{
  "step": "C323",
  "steps_consolidated": [
    {
      "step": "C314",
      "title": "Reversed index and phase correspondence",
      "assertions": 60,
      "source_checks": 14,
      "result": "Five source-labelled500+600 biographies and ten components succeed under i=10−j, eN=−eS. The selected finite map is involutive; only j=i5 has full C287 support at both indices.",
      "certificate_sha256": "0a213714c561534edece77da3dc1b2e22a950c23398c471983520e50686ab6bc"
    },
    {
      "step": "C315",
      "title": "Full SP biography and fixed8395 Flood interface",
      "assertions": 47,
      "source_checks": 15,
      "result": "Five complete source biographies and ten exact components pass. None matches the same-ancestry8395 Flood endpoint: residual+2 in every case, with three wrongGear aliases and two unadmitted candidates.",
      "certificate_sha256": "0259e7f3c63444d7470cd6434db3903babe1ba21f97f924899c1faf9d801e8e7"
    },
    {
      "step": "C316",
      "title": "Fixed paths with distinct cumulative antecedents",
      "assertions": 54,
      "source_checks": 15,
      "result": "All five8395 routes work uniquely with h=i−2 and matching Noah ancestry phase. The existingC271 route instead starts at cumulativeShem_i via17K. Equal outputs do not merge these antecedents. RegularGear descent agrees in only three cases.",
      "certificate_sha256": "e18937e038aa0ff22349bceb7d8fb22cbb44f40f5241593bba8f57f562a163e7"
    },
    {
      "step": "C317",
      "title": "Source-qualified600 rectangles carried by17K",
      "assertions": 46,
      "source_checks": 14,
      "result": "Five600 rectangles and ten phase rectangles share two17K paths. Their duration rank is3. Replacing both lower corners by−458 recoversC287 only at i3…5; no independent second17K constraint follows.",
      "certificate_sha256": "726d3ff78ca71bee3af46200ae1b3be16d155e3175a74d9b68ca3490ec5b5497"
    },
    {
      "step": "C318",
      "title": "Typed decomposition of the paired458 replacement",
      "assertions": 57,
      "source_checks": 14,
      "result": "Thepaired−458 replacement decomposes as cumulative−460+2 and regular−650+130+60+2. All intermediate states pass; finalsource endpoints exist onlyi3…5. The sources permit ingredients but do not prescribe the exactpairedselection.",
      "certificate_sha256": "73433920aa81faafe2e5b8f356edf17d5cd7058e50c1887724907d5e5158d313"
    },
    {
      "step": "C319",
      "title": "Four-case sensitivity of the paired two-year selections",
      "assertions": 121,
      "source_checks": 15,
      "result": "The00 and22 choices both retain two17K paths. Only22 gives2K sides/allK in the fixedfour-case test. Of20annual/40phase cases,14/28are source-admitted; allKsurvives3annualcases.",
      "certificate_sha256": "fb9678b840a85a077161047d2948eb43465c380d0a63af50ef6294590edbf670"
    },
    {
      "step": "C320",
      "title": "Complete fixed17K Noah Flood rectangle census",
      "assertions": 77,
      "source_checks": 15,
      "result": "All eightOFFannual pairs against528existingregularrecords yield6coordinate/9labelled600rectangles:6SPand3LXX, allOFF/T0/full430. G1companion i2 isvalidbutneedsabsentj8forreversed500. C287hasfourrowsi2…5.",
      "certificate_sha256": "7785a0072d50c17a87be11a817d9fec6d135b239c51ffb12b3ee7eebc07ee443"
    },
    {
      "step": "C321",
      "title": "Native ON counterpart of the17K600 rectangles",
      "assertions": 35,
      "source_checks": 15,
      "result": "NativeLXX_ON yields3complete17K600rectangles at i3/5/7 inMTON/T60/full430. Allfourcorners shift−460 fromtheOFFSPprimaryfamily, withsixexactphase matches. ThreeFloodcloses have noMTNoah counterparts.",
      "certificate_sha256": "21d467d460d1ec037f1d321986fe5ca64cc77ba0f79386d504d70995be826106"
    },
    {
