{
  "status": "Root-adoption pack only; no numbered actions or journal writes. Results from frozen existing diagnostics; snippets recompute selected exact assertions.",
  "setup": "from fractions import Fraction as F\nfrom adoption_helpers import solve_key_from_completion, allocation, anchored, retained_totals, recover_retained_parts, component_defect, coarsening_commutes, affine_stage_coset, whole_field_in_coset, mixed_calendar_measure",
  "use": "Select one record, assign its results to results, run the fragment if present, and provide the root-owned begin/finish/artifact wrapper. Conceptual proofs are supplied explicitly rather than given fabricated automated checks.",
  "records": [
    {
      "id": "KQ01",
      "question": "Which completed results are premises rather than new discoveries for this packet?",
      "object": "Prior family index and selected results",
      "new_burden": "Explicit novelty and dependency basis",
      "priority": "supporting/inherited",
      "sources": [
        "Strategy\u00a7\u00a75D\u2013G,6",
        "prior family index and selected sourcepacket records"
      ],
      "results": {
        "premises": [
          "C505\u2013511:529 ladder, pivot compatibility and coordinate charts",
          "C568\u2013586,C609:allocation and calibration identities",
          "C666\u2013667,C690,C713\u2013715:retained-part whole fields",
          "C872\u2013889:scalar grid domains and fixed finite Key words"
        ],
        "new_burdens": [
          "equation dependence",
          "operator coarsening criterion",
          "two-measurement reconstruction",
          "affine stagewise cosets with pivot obstruction",
          "conditional componentwise calendar calibration"
        ]
      },
      "fragment": null,
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ02",
      "question": "Can the source five-to-one partition and336/360 calibration determine E and P uniquely?",
      "object": "File62/63 dual490 plus File12 calendars",
      "new_burden": "Solve for operators from independently stated partition and calendar measures",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "E_from_336_360_1over6": "25/23",
        "common_K": "8400/23"
      },
      "fragment": "e=solve_key_from_completion(336,360,F(1,6)); p=(5+e)/6\nchecks={'E':e==F(25,23),'P':p==F(70,69),'calibration':336*e==360*p}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ03",
      "question": "Does the source25-to-one partition with336/364 independently impose the same E?",
      "object": "Actual12558 path and File12 calendars",
      "new_burden": "Determine compatibility constraint rather than recount scalar equality",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "E_from_336_364_1over26": "25/23",
        "common_K": "8400/23"
      },
      "fragment": "e=solve_key_from_completion(336,364,F(1,26)); j=(25+e)/26\nchecks={'E':e==F(25,23),'J':j==F(300,299),'calibration':336*e==364*j}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ04",
      "question": "What is the rank and exact dependence of the four calibration/allocation equations?",
      "object": "Three unknown Keys, four declared relations",
      "new_burden": "Minimal independent equation basis",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "coefficient_matrix": [
          [
            336,
            -360,
            0
          ],
          [
            336,
            0,
            -364
          ],
          [
            1,
            -6,
            0
          ],
          [
            1,
            0,
            -26
          ]
        ],
        "rhs": [
          0,
          0,
          -5,
          -25
        ],
        "rank": 3,
        "augmented_rref": [
          [
            1,
            0,
            0,
            "25/23"
          ],
          [
            0,
            1,
            0,
            "70/69"
          ],
          [
            0,
            0,
            1,
            "300/299"
          ],
          [
            0,
            0,
            0,
            0
          ]
        ],
        "left_dependence": [
          7,
          -6,
          -420,
          84
        ]
      },
      "fragment": "a=results['coefficient_matrix']; b=results['rhs']; c=results['left_dependence']\nchecks={'column_dependency':all(sum(c[i]*a[i][j] for i in range(4))==0 for j in range(3)),'constant_dependency':sum(c[i]*b[i] for i in range(4))==0}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ05",
      "question": "How many primitive choices remain if only common calibration is retained?",
      "object": "Three-Key calibration system",
      "new_burden": "Identify its free common-volume parameter without fitting endpoints",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "remaining_family": "(E,P,J)=K*(1/336,1/360,1/364) before adding a source allocation",
