{
  "step": "C433",
  "completed_steps": [
    "C424",
    "C425",
    "C426",
    "C427",
    "C428",
    "C429",
    "C430",
    "C431",
    "C432",
    "C433"
  ],
  "predecessor_summaries": [
    {
      "step": "C424",
      "title": "The sixteen Flood-start to Noah-death 2K pairs",
      "main_result": "The16 labelled Flood-start/Noah-death2K pairs occupy eight coordinates, with SP/LXX aliases. All768 fixed-context station comparisons yield no additional2K station. Corresponding primary/native person and Flood roles differ708; SP companion person roles differ707. The mixed-role2K matches are separate from the C416 same-role profile.",
      "calculation_checks": 17,
      "authentication_checks": 14
    },
    {
      "step": "C425",
      "title": "The source equation behind the 708 plus 350 class",
      "main_result": "All6912 Flood-start/Noah-death record pairs were tested; exactly16 hits recover C424. Their single source equation is1058=350+650+60−2. Cainan and sojourn settings match, Terah differs+60, upper Gear is one below lower, and lower Noah death is MT. The16 labels are eight coordinate repetitions of one708-context/350-role relation.",
      "calculation_checks": 6914,
      "authentication_checks": 13
    },
    {
      "step": "C426",
      "title": "Four context templates behind the complete 2K census",
      "main_result": "All46 labelled2K pairs reduce to four context offsets:458 (20 labels/12 coordinates),708 (16/8),1057 (4/2),1059 (6/5). Role and local companion terms complete1058. Their coordinate union has26 rather than27 pairs because3298/2240 belongs to both708 and1057 templates through two distinct MT lower records: Noah deathG3/C1/T0/F1 and Flood closeG1/C0/T0/F0.",
      "calculation_checks": 575,
      "authentication_checks": 14
    },
    {
      "step": "C427",
      "title": "The MT 2240 coincidence behind the template overlap",
      "main_result": "The576 MT Noah-death/Flood-close comparisons yield only2240 and2300, both from349=130+215+4 with matched Terah. Only2240 has an existing2K upper coordinate3298;3358 is absent. At2240, Noah3190→2240/Flood2590→2589 and Noah2841→1891/Flood2241→2240 remain separate contexts. The template overlap is a coordinate alias, not one historical identity.",
      "calculation_checks": 585,
      "authentication_checks": 13
    },
    {
      "step": "C428",
      "title": "Complete fixed 17K joins of the regular 2K census",
      "main_result": "All26 regular2K pairs × six cumulative2K Shem/Flood pairs give156 fixed17K trials. Four coordinate joins survive, with six labelled regular realizations: precisely C287 i2–i5, all T1. Companion i2/i4 remain valid source rectangles; later primary i3/i5 operator qualifications remain separate. T2/T3/T4 add no Mirror branch.",
      "calculation_checks": 160,
      "authentication_checks": 16
    },
    {
      "step": "C429",
      "title": "Complete harmonic endpoints of all source 2K pairs",
      "main_result": "All26 source2K pairs under E/E²/P/J give104 trials:13 sourced E outputs,13 sourced E² outputs, no P/J outputs, and four complete two-E ladders. T2/T3 supply nine distinct Flood-held E arrows to MT Shem death, sharing3298/2240. Nine E² cases remain endpoint-only. Existing source aliases at outputs remain explicit.",
      "calculation_checks": 130,
      "authentication_checks": 15
    },
    {
      "step": "C430",
      "title": "Source rules and Gear boundary of the Flood-held E family",
      "main_result": "Nine Flood-held E coordinate arrows have20 labelled realizations. T2 uses next-Gear MT Noah death/Terah0 to same-Gear MT Shem death/Terah60 at fixed SP/LXX Flood/Terah60, with common C/F. T3 supplies a Flood-close route at C=F=1. The strip3296/3298/3300 has inputs2238 NoahG2,2240 NoahG3 or FloodcloseG1,2242 FloodcloseG2, and outputs2146/2148/2150. Two two-Gear input families meet; no Gear4 Noah or single three-Gear input role is admitted.",
      "calculation_checks": 54,
      "authentication_checks": 15
    },
    {
      "step": "C431",
      "title": "All sourced realizations of the thirteen squared-E maps",
      "main_result": "The13 sourced E² targets ×373 first pivots yield39 sourced pivot-pair solutions and five complete coordinate paths. Four are known fixed-pivot Noah ladders. One new distinct-pivot path repairs the held3206 map:2148→2020→1956 about3620 then2756, with effective pivot3206. Parameter t18 gives gap expansions64×23→64×25 and32×23→32×25, gains128+64=192. Eight endpoint-only maps remain unrepaired; fixed intermediate2056 remains absent.",
      "calculation_checks": 4850,
      "authentication_checks": 14
    },
    {
      "step": "C432",
      "title": "Source and component audit of the 128 plus 64 factorization",
      "main_result": "Nine current excerpts reconstruct18 records and two labelled paths for2148→2020→1956. Pivot3620 is SP companion Noah birth G1/C1/T0/F0;2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The three stations are MT Shem-death states G2→G3→G1. The map equals(625t−307776)/529, effective pivot3206. Actual Noah biographies stay950; pivot gap864 crosses contexts. The+2 counterpart lacks2022 (analogous Gear4); no fixed quarter-component assignment passes. The composition is derived, not a reviewed combined source prescription.",
