{
  "title": "Admitted operation inventory",
  "operation_ids": [
    "row_repartition",
    "life_adjustment",
    "accumulate_measure",
    "insert_source_row",
    "cap_resolved_life",
    "round_resolved_count",
    "translate_with_residual",
    "anchored_Key",
    "scoped_translation",
    "reverse_original_components_once",
    "group_source_blocks",
    "source_reflection"
  ],
  "modules": [
    {
      "path": "model/operations_row_changes.json",
      "sha256": "c47e3d756c6f6a68a4fbce1c87b14ef2681892ad3c0c8e10f1daf87c95668903",
      "content": {
        "operations": [
          {
            "id": "row_repartition",
            "input_object": "ordinarycompatible(b,r,L),L=b+r",
            "action": "(b+d,r−d,L)",
            "preserved": "L",
            "lost": "nonewhen d retained",
            "domain": "b+d>=0 andr−d>=0; sourcechoosesallowedd androws",
            "source_support": "namedrowmask",
            "evidence": [
              "C1152",
              "C1173",
              "C1175"
            ]
          },
          {
            "id": "life_adjustment",
            "input_object": "ordinarycompatible(b,r,L),L=b+r",
            "action": "(b,r+e,L+e)",
            "preserved": "b",
            "lost": "nonewhen e retained",
            "domain": "r+e>=0; sourcechoosesallowede androws",
            "source_support": "namedrowmask",
            "evidence": [
              "C1152",
              "C1182"
            ]
          }
        ],
        "combined": "Uniqueordinaryrowdifference hasd=delta_b ande=delta_L.",
        "composition": "Unrestrictedmapscommute; intermediatevalidity andsourceadmission areadditionalconditions.",
        "not_applied": "InclusiveSPcountrows arenotsilentlyordinarybiographies."
      }
    },
    {
      "path": "model/operations_measure_and_insert.json",
      "sha256": "cfbb6e920db5eb788f74fb7c86f2dd626159d63a619c7cd7f93085bc6184951c",
      "content": {
        "operations": [
          {
            "id": "accumulate_measure",
            "input": "orderedlabelledweightsw andterminala",
            "action": "X_i=a+sum(w_j forj>=i)",
            "output": "completeboundaryfield",
            "preserved": "order and everyedgeweight whencompletefield+terminalretained",
            "lost": "internalweightsifonlyheadtotalretained",
            "measure_choices": "effectivebirthinterval,selectedlifespan,NTslot,countcategory",
            "evidence": [
              "C1185",
              "C1234",
              "C1267"
            ]
          },
          {
            "id": "insert_source_row",
            "input": "source-authorizedlocation androw(b,r,L)",
            "action": "addnamedvertex anditsselectededge/rowmeasure",
            "output": "neworderedsourceobject",
            "preserved": "unaffecteddownstreamsourcefield",
            "lost": "noneifinsertionidentityretained",
            "Cainan": "130Regular,460Cumulative; nativeLXXalreadyON",
            "evidence": [
              "C1187",
              "C1188",
              "C1255"
            ]
          }
        ],
        "connection": "Differentmeasurements ofoneinsertedrow arelinkedbyitsbiographicaldata, notbyidentifying130and460."
      }
    },
    {
      "path": "model/operations_cap_and_round.json",
      "sha256": "7283fef390fea970c5f46796435bcb3ca98ae84d8b6a149a0ffb60fe06563008",
      "content": {
        "operations": [
          {
            "id": "cap_resolved_life",
            "input": "labelledbaselineL andresolvedcapacityc",
            "action": "y=min(L,c)",
            "output": "selectedlifecountwithsourcecounttag",
            "preserved": "orderundercoordinatewiseincrease; unchangedinputbelowcap",
            "lost": "excessL−c abovecap",
            "retained_recovery": "branch-appropriateexcess/residualregister",
            "evidence": [
              "C1202",
              "C1204",
              "C1206"
            ]
          },
          {
            "id": "round_resolved_count",
            "input": "specifiednonnegativeintegerrowcount",
            "action": "Q(x)=5floor((x+2)/5)",
            "output": "roundedrowcountplusoptionalrho=x−Q(x)",
            "preserved": "order;translationsby5Z",
            "lost": "within-cellresidualwhenomitted",
            "retained_recovery": "Q(x)+rho=x;aggregatepathresidualisun-normalizedsum",
            "evidence": [
              "C1190",
              "C1213",
              "C1277",
              "C1278"
            ]
          }
        ],
        "composition": "Q(min(L,c))=min(Q(L),Q(c)) forconsistentlyresolvedcounts; separatelyroundeddatecapacitiesarenotthesameinput.",
        "classification": "Monotone many-to-onemaps; notinvertibleaffinesymmetries."