        "free_scalar_parameters": 1,
        "necessary_addition": "a partial/whole completion relation, not merely the existence of a source partition"
      },
      "fragment": null,
      "proof_only": true,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ06",
      "question": "Can one source partition plus calendar ratios predict the other allocation fraction?",
      "object": "Same fixed source packet",
      "new_burden": "Conditional prediction of1/26 from1/6; explored-source compatibility, not a fresh holdout",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "predicted_fraction": "1/26",
        "status": "same explored source family; alternate constraint basis, not new holdout evidence"
      },
      "fragment": "e=solve_key_from_completion(336,360,F(1,6)); j=336*e/F(364); f=(j-1)/(e-1)\nchecks={'predicted_fraction':f==F(1,26)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ07",
      "question": "Does a controlled replacement of the26-fold partition break that compatibility?",
      "object": "Diagnostic25-fold comparison only",
      "new_burden": "Show the source constraint is substantive without adopting the perturbation",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "diagnostic_fraction": "1/25",
        "new_E": "312/287",
        "minus_controlling_E": "1/6601",
        "status": "unadopted negative diagnostic"
      },
      "fragment": "e=solve_key_from_completion(336,364,F(1,25))\nchecks={'changed_factor':e==F(312,287),'nonzero_difference':e-F(25,23)==F(1,6601)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ08",
      "question": "Do the three allocation fractions form a coherent nested-selection triangle?",
      "object": "A_f(k)=1+f(k\u22121)",
      "new_burden": "Derive E-to-P,P-to-J,E-to-J and their dependency",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "fractions": {
          "E\u2192P": "1/6",
          "P\u2192J": "3/13",
          "E\u2192J": "1/26"
        },
        "nested_product": "1/26",
        "nested_selected_factor": "300/299",
        "sequential_PJ_factor": "7000/6877",
        "proof": "A_g(A_f(k))=1+g*f*(k-1)=A_(gf)(k); this is selection composition, not applying two chronological Keys in succession."
      },
      "fragment": "f,g=F(1,6),F(3,13); e=F(25,23)\nchecks={'fraction_composition':f*g==F(1,26),'factor_composition':allocation(g,allocation(f,e))==allocation(f*g,e)==F(300,299)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ09",
      "question": "How does nested selection differ from sequential chronological expansion?",
      "object": "A_g(A_f(E)) versus multiplication of Keys",
      "new_burden": "Separate allocation composition from Key-word composition",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "nested_selected_factor": "300/299",
        "sequential_PJ_factor": "7000/6877",
        "interpretation": "nested selection and chronological Key multiplication are different operations"
      },
      "fragment": "nested=allocation(F(3,13),allocation(F(1,6),F(25,23))); sequential=F(70,69)*F(300,299)\nchecks={'different_operations':nested!=sequential,'nested':nested==F(300,299),'sequential':sequential==F(7000,6877)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ10",
      "question": "Which allocations are source-appointed cuts and which are only computed fractions?",
      "object": "483,12558 and12600 source paths",
      "new_burden": "Source-support ledger; no new target assignment",
      "priority": "supporting/inherited",
      "sources": [
        "Strategy\u00a7\u00a73.3,5D\u2013G",
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4,9.7",
        "C568\u2013570 inherited"
      ],
      "results": {
        "source_supported": [
          {
            "object": "483",
            "parts": [
              "805/2",
              "161/2"
            ],
            "selected_fraction": "1/6",
            "existing_relation": "final E total equals whole P"
          },
          {
            "object": "12558",
            "parts": [
              12075,
              483
            ],
            "selected_fraction": "1/26",
            "existing_relation": "final E total equals whole J"
          },
          {
            "object": "12600",
            "parts": [
              9660,
              2940
            ],
            "selected_fraction": "23/30",
            "existing_relation": "upper P/E with2940 retained"
          }
        ],
        "computed_only": {
          "P_allocation_to_J": "3/13",
          "no_named_cut_adopted": true
        }
      },
      "fragment": null,
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ11",
      "question": "What exact part vector records the information erased when partial and uniform expansions share a total?",