      "calculation_checks": 44,
      "authentication_checks": 15
    }
  ],
  "predecessor_calculation_checks": 13329,
  "predecessor_authentication_checks": 129,
  "predecessor_sealed_audit_totals": {
    "packets": 9,
    "manifest_payloads": 210,
    "certificate_bindings": 108,
    "frozen_source_payloads": 93,
    "predecessor_links": 9,
    "main_output_comparisons": 18,
    "root_secondary_output_comparisons": 0,
    "successful_publications": 27
  },
  "root_second_method_checks": 719,
  "reading_index_summary": "C424–C433 complete. The46 labelled regular2K pairs at26 coordinate pairs reduce to four context offsets:458,708,1057,1059, with separate role and local companion terms. The Flood-start/Noah-death class is1058=350+650+60−2 and has16 labels/eight coordinates; it adds no second2K station within its fixed contexts. The sole coordinate-template overlap3298/2240 comes from distinct MT Noah-death and Flood-close contexts;349=130+215+4 also produces2300, whose required2K upper3358 is absent. All156 fixed17K join trials recover only existing C287 i2–i5, all in the458 template; companion rectangles do not remove narrower primary operator qualifications. The104 fixed-upper E/E²/P/J tests have13 sourced E and13 sourced E² outputs, no P/J outputs and four complete fixed-pivot Noah ladders. Nine Flood-held E coordinate arrows have20 labelled realizations: two two-Gear input families meet at2240, while the three-Gear strip uses Noah death2238, Noah death/Flood close2240, and Flood close2242, with Shem-death outputs2146/2148/2150. No Gear4 is admitted. The all-pivot squared-E search gives39 sourced pivot-pair solutions and five sourced coordinate paths. One is new:2148→2020→1956, using pivots3620 then2756, exactly the held3206 squared-E map. Its64×23→64×25 and32×23→32×25 legs give128+64=192. Pivot3620 is SP companion Noah birth G1/C1/T0/F0;2756 is SP-primary or LXX-OFF Noah death G1/C0/T0/F1. The stations are different MT Shem-death states G2→G3→G1. Their own Noah biographies remain950; pivot separation864 crosses contexts. The fixed3206 intermediate2056 remains absent. The+2 target still lacks2022; eight other endpoint-only squared-E maps remain unrepaired. Nine current source cards reconstruct18 relevant records; fixed quarter components do not follow the two fixed pivots, although jointly shifted comparisons remain exact. No combined source prescription, new phase, global529/Mirror action or canonical edit is established.",
  "restart_checkpoint": "Latest completed C433. C434 is proposed and unexecuted, outside this completed authorization. Use the C433 compact restart kit as the active packet; read synthesis/checkpoint then the C424–C433 locator. Preserve C423 and older checkpoints as selective references, with their historical next-step paragraphs superseded. The important new positive result is the sourced varying-pivot factorization2148→2020→1956 about3620 then2756, equal to E² about3206. It replaces neither the missing fixed-pivot2056 nor the absent+2 intermediate2022. Its two source-labelled versions differ only in the second pivot SP-primary/LXX-OFF label. The pivots cross contexts and are not one864-year Noah biography. The four source-context templates and the sole2240 alias explain the complete2K census; all fixed17K joins remain old C287 i2–i5. The Flood-held E strip uses two overlapping two-Gear input families, not a Gear4 Noah or one unchanged three-Gear input role. The larger C431 pivot menu is distinct from earlier restricted return-graph searches; their negative results retain their stated scopes. Keep source points, roles, rails, variants, Gear bindings, generated coordinates and quarter ancestry distinct. Regular Gears Noah/Shem/Flood only; SP person companions local; Flood close independent; SP primary Noah death inclusive/harmonic; both500/100 and502/98 valid; LXX native CainanON and theoretical OFF distinct. K529, E25/23, P70/69; J300/299 is File02 gap conversion, not Residue Protocol or a global calendar operator. Global paired Mirror January AD1, local junction January AD2, no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical graph edit. Corrected LXX8464 supplement stays awareness only:1564→1700,2484→2700,920→1000; AD3746/2300 superseded. C-series reports, original unprefixed reports and Engine reports remain distinct. The earlier incomplete September17 local ZIP differs from the subsequently verified intact original. Repeated coordinates, labels and verification implementations are not independent historical witnesses. Proposed C434 tests whether the existing Noah950, Noah–Shem500 and sojourn/Cainan/SP-companion context shift explain the new factorization through one source formula, then checks its finite Gear/Terah family without fitting pivots. That derivation and family census have not been executed in this batch.",
  "source_access": {
    "File_18_File_09": "current bytes match retained controlling hashes",
    "File_02_File_46_File_11_C365": "current bytes match C423 frozen source manifest",
    "C265": "actual checkpoint readable; certificate hash retained"
  },
  "new_independent_agent_review": false,
  "C434_executed": false,
  "canonical_or_graph_edits": false
}