      }
    },
    {
      "path": "model/operation_rounded_residual_lift.json",
      "sha256": "bd2161f77a5734cf947305a44807fda26a4662b73b0caf57042f145a29dc7c11",
      "content": {
        "id": "translate_with_residual",
        "input": "(y,rho),y in5Z,rho in[-2,2],x=y+rho;source-authorizedintegerd",
        "action": "(y+Q_Z(rho+d),rho+d−Q_Z(rho+d))",
        "output": "losslessRoundedplusresidualencodingofx+d",
        "preserved": "exactreconstructedvalueunderknownshift;T_eT_d=T_(d+e)",
        "lost": "nonewhilebothcoordinatesretained",
        "without_residual": "Universalactiononroundedcellsexistsonlyfor d in5Z",
        "source_domain": "Algebraicnegativeauxiliaryresidualallowed;originaldurationandchronologystatesremain source-qualified.",
        "evidence": [
          "C1218",
          "C1219 all105measurements",
          "C1220",
          "C1221"
        ]
      }
    },
    {
      "path": "model/operations_Key_and_translation.json",
      "sha256": "378a5168356f3f31aff4f1290967e70e8ad64bad0b69bf2c3903e7f205bad224",
      "content": {
        "operations": [
          {
            "id": "anchored_Key",
            "input": "typedcoordinatex,pivota,exactfactork,coordinatechartandunits",
            "action": "a+k(x−a)",
            "output": "generatedcomparisoncoordinateinthesamedeclaredchart",
            "preserved": "ratiosofdifferencesaboutheldpivot; schematicdayvolume when calendarunitmatched",
            "lost": "noneoverrationalswithpivotandnonzerofactorretained",
            "domain": "Sourceappointedroute;integerstagedomainrequiresdivisibility",
            "evidence": [
              "Strategy3.3/5C",
              "C984–C1007 inherited",
              "C1226"
            ]
          },
          {
            "id": "scoped_translation",
            "input": "declaredsourcefieldandmovingmask,magnitudet",
            "action": "x_i→x_i+t onallowednodes",
            "output": "sourcevariantorcomparisonfieldwithsamecounttags",
            "preserved": "internaldifferenceswhensamenodestranslate together",
            "lost": "absoluteframeiftranslationforgotten",
            "domain": "PrimarySojournscope,ApparentAgeandlocalGearscopeseachseparate",
            "evidence": [
              "C1256",
              "C1263",
              "C1228"
            ]
          }
        ],
        "order_relation": "D_k T_t=T_(kt) D_k inlinearcoordinates;generallynotT_t D_k",
        "pivot_relation": "Changingonlyananchorisnottranslatingthecompleteobject."
      }
    },
    {
      "path": "model/operation_single_reversal.json",
      "sha256": "491fcb2e22c636250b8114a27e689cd1f67e448859dd29c290f1799c72d28fbe",
      "content": {
        "id": "reverse_original_components_once",
        "input": "source-appointedorderedwordoforiginalnonnegativeintegerdurations",
        "action": "Forpositive10^z m with10notdividingm, keep10^z andreverse decimaldigitsofm;zero maps tozero. Applyonceto eachadmittedoriginalpart.",
        "output": "orderedtransformedwordwithoriginalpartitionprovenance",
        "preserved": "sourcepartlabelsanddeclaredplaceholderpolicy;notgeneralsums",
        "lost": "Repartitioningchangesoutput; do nottreattransformedwordasoriginalinput",
        "domain": "File52c admittedsinglepassroutes;notgeneralMirror orsame-sidereflection",
        "composition_conditions": "UniformrationalKeymayfollowondeclaredspan; sourcegridinterpretationandheldanchorretained",
        "evidence": [
          "File52c1.2",
          "C1058–C1068 inherited",
          "C1273–C1276"
        ],
        "excluded": "inverseoftheinverse"
      }
    },
    {
      "path": "model/operations_group_and_reflect.json",
      "sha256": "e544e9ff27d160fd1748095fbf88dbbc486a9c463725d99acc71e9833ca11448",
      "content": {
        "operations": [
          {
            "id": "group_source_blocks",
            "input": "orderedweightedsourceobjectanddeclaredblockmap",
            "action": "sumweightsinblocks; retainmultiplicityforidentifiedoccurrences",
            "output": "coarserlabelledmeasure",
            "preserved": "totalmeasurewhenweightsandmultiplicitiescarried",
            "lost": "internalpositionsandweightsunlessretainedseparately",
            "domain": "Sourcecategoriesandorderdeclaredbeforeexecution",
            "evidence": [
              "C1009–C1029",
              "C1277"
            ]
          },
          {
            "id": "source_reflection",
            "input": "declaredcoordinatechartorfiniteorderedobjectwithappointedcenter/reversal",
            "action": "applythesource-definedreflectiononthatobject",
            "output": "reflectedfieldwithsameobjecttags",
            "preserved": "dependsonthefixedsourceaction;groupingmustmapwholefibrescompatiblyfordescent",
            "lost": "noautomaticdescenttoarbitraryquotients",
            "domain": "RoundedqMirror,civil-displayreflectionandsame-sidereflectionaredistinct",
            "evidence": [
              "Strategy4.5/5E",
              "C1024–C1029 inherited"
            ]
          }
        ],
        "contrast": "NTseven-edgegroupingpreservesitsreflection;Toledotoccurrencecollapsepreservesmeasurewithmultiplicitybutnotitsreflection."
      }
    }
  ],
  "interpretation": "Onevocabularyofsource-qualifiedoperations; notoneoperationavailableoneveryfamily.",
  "composition_rule": "Outputmeasure,state,count,role,anchor andinformation mustsatisfythestatednextinputdomain.",
  "reader_notes": [
    "Each operation carries its source object, measurement, domain, moving support and output role.",
    "Composition is admitted only when the next operation receives the required source information.",
    "A shared operation does not imply that two families share the same inputs.",
    "Single reversal applies once to original source components; its output is not a new reversal input in this cycle."
  ]
}