      "object": "Two-component path",
      "new_burden": "Kernel formula independent of specific coordinates",
      "priority": "supporting/inherited",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "formula": "For upper fractionf and factor k there, delta=(k\u22121)f(1\u2212f)S*(1,\u22121); reverse component order reverses the sign.",
        "kernel": "sum of component differences is zero",
        "example": {
          "name": "483_final_E",
          "source_parts": [
            "805/2",
            "161/2"
          ],
          "component_factors": [
            1,
            "25/23"
          ],
          "effective_factor": "70/69",
          "partial_image": [
            "805/2",
            "175/2"
          ],
          "uniform_image": [
            "1225/3",
            "245/3"
          ],
          "difference_vector": [
            "-35/6",
            "35/6"
          ],
          "difference_sum": 0
        }
      },
      "fragment": "v=component_defect([F(805,2),F(161,2)],[1,F(25,23)])\nchecks={'kernel':sum(v['defect'])==0,'nonzero':v['defect']==[F(-35,6),F(35,6)]}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ12",
      "question": "Can the full source family be normalized to one component-defect form?",
      "object": "483 and12558 source partitions plus9660|2940 retained-arm family",
      "new_burden": "Whole-family rank and invariant, retaining inherited numbers as examples",
      "priority": "supporting/inherited",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "rows": [
          {
            "name": "483_final_E",
            "source_parts": [
              "805/2",
              "161/2"
            ],
            "component_factors": [
              1,
              "25/23"
            ],
            "effective_factor": "70/69",
            "partial_image": [
              "805/2",
              "175/2"
            ],
            "uniform_image": [
              "1225/3",
              "245/3"
            ],
            "difference_vector": [
              "-35/6",
              "35/6"
            ],
            "difference_sum": 0
          },
          {
            "name": "12558_final_E",
            "source_parts": [
              12075,
              483
            ],
            "component_factors": [
              1,
              "25/23"
            ],
            "effective_factor": "300/299",
            "partial_image": [
              12075,
              525
            ],
            "uniform_image": [
              "157500/13",
              "6300/13"
            ],
            "difference_vector": [
              "-525/13",
              "525/13"
            ],
            "difference_sum": 0
          },
          {
            "name": "12600_upper_P",
            "source_parts": [
              9660,
              2940
            ],
            "component_factors": [
              "70/69",
              1
            ],
            "effective_factor": "91/90",
            "partial_image": [
              9800,
              2940
            ],
            "uniform_image": [
              "29302/3",
              "8918/3"
            ],
            "difference_vector": [
              "98/3",
              "-98/3"
            ],
            "difference_sum": 0
          },
          {
            "name": "12600_upper_E",
            "source_parts": [
              9660,
              2940
            ],
            "component_factors": [
              "25/23",
              1
            ],
            "effective_factor": "16/15",
            "partial_image": [
              10500,
              2940
            ],
            "uniform_image": [
              10304,
              3136
            ],
            "difference_vector": [
              196,
              -196
            ],
            "difference_sum": 0
          }
        ],
        "status": "Existing source examples C609/C714\u2013715; new compression into the kernel of total evaluation."
      },
      "fragment": "checks={'all_four':len(results['rows'])==4,'zero_total_defects':all(sum(F(x) for x in r['difference_vector'])==0 for r in results['rows'])}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ13",
      "question": "When does coarsening commute with componentwise conversion for every possible weight vector?",
      "object": "Fixed partition map and diagonal operator",
      "new_burden": "Necessary and sufficient operator condition",
      "priority": "new compression or transfer",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "criterion": "C*diag(k_i)=diag(kbar_B)*C for all vectors iff all k_i in each coarsened blockB equal kbar_B.",
        "proof": "In a coarse block, the coefficient of fine component i is k_i on C D and kbar_B on Dbar C; equality for every vector is exactly coefficient equality."
