{
  "title": "Verified operation relations and additional source conditions",
  "claim_classes": {
    "classes": [
      {
        "id": "identity",
        "meaning": "Followsforalldeclaredinputsfromoperationdefinitions",
        "example": "Accumulationofrowdifferences equalsdifferenceofaccumulatedfields"
      },
      {
        "id": "domain_condition",
        "meaning": "Determineswhenaspecifiedcompositionisvalid",
        "example": "Intermediateintegergrid ornonnegativeR/A path"
      },
      {
        "id": "source_constraint",
        "meaning": "Additionalrelationamongreceivedsourcevaluesorroles",
        "example": "Eber40+Nahor60=u100;C=1.3u andT=.6u"
      },
      {
        "id": "family_reconstruction",
        "meaning": "Completefixedsourcefield generatedbyretaineddataandmaps",
        "example": "Moses25nodes andthreeinverseinputwords"
      },
      {
        "id": "interpretive_comparison",
        "meaning": "Literaryorhistoricalmeaningattachedtotheverifiedarithmetic",
        "example": "ArphaxadassecondAdam"
      }
    ],
    "counting_rule": "Dependentdisplaysremainonefamily; identitychecksarenotindependenthistoricalwitnesses.",
    "source_origin": "No classbyitselfestablishesthesourcevalueshistoricalorigin."
  },
  "relations": [
    {
      "path": "model/relation_accumulation.json",
      "sha256": "9f2772db1df27cda5f061f53aa369e7aa413e20763e0bb77fd80e14b4f8734ee",
      "content": {
        "id": "accumulation_linearity",
        "class": "identity",
        "inputs": "sameorderedlabeldomain,weightvectorsw,wprime,retainedterminals",
        "statement": "Forcommonterminala, Xprime−X=U(wprime−w), U_ij=1 ifj>=i. Differentterminalsaddtheexplicitconstantoffset.",
        "proof": "Subtractthetwosuffixsums termbyterm. Adjacentdifferencesrecovereachlocalchange.",
        "source_applications": [
          "MT/LXX complete19rowb/L fields",
          "SP/LXX postFloodlife field",
          "Roundedlocalerrorfieldwithzeroheaderror"
        ],
        "evidence": [
          "model/regular_kernel_complete_staircase.json",
          "model/whole_genealogy_rounding_interior_field.json"
        ],
        "limit": "Differentlabeldomainsfirstrequireadeclaredinsertionorcomparisonadapter."
      }
    },
    {
      "path": "model/relation_cap_round.json",
      "sha256": "8e7c569b7af4de1b2ac28931c7641db8baba7a4527764440c0a36f6023265651",
      "content": {
        "id": "cap_round_monotonicity",
        "class": "identity",
        "statement": "Q(min(L,c))=min(Q(L),Q(c))",
        "inputs": "SameintegerL,c andsameorder-preservingQ onresolvedcountmeasures",
        "proof": "WhicheverofL,c issmallerhasthenolargerQvalue;bothroutesselectthatvalue.",
        "application": "NineSPpreNoah lifecounts,withinclusivecapacityresolvedbeforeQ",
        "information": "Equalityofroutesdoesnotrestoreexcesslifeorroundingresidual.",
        "limits": [
          "Usingexactc ononlyonerouteisadifferentcomparison",
          "RoundingBCbirth/Floodlabelsfirstdoesnotcomputethesameresolvedcapacity",
          "OrdinarybiographicalL=b+r isnotinferredforinclusiveSPcounts"
        ],
        "evidence": [
          "C1202–C1212",
          "model/cap_round_commutation_scope.json",
          "model/cap_round_visibility_witnesses.json"
        ]
      }
    },
    {
      "path": "model/relation_rounded_residuals.json",
      "sha256": "1c0b4aa4f98bb9e353a968eb99533277ba860ce60b040fe488a24060ad35574e",
      "content": {
        "id": "rounded_residual_coherence",
        "class": "identity",
        "statement": "encode(x+d)=T_d(encode(x));T_eT_d=T_(d+e),whereencode(x)=(Q(x),x−Q(x))",
        "proof": "Bothsidesreconstructtheuniqueexactvaluex+doreventuallyx+d+e,andnearestfiveencodingisunique.",
        "aggregate_statement": "Fororderedrowdataw=y+rho, Uw=Uy+Urho;Urhoisnotrenormalized.",
        "applications": [
          "105ordinaryintertraditionmeasurements",
          "complete25-nodeMosesexactfield"
        ],
        "limits": [
          "Droppingrhoallowsall-inputtranslationonlyford in5Z",
          "ChronologicaladmissionofintermediateTstatesremainsaseparatesourcecondition",
          "BlockroundingQ(Bw)usuallydiffersfromB Q(w)"
        ],
        "evidence": [
          "model/all_ordinary_lifted_translations.json",
          "model/rounded_translation_composition.json",
