Relation Ledger C1313.json

{
  "title": "Verifiedrelations andadditionalconditions",
  "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\u2212X=U(wprime\u2212w), 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\u2013C1212",
          "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\u2212Q(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\u2019scomponentfactorsareconstant.",
        "proof": "Uniformcaseisdistributivity; mixedcasecomparesthecoefficientofeachindependentcomponentwithinablock.",
        "applications": [
          "threeKeyscommoncalendarvolume",
          "fourcompletedinversepathwhole-spans",
          "partialversusuniform483\u2192490 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\u2013C1007 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\u2013C1029"
        ]
      }
    },
    {
      "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\u2212D,whereC_KiscumulativeKohathandDisfullregularLevideath",
        "forced_join1": "C_K\u2212d=D bydefinition",
        "forced_join2": "C_L\u2212d=B becausebothpathsuseLevi\u2019s137-yearlife",
        "additional_join": "C_J\u2212d=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\u221213R_radius=0",
            "values": "unwrapped61 plus3*10\u221213*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."
}