      },
      "fragment": null,
      "proof_only": true,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ14",
      "question": "Can one supplied path hide a failure of universal coarsening compatibility?",
      "object": "Same fixed source partitions",
      "new_burden": "Distinguish a weight-dependent effective factor from an operator identity",
      "priority": "new compression or transfer",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "source_case": {
          "name": "483_final_E",
          "source_parts": [
            "805/2",
            "161/2"
          ],
          "component_factors": [
            1,
            "25/23"
          ],
          "effective_factor": "70/69",
          "partial_image": [
            "805/2",
            "175/2"
          ],
          "uniform_image": [
            "1225/3",
            "245/3"
          ],
          "difference_vector": [
            "-35/6",
            "35/6"
          ],
          "difference_sum": 0
        },
        "fine_factors": [
          1,
          "25/23"
        ],
        "coarse_factor": "70/69",
        "universal_square": false,
        "fixed_weight_total_equality": true
      },
      "fragment": "v=component_defect([F(805,2),F(161,2)],[1,F(25,23)])\nchecks={'fixed_total':sum(v['selective'])==sum(v['uniform'])==490,'not_universal':not coarsening_commutes([[0,1]],[1,F(25,23)],[F(70,69)])}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ15",
      "question": "What linear constraint generates the whole native/P/E retained-part output field?",
      "object": "Complete SupplementA690/30 table and12600/12740/13440 paths",
      "new_burden": "Rank-two reconstruction with one dependent output",
      "priority": "new compression or transfer",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "matrix": [
          [
            1,
            1
          ],
          [
            "70/69",
            1
          ],
          [
            "25/23",
            1
          ]
        ],
        "rank": 2,
        "left_constraint": [
          5,
          -6,
          1
        ],
        "det_native_P": "-1/69"
      },
      "fragment": "m=[[F(x) for x in row] for row in results['matrix']]; c=results['left_constraint']\nchecks={'left_kernel':all(sum(c[i]*m[i][j] for i in range(3))==0 for j in range(2)),'rank_two_minor':m[0][0]*m[1][1]-m[1][0]*m[0][1]==F(-1,69)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ16",
      "question": "Can the converted component and retained component be recovered from two total measurements?",
      "object": "Native total andP total",
      "new_burden": "Invertible measurement pair and explicit source-role limit",
      "priority": "new compression or transfer",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "inverse": "u=69(T_P\u2212T_0); v=T_0\u2212u",
        "complete_fixed_rows": [
          {
            "source_u_v": [
              690,
              0
            ],
            "native_P_E": [
              690,
              700,
              750
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              0
            ]
          },
          {
            "source_u_v": [
              690,
              30
            ],
            "native_P_E": [
              720,
              730,
              780
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              30
            ]
          },
          {
            "source_u_v": [
              690,
              60
            ],
            "native_P_E": [
              750,
              760,
              810
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              60
            ]
          },
          {
            "source_u_v": [
              9660,
              2940
            ],
            "native_P_E": [
              12600,
              12740,
              13440
            ],
            "constraint": 0,
            "recovered_u_v": [
              9660,
              2940
            ]
          }
        ],
        "limitation": "Recovers numerical parts only; does not infer their source roles, order, anchors or source authorization."