          "model/Moses_complete_residual_recovery.json"
        ]
      }
    },
    {
      "path": "model/relation_Key_sums.json",
      "sha256": "ba7b84e3f9838473c66fb0ecd9dfd3cb849acc3fa0a8048d0e8ad48449a34954",
      "content": {
        "id": "Key_sum_compatibility",
        "class": "identity_with_domain_condition",
        "uniform_statement": "k sum(w_i)=sum(k w_i)",
        "anchored_statement": "Applytospansaboutthedeclaredpivot;do notmultiplyrawBClabels.",
        "mixed_statement": "ForblocksumB anddiagonalfactorsK,thereexistsblockfactorKbar withBK=Kbar B forallinputs iff eachblock’scomponentfactorsareconstant.",
        "proof": "Uniformcaseisdistributivity; mixedcasecomparesthecoefficientofeachindependentcomponentwithinablock.",
        "applications": [
          "threeKeyscommoncalendarvolume",
          "fourcompletedinversepathwhole-spans",
          "partialversusuniform483→490 comparison"
        ],
        "limits": [
          "Rationalwhole-spancompletiondoesnotmaketheproperprefixesintegral",
          "DifferentcomponentKeysneedsource-appointedcutroles",
          "Equalendpoint490doesnotimplyequalinteriors"
        ],
        "evidence": [
          "inherited/model/completed_path_prefix_field.json",
          "inherited/model/retained_part_complete_field.json",
          "inherited/model/mixed_calendar_complete_field.json"
        ]
      }
    },
    {
      "path": "model/relation_affine_grid_domains.json",
      "sha256": "99bb3e4f0350677d6ba82dc8f15f381d7c78ebc4822e14412e2ce912230bde8b",
      "content": {
        "id": "affine_composition_and_grid",
        "class": "identity_with_domain_condition",
        "identity": "D_k T_t=T_(kt) D_k inlinearcoordinates;anchoredoffsetscarriedexplicitly",
        "rational_domain": "Nonzeroexactfactorscomposeoverrationalspans.",
        "integer_example": {
          "first": "J=300/299 about14006",
          "second": "P=70/69 about4836",
          "first_integer_input": "x=14006+299t",
          "first_integer_output": "y=14006+300t",
          "second_span": "9170+300t",
          "residue_mod3": 2,
          "conclusion": "Neverdivisibleby69;integerintermediatestageconditionfailsforallintegert."
        },
        "source_scope": "Theobstructionbelongstothesefixedpivotsandgridrequirements,notallJ/Papplications.",
        "evidence": "inheritedC984–C1007 fixedpivotdomainclassification"
      }
    },
    {
      "path": "model/relation_grouping_reflection.json",
      "sha256": "4c6ff0cb4fb2a646e79edc4982ea4aaa54b2a197bb01ec1f55131bbfa7b2425b",
      "content": {
        "id": "grouping_reflection_descent",
        "class": "domain_condition",
        "criterion": "Reflectiondescendsiff anytwoelementsinthesamegroup havereflections inthesamegroup.",
        "proof": "Amaponthequotientiswell-defined exactlywhentherepresentativechoice doesnotchangeitsoutputclass.",
        "measure_relation": "Pushforwardofoccurrencemeasureusesmultiplicity evenwhenreflectiondoesnotdescend.",
        "Toledot_witness": {
          "collapsed_occurrences": [
            9,
            10
          ],
          "reflections": [
            3,
            2
          ],
          "output_sections": [
            3,
            2
          ]
        },
        "NT_contrast": "Theinheritedprimaryseven-edgegroupinghasreflection-compatiblefibres.",
        "evidence": [
          "inherited/model/toledot_quotient.json",
          "C1024–C1029"
        ]
      }
    },
    {
      "path": "model/relation_inverse_partition.json",
      "sha256": "66d109ae0238a81f415ee8847be71eabc366b94683328289ae877a38ffe77ef5",
      "content": {
        "id": "reversal_partition_dependence",
        "class": "noncommutation_witness",
        "original_source_parts": [
          1650,
          1050
        ],
        "original_whole": 2700,
        "whole_one_pass_image": 7200,
        "separate_one_pass_images": [
          5610,
          5010
        ],
        "separate_image_total": 10620,
        "statement": "Reverseaftercoarsening differsfromcoarsenaftercomponentreversal.",
        "source_scope": "Botharguments areoriginalsource durations, notinheritedinverseoutputs; eachisreversedoncefor thisexistingcomparison.",
        "consequence": "Originalpartitionandoperationroute arepartoftheinput, notdecorativeannotations."