      "step": "C322",
      "title": "Full biography and joint support diagnostic",
      "assertions": 39,
      "source_checks": 16,
      "result": "All3sameGearNoah-boundSP→MTbiographies transfer−460 at15endpoints/30components. MTtextual502 is a distinctbinding, notsameGearfailure. JointOFF/ON/reversed500/C287-i supporti3,5; additionalC287-j condition leavesi5.",
      "certificate_sha256": "f964fe742c3d64c89b0905000105a6c3e1a343ef138e2b355445531b7df7cdf3"
    }
  ],
  "support_sets": {
    "OFF600": [
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "ON600": [
      3,
      5,
      7
    ],
    "reversed_SP500": [
      3,
      4,
      5,
      6,
      7
    ],
    "C287_at_i": [
      2,
      3,
      4,
      5
    ],
    "C287_at_reversed_j": [
      5,
      6,
      7
    ],
    "OFF_ON_reversed_and_C287_i": [
      3,
      5
    ],
    "with_partner_C287": [
      5
    ]
  },
  "claims": [
    {
      "claim": "Five reversed500 biographies",
      "status": "verified conditional correspondence",
      "conditions": "indicesi+j10, oppositecumulativephases; fivefinitesourcecases",
      "steps": [
        "C314"
      ]
    },
    {
      "claim": "Commonancestor8395matches600biography",
      "status": "fails by2",
      "conditions": "fixedsamecumulativeancestor; allfivecases",
      "steps": [
        "C315"
      ]
    },
    {
      "claim": "Distinctantecedentscanretaintwofixedpaths",
      "status": "verified derivedalternative",
      "conditions": "Floodh=i−2 distinctfromrecordedShemi ancestry",
      "steps": [
        "C316"
      ]
    },
    {
      "claim": "Two17K paths are independent confirmations",
      "status": "not supported",
      "conditions": "equal600sidesmakethesecondpathdependent",
      "steps": [
        "C317",
        "C319"
      ]
    },
    {
      "claim": "AllK requirescoupledtwo-yearchoices",
      "status": "verifiedinheld2x2domain",
      "conditions": "22selectedbyallKcriterion,notbytwo17Kalone",
      "steps": [
        "C318",
        "C319"
      ]
    },
    {
      "claim": "OFF andnativeONwhole600families",
      "status": "verifiedfinitecensuses",
      "conditions": "6OFFcoordinate/9labels;3ONMTcoordinates; companionboundary",
      "steps": [
        "C320",
        "C321"
      ]
    },
    {
      "claim": "Uniform460wholeNoahShembiography",
      "status": "verifiedstatequalified",
      "conditions": "3primarysameGearNoah-bound500biographies; textual502moderetained",
      "steps": [
        "C322"
      ]
    },
    {
      "claim": "Centraljointrowisuniquelyprescribed",
      "status": "notestablished",
      "conditions": "i5uniqueonlyafterallfivechosenpredicates",
      "steps": [
        "C322"
      ]
    }
  ],
  "minimal_dependency_ledger": [
    {
      "premise": "fixedK529andadmittedsourcecoordinates/roles",
      "kind": "retainedinputs"
    },
    {
      "premise": "both17Kpathsplus600sides",
      "kind": "rank3durationgeometry; oneedgeconsequence"
    },
    {
      "premise": "pairedannual/Gear+2",
      "kind": "twodistinctchoices; equalbridgesonlyconstrainscoupling"
    },
    {
      "premise": "C314 index/phase reversal",
      "kind": "forcedconditionalonselected500targetandendpointformulas"
    },
    {
      "premise": "460sourcecomparison",
      "kind": "typedcomposition; Cainanoperatorsremaindistinct"
    },
    {
      "premise": "bothi/jC287admission",
      "kind": "additionaloptionaljointsupportcriterion"
    }
  ],
  "verification_inventory_prior_steps": {
    "main_assertions": 536,
    "authentication_checks": 133,
    "scientific_independent_witness_count": null
  },
  "scope": "Consolidation of completed results only; no newendpoint/anchor orC324research.",
  "latest_complete_after_publication": "C323",
  "next_step": "C324 unexecuted"
}