      },
      "fragment": "checks={'full_reconstruction':all(recover_retained_parts(*r['native_P_E'][:2])==r['source_u_v'] for r in results['complete_fixed_rows'])}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ17",
      "question": "Which apparent calendar-completion checks become dependent under that recovery?",
      "object": "Same complete fields",
      "new_burden": "Minimal consistency ledger, no inflated witness tally",
      "priority": "new compression or transfer",
      "sources": [
        "File63\u00a71.3,\u00a7\u00a77.3\u20137.4",
        "SupplementA\u00a7\u00a71.2,10.3",
        "C609,C713\u2013715 inherited"
      ],
      "results": {
        "dependent_output": "T_E=6*T_P\u22125*T_0",
        "source_choices_still_required": [
          "which component converts",
          "which is retained",
          "order",
          "anchors",
          "chronological authorization"
        ],
        "examples": [
          {
            "source_u_v": [
              690,
              0
            ],
            "native_P_E": [
              690,
              700,
              750
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              0
            ]
          },
          {
            "source_u_v": [
              690,
              30
            ],
            "native_P_E": [
              720,
              730,
              780
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              30
            ]
          },
          {
            "source_u_v": [
              690,
              60
            ],
            "native_P_E": [
              750,
              760,
              810
            ],
            "constraint": 0,
            "recovered_u_v": [
              690,
              60
            ]
          },
          {
            "source_u_v": [
              9660,
              2940
            ],
            "native_P_E": [
              12600,
              12740,
              13440
            ],
            "constraint": 0,
            "recovered_u_v": [
              9660,
              2940
            ]
          }
        ]
      },
      "fragment": "checks={'complete_field_dependency':all(5*F(r['native_P_E'][0])-6*F(r['native_P_E'][1])+F(r['native_P_E'][2])==0 for r in results['examples'])}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ18",
      "question": "Does the primitive529 ladder determine the four elementary increment coefficients, and which are independent?",
      "object": "Known529\u2192575\u2192625 duration ladder",
      "new_burden": "Constraint-basis classification rather than re-running ladder",
      "priority": "supporting/inherited",
      "sources": [
        "Strategy\u00a7\u00a75D\u2013G,6",
        "prior family index and selected sourcepacket records"
      ],
      "results": {
        "primitive_pair": [
          23,
          25
        ],
        "normalized_ladder": [
          529,
          575,
          625
        ],
        "gain_pair": [
          46,
          50
        ],
        "geometric_relation": 0,
        "second_difference": 4,
        "total_gain": 96,
        "middle_minus_arithmetic_midpoint": -2,
        "novelty": "Low priority compression only; C505 already proved the ladder."
      },
      "fragment": "a,b,c=results['normalized_ladder']\nchecks={'geometric':b*b==a*c,'second_difference':c-2*b+a==4}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ19",
      "question": "How do source-appointed pivots enter a finite affine composition as one rational congruence condition?",
      "object": "Two general reduced ratios with fixed integer pivots",
      "new_burden": "Unified affine prefix-domain formulation beyond same-origin words",
      "priority": "new compression or transfer",
      "sources": [
        "File46\u00a7\u00a72,6A.5",
        "C505\u2013507 inherited",
        "C873\u2013889 inherited",
        "Strategy\u00a7\u00a75C,5E\u2013G"
      ],
      "results": {
        "derivation": [
          "First integer image iff x=a+q1*t.",
          "First image is a+p1*t.",
          "Second integer image iff p1*t\u2261b\u2212a modq2.",
          "g=gcd(p1,q2); solvable iff g dividesb\u2212a; periodq1*q2/g."
        ],
        "scope": "Whole-stage integer membership for fixed integer pivots, diagnostic compositions unless source already licensed."
