate loops, including one complete E/P/J graph, by mapping originalG2–G3 to targetG1–G2. All six other502 cases require unavailableGear0 births; the admitted images are existing500 configurations.", "checks": 50, "source_checks": 17 }, { "step": "C408", "title": "Return-path obstruction to the missing squared-E factorization", "main_result": "C361 already supplies the translated squared-E endpoints. The new Shem graphs have exactly three slope-compatible EE paths; all six comparisons with the two target maps fail. Prime valuations exclude every longer positive E/P/J replacement. The closest companion-path discrepancy is−4/529; all48 existing-phase comparisons also fail.", "checks": 59, "source_checks": 18 }, { "step": "C409", "title": "Fixed Mirror-corner test of the Shem loop translation", "main_result": "Both original2K short sides remain1058 after translating the regular endpoints−500, but both17K cross-spans become8493. Under the unchanged corner exchanges−2639/−2635, all104 labelled reflected Shem-loop slots and208 reversed-phase components are absent from the frozen cumulative menu.", "checks": 112, "source_checks": 20 }, { "step": "C410", "title": "Complete regular-source domain of the fixed 500-year translation", "main_result": "The373-coordinate−500 census has169 coordinate arrows,392 labelled endpoint pairings and141 maximal coordinate chains:115 of length1,25 of length2 and one of length4. The identified role relations cover168 arrows; the sole extra coordinate bridge3395→2895 creates3895→3395→2895→2395→1895. Source identities remain separate at coincident coordinates.", "checks": 3, "source_checks": 15 }, { "step": "C411", "title": "Source formula and record-path lift of the four-step 500 chain", "main_result": "The new bridge3395→2895 is uniquely forced within the SP field by100+130+60+215−4−1=500. The four-step chain has two continuous record lifts, using SP or LXX OFF for the G3 Flood/death pair.240 role-defined arrows give192 paths of length≤2; adding the two bridge labels yields191 paths including two length4 lifts. Only uniform±¼ assignments pass; own950/600 lifespans remain unchanged.", "checks": 10, "source_checks": 15 }, { "step": "C412", "title": "Direct reconstruction and source warrant of the 500 comparison domain", "main_result": "Twelve exact source excerpt cards independently reconstruct all528 regular records, including all52 translated loop slots and ten long-chain slots. Source500/502 bindings, SP-local companions, independent Flood close, native LXX Cainan and Noah950/Shem600 qualifications remain explicit. The loop grammar and3395→2895 bridge are derived comparisons, with no new source prescription established.", "checks": 543, "source_checks": 20 } ], "predecessor_main_checks": 1780, "predecessor_authentication_checks": 157, "predecessor_sealed_audit_totals": { "packets": 9, "manifest_payloads": 238, "certificate_bindings": 108, "predecessor_links": 9, "frozen_source_payloads": 121, "main_output_comparisons": 18, "root_secondary_output_comparisons": 0, "successful_publications": 27 }, "root_second_method_checks": 1041, "reading_index_summary": "C404–C413 complete. The existing Noah-to-Shem E charts retain only the two sourced J arrows; required Shem E pivots3016/3018 and P pivots2853/2855 are absent. The fixed source500 correspondence succeeds: all12 labelled/six coordinate Noah E/J loops translate to Shem births/deaths, including both complete E/P/J graphs. The complete target graph has MT Shem2531,2533,2535, E pivots2556/2558, J death pivots1933/1935 and P death pivots2393/2395. Every path is conjugated byT(t)=t−500 with unchanged slope and circuit multipliers1750/(3K),7500/(13K). A direct2048-case Shem-family census recovers exactly those loops. The valid502/98 binding maps only originalG2–G3 to targetG1–G2; the other six labelled cases would require unavailableGear0. The older translated squared-E endpoints were already established inC361/C363; the new return paths cannot replace their missing2056/2058 intermediate. Three slope-compatible EE paths fail all six whole-map comparisons and48 phase comparisons; the closest discrepancy is−4/529. The existing Mirror corner exchanges admit none of104 reflected loop-record slots or208 inherited components. Translating the original regular2K side−500 preserves1058 but changes both17K cross-spans to8493. The full fixed−500 source-domain census has169 coordinate arrows,392 labelled pairings and141 maximal coordinate chains. A single extra coordinate bridge3395→2895 produces3895→3395→2895→2395→1895. Its formula100+405−4−1=500 forces all three variant differences, SP companionG1 and FloodG3. It has two continuous record lifts, choosing SP or LXX CainanOFF for the Flood/death pair; the sequence is not one biography. All528 regular records reconstruct from twelve current source excerpts. The new graphs and bridge remain derived comparisons; no new source endpoint, protocol prescription, canonical edit or global529/Mirror action is established.", "restart_checkpoint": "Latest completed C413; C414 is unexecuted and outside this completed authorization. Use the C413 compact restart kit as the active packet; read synthesis/checkpoint then locator. C404 separates failed E-chart closure from C405 positive−500 role correspondence. C406 gives the independent target-family census; C407 the500/502 Gear boundary; C408 the all-positive-word obstruction to substituting a new return path for C361 squared-E map; C409 the fixed Mirror source obstruction; C410 the complete−500 coordinate domain; C411 the bridge formula and record-path lifts; C412 the direct528-record source reconstruction and warrant matrix. The complete Shem graphs are2531↔2533↔2535, with E return pivots2556/2558, J forward death pivots1933/1935 and P forward death pivots2393/2395. Their source correspondence with the C400 Noah graph isT_-500, not the earlier E charts toSP/LXX Shem2991/2993/2995. Preserve source labels even when affine maps agree. The four-step500 chain3895→3395→2895→2395→1895 begins with SP companionG1 CainanON/Terah60/full430 Noah and Shem births, crosses toSP or LXX OFF G3/base-Terah/half430 Flood start and Shem death, then ends atMT Noah death. Its opening own deaths remain2945 and2795, giving950/600. The bridge alone is a derived cross-context comparison; no2000-year biography is adopted. C361/C363 already recorded the−500 squared-E endpoints; newC408 is the replacement-path obstruction, not a new discovery of that translation. Retain C403/C393/C383 finite source normal forms, conditional529 equivalences and missing Mirror/pivot members. No global2K/17K-preserving action is established. K529,E25/23,P70/69; File02 J300/299 is gap conversion, not Residue Protocol or permission to transform dates globally. Global paired MirrorJanuaryAD1; local junctionJanuaryAD2; no civil yearzero; signed cumulative coordinates are not civil dates. Regular Gears Noah/Shem/Flood only. SP person companions remain local, Flood close independent, primary Noah death inclusive/harmonic; both500/100 and502/98 valid. LXX nativeCainanON is not given a second insertion; OFF is theoretical removal. No new source endpoint, phase, fitted anchor, global axis, upstream/cumulative Gear, primer reopening or canonical graph edit. Corrected LXX8464 supplement awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. C-series, original unprefixed reports and Engine reports remain distinct. The earlier incompleteSeptember17 ZIP differs from the later verified intact original. Counts, aliases, repeated paths and second implementations are not independent historical witnesses. Proposed C414 tests existing2K regular source pairs under one and two applications of the fixed−500 comparison; no such new pair census has been executed.", "source_access": { "File_18": "actual bytes match retained SHA256", "File_09": "actual bytes match retained SHA256", "File_02_File_46_File_11_C365": "actual bytes match C403 frozen manifest", "C265": "checkpoint readable; certificate matches retained hash" }, "new_independent_agent_review": false, "C414_executed": false, "canonical_or_graph_edits": false }