      }
    },
    {
      "path": "model/relation_Covenant_joins.json",
      "sha256": "ab887e864f689b1b575d9b2f8b5f4cc06f40c5281f307d6ffb046a2978fef8bb",
      "content": {
        "id": "Covenant_clutch_joins",
        "class": "definition_plus_source_constraint",
        "definition": "d=C_K−D,whereC_KiscumulativeKohathandDisfullregularLevideath",
        "forced_join1": "C_K−d=D bydefinition",
        "forced_join2": "C_L−d=B becausebothpathsuseLevi’s137-yearlife",
        "additional_join": "C_J−d=regularIsaacbirth requiresregularIsaac-to-Levibirth=Jacoblife147",
        "source_relation": "60+77+10=147",
        "generated_example": {
          "Kohath_after": 1782,
          "Levi_after": 1919,
          "Jacob_after": 2066
        },
        "phase": "SameNisanderivedd actsontheexact+3.5Aaron/Tishrifield; nosecondclutchtocancelphase",
        "evidence": [
          "inherited/model/covenant_clutch_dependency_ledger.json",
          "inherited/model/covenant_cumulative_regenerated.json"
        ]
      }
    },
    {
      "path": "model/relation_additional_source_conditions.json",
      "sha256": "c248671ae7c423a070cea3b44a196e9ce3502850a9de2f3ce49bc66a453d678c",
      "content": {
        "conditions": [
          {
            "id": "postFlood_four_amplitude",
            "relation": "EberdeltaL+NahordeltaL=u",
            "values": "40+60=100",
            "role": "fittedsource-valuecompression",
            "evidence": "model/whole_genealogy_four_model.json"
          },
          {
            "id": "regular_fivefold",
            "relation": "C=13u/10 andT=3u/5",
            "values": "130=1.3*100;60=.6*100",
            "role": "cross-layercalibration",
            "evidence": "model/regular_kernel_five_calibration.json"
          },
          {
            "id": "SP_rectangle_openings",
            "relation": "3C_radius−13R_radius=0",
            "values": "unwrapped61 plus3*10−13*7=0",
            "role": "sourceappointednode-openingscompleteequal-gainrelation",
            "evidence": "model/SP_rectangle_wrapper_residual.json"
          },
          {
            "id": "Moses_recapitulation",
            "relation": "A=Adam_b andB=Adam_r",
            "values": "130|800",
            "role": "twocomponentcomparisonconditions;930totaldependent",
            "evidence": "model/Moses_Adam_component_correspondence.json"
          }
        ],
        "interpretation": "Allareexactinthedeclaredsourcepacket. Noneisgeneratedbythegeneraloperationidentitiesalone.",
        "independence": "Logicaladditionalconditions inadeclaredmodelarenotindependenthistoricalwitnesses."
      }
    }
  ],
  "principle": "Compositionisassertedonlyforthespecifiedobjectsanddomains;universaldateconversionisnotinferred.",
  "newness": "Thisledgerorganizescompletedproofsandtheirsourceapplications;itsentriesarenotnewindependentdiscoveries.",
  "reader_notes": [
    "An identity follows throughout its declared domain; a source condition adds information about the selected inputs.",
    "A complete family reconstruction can reuse several identities while still requiring source ages, cuts and anchors.",
    "The Regular fivefold calibration, SP wrapper balance and third Covenant join retain their additional source conditions.",
    "Equal output totals alone do not identify full paths or their source roles."
  ]
}