      },
      "fragment": null,
      "proof_only": true,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ20",
      "question": "What determines whether a whole finite source field shares an admissible affine-prefix residue?",
      "object": "Fixed labelled point field",
      "new_burden": "Difference lattice plus one placement residue; no pivot search",
      "priority": "new compression or transfer",
      "sources": [
        "File46\u00a7\u00a72,6A.5",
        "C505\u2013507 inherited",
        "C873\u2013889 inherited",
        "Strategy\u00a7\u00a75C,5E\u2013G"
      ],
      "results": {
        "complete_nine_pairs": [
          {
            "execution": "E\u2192E",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 68,
            "period": 529,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "E\u2192P",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 1126,
            "period": 1587,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "E\u2192J",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 68,
            "period": 6877,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "P\u2192E",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 206,
            "period": 1587,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "P\u2192P",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 206,
            "period": 4761,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "P\u2192J",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 4967,
            "period": 20631,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "J\u2192E",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 2345,
            "period": 6877,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          },
          {
            "execution": "J\u2192P",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": false,
            "obstruction_divisor": 3,
            "pivot_difference_mod_g": 1
          },
          {
            "execution": "J\u2192J",
            "first_pivot": 14006,
            "second_pivot": 4836,
            "nonempty": true,
            "obstruction_divisor": 1,
            "residue": 43607,
            "period": 89401,
            "formula": "x=residue+period*n, n integer; representative is not an event date"
          }
        ],
        "whole_field_rule": "A nonempty coset contains all points iff one point has the right residue and every source difference is divisible by its period.",
        "status": "fixed14006/4836 pivots; generated residues are congruence labels, not event dates"
      },
      "fragment": "ks={'E':F(25,23),'P':F(70,69),'J':F(300,299)}\ncomputed=[]\nfor r in results['complete_nine_pairs']:\n    u,v=r['execution'].split('\u2192'); z=affine_stage_coset(ks[u],ks[v],r['first_pivot'],r['second_pivot']); computed.append((r,z))\nchecks={'complete':len(computed)==9,'matching_domains':all(r['nonempty']==z['nonempty'] and (not z['nonempty'] or (r['residue'],r['period'])==(z['residue'],z['period'])) for r,z in computed),'only_JP_empty':[r['execution'] for r,z in computed if not z['nonempty']]==['J\u2192P']}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ21",
      "question": "Can width and placement constraints be represented as separate coordinates without losing tags?",
      "object": "Existing C480 pair and fixed12026 comparison",
      "new_burden": "Explicit recoverable field normal form; source pivots unchanged",
      "priority": "new compression or transfer",
      "sources": [
        "File46\u00a7\u00a72,6A.5",
        "C505\u2013507 inherited",
        "C873\u2013889 inherited",
        "Strategy\u00a7\u00a75C,5E\u2013G"
      ],
      "results": {
        "existing_cases": [
          {
            "case": "C480",
            "fixed_points": [
              2148,
              3206
            ],
            "coset": {
              "nonempty": true,
              "obstruction_divisor": 1,
              "residue": 32,
              "period": 529,
              "formula": "x=residue+period*n, n integer; representative is not an event date"
            },
            "placement_matches": [
              true,
              true
            ],
            "difference_lattice_divides_period": true
          },
          {
            "case": "fixed12026",
            "fixed_points": [
              4114,
              3056
            ],
            "coset": {
              "nonempty": true,
              "obstruction_divisor": 1,
              "residue": 388,
              "period": 529,
              "formula": "x=residue+period*n, n integer; representative is not an event date"
            },
            "placement_matches": [
              false,
              false
            ],
            "difference_lattice_divides_period": true
          }
        ],
        "normal_form": "one source point plus ordered differences; retain the point/pivot/source tags"
      },
      "fragment": "e=F(25,23); first=affine_stage_coset(e,e,3620,2756); second=affine_stage_coset(e,e,12026,12026)\nchecks={'C480_field':whole_field_in_coset([2148,3206],first),'fixed_field_fails':not whole_field_in_coset([4114,3056],second),'cosets':first['residue']==32 and second['residue']==388}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ22",
      "question": "What is the minimal lattice carrying every fixed diagnostic image when integer closure fails?",
      "object": "File46 five-head field and declaredE anchor",
      "new_burden": "Exact output grid denominator instead of repairing dates",
      "priority": "new compression or transfer",
      "sources": [
        "File46\u00a7\u00a72,6A.5",
        "C505\u2013507 inherited",
        "C873\u2013889 inherited",
        "Strategy\u00a7\u00a75C,5E\u2013G"
      ],
      "results": {
        "source_anchor": 14006,
        "difference_mesh": 10,
        "labelled_indices": [
          92,
          89,
          46,
          43,
          0
        ],
        "source_heads": [
          14926,
          14896,
          14466,
          14436,
          14006
        ],
        "image_difference_mesh": "250/23",
        "image_heads": [
          15006,
          "344388/23",
          14506,
          "332888/23",
          14006
        ],
        "integer_image_indices": [
          92,
          46,
          0
        ],
        "formula": "Source=a+10*n; image=a+(250/23)*n. The finite index pattern is retained; its comparison mesh changes.",
        "status": "Exact affine comparison lattice, not a new calendar or historical date grid."
      },
      "fragment": "a=results['source_anchor']; ids=results['labelled_indices']; mesh=F(results['image_difference_mesh']); source=results['source_heads']; image=results['image_heads']\nchecks={'source_reconstruction':[a+10*n for n in ids]==source,'image_reconstruction':[a+mesh*n for n in ids]==[F(x) for x in image],'full_anchored_map':[anchored(F(25,23),a,x) for x in source]==[F(x) for x in image]}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ23",
      "question": "How does source translation transport the affine congruence field?",
      "object": "Whole-frame translation with anchor tags",
      "new_burden": "Domain covariance on full fields, citing inherited affine identity",
      "priority": "new compression or transfer",
      "sources": [
        "File46\u00a7\u00a72,6A.5",
        "C505\u2013507 inherited",
        "C873\u2013889 inherited",
        "Strategy\u00a7\u00a75C,5E\u2013G"
      ],
      "results": {
        "covariance": "Adding the same integer t to all points and both pivots adds t to the residue; the period and obstruction are unchanged.",
        "unchanged": [
          "period",
          "pivot obstruction divisor",
          "emptiness/nonemptiness"
        ],
        "scope": "whole-frame mathematical covariance, not a newly authorized chronology translation"
      },
      "fragment": "ks=[F(25,23),F(70,69),F(300,299)]; pairs=[]\nfor k in ks:\n    for l in ks:\n        a=affine_stage_coset(k,l,14006,4836); b=affine_stage_coset(k,l,14036,4866); pairs.append((a,b))\nchecks={'all_nine_covariant':all(a['nonempty']==b['nonempty'] and (not a['nonempty'] or (a['period']==b['period'] and b['residue']==(a['residue']+30)%a['period'])) for a,b in pairs)}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ24",
      "question": "What is the smallest explanatory basis supported by all these fixed objects?",
      "object": "Key/calendar/allocation/shape/placement dependency map",
      "new_burden": "Compact source-constraint ledger; no unique-global-minimality claim",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a75D\u2013G,6",
        "prior family index and selected sourcepacket records"
      ],
      "results": {
        "basis": [
          "calendar measures plus declared completion relations",
          "source part weights and their order",
          "choice of converted component",
          "measurement grid",
          "held pivot pair",
          "source authorization"
        ],
        "compression": [
          "three independent Key equations",
          "two retained-total measurements",
          "one placement residue plus difference lattice"
        ],
        "ceiling": "No unique or globally minimal grammar is claimed."
      },
      "fragment": null,
      "proof_only": true,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ25",
      "question": "Does a common calibrated day-volume survive all nine predetermined E/P/J assignments to the source299|161 partition?",
      "object": "File60 Covenant partition, two typed calendar-output components",
      "new_burden": "Whole mixed-unit assignment field; source-authorized mixedJ/E distinguished from diagnostics",
      "priority": "new compression or transfer",
      "sources": [
        "File60\u00a75 source299|161",
        "Strategy\u00a73.3 calibrated measures",
        "C532\u2013533 inherited comparisons"
      ],
      "results": {
        "source_parts": [
          299,
          161
        ],
        "complete_nine_assignments": [
          {
            "assignment": [
              "E",
              "E"
            ],
            "calendar_measures": [
              336,
              336
            ],
            "output_components": [
              325,
              175
            ],
            "naked_sum": 500,
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "E",
              "P"
            ],
            "calendar_measures": [
              336,
              360
            ],
            "output_components": [
              325,
              "490/3"
            ],
            "naked_sum": "1465/3",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "E",
              "J"
            ],
            "calendar_measures": [
              336,
              364
            ],
            "output_components": [
              325,
              "2100/13"
            ],
            "naked_sum": "6325/13",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "P",
              "E"
            ],
            "calendar_measures": [
              360,
              336
            ],
            "output_components": [
              "910/3",
              175
            ],
            "naked_sum": "1435/3",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "P",
              "P"
            ],
            "calendar_measures": [
              360,
              360
            ],
            "output_components": [
              "910/3",
              "490/3"
            ],
            "naked_sum": "1400/3",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "P",
              "J"
            ],
            "calendar_measures": [
              360,
              364
            ],
            "output_components": [
              "910/3",
              "2100/13"
            ],
            "naked_sum": "18130/39",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "J",
              "E"
            ],
            "calendar_measures": [
              364,
              336
            ],
            "output_components": [
              300,
              175
            ],
            "naked_sum": 475,
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "J",
              "P"
            ],
            "calendar_measures": [
              364,
              360
            ],
            "output_components": [
              300,
              "490/3"
            ],
            "naked_sum": "1390/3",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          },
          {
            "assignment": [
              "J",
              "J"
            ],
            "calendar_measures": [
              364,
              364
            ],
            "output_components": [
              300,
              "2100/13"
            ],
            "naked_sum": "6000/13",
            "component_day_volumes": [
              109200,
              58800
            ],
            "total_day_volume": 168000,
            "common336_count": 500,
            "common360_count": "1400/3",
            "common364_count": "6000/13"
          }
        ],
        "shared_volume": 168000,
        "status": "Scalar assignments except the inherited source branches are diagnostic. Interpreting each output in its matching Key calendar is conditional; no assertion that475 is literally a mixed-calendar elapsed chronology."
      },
      "fragment": "checks={'complete_nine':len(results['complete_nine_assignments'])==9,'pointwise_volume':all(r['component_day_volumes']==[109200,58800] for r in results['complete_nine_assignments']),'total':all(r['total_day_volume']==168000 for r in results['complete_nine_assignments'])}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ26",
      "question": "What changes if the numerical outputs are retained but their calendar-unit labels are swapped?",
      "object": "Conditional300@364 plus175@336 calendar realization",
      "new_burden": "Expose unit-label information that the naked475 total loses",
      "priority": "new compression or transfer",
      "sources": [
        "File60\u00a75 source299|161",
        "Strategy\u00a73.3 calibrated measures",
        "C532\u2013533 inherited comparisons"
      ],
      "results": {
        "source_mixed_JE": [
          300,
          175
        ],
        "matched_unit_volume": 168000,
        "swapped_unit_volume": 164500,
        "swap_defect": -3500,
        "status": "Scalar assignments except the inherited source branches are diagnostic. Interpreting each output in its matching Key calendar is conditional; no assertion that475 is literally a mixed-calendar elapsed chronology."
      },
      "fragment": "matched=mixed_calendar_measure([299,161],[F(300,299),F(25,23)],[364,336]); swapped=mixed_calendar_measure([299,161],[F(300,299),F(25,23)],[336,364])\nchecks={'same_naked_total':matched['naked_sum']==swapped['naked_sum']==475,'different_measure':matched['total_volume']==168000 and swapped['total_volume']==164500}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ27",
      "question": "When do differently weighted calendar legs admit one common year-count representation?",
      "object": "Same fixed nine assignment field",
      "new_burden": "Exact remeasurement into a chosen calendar; no literal elapsed-time promotion",
      "priority": "new compression or transfer",
      "sources": [
        "File60\u00a75 source299|161",
        "Strategy\u00a73.3 calibrated measures",
        "C532\u2013533 inherited comparisons"
      ],
      "results": {
        "common_volume": 168000,
        "remeasured_counts": {
          "336": 500,
          "360": "1400/3",
          "364": "6000/13"
        },
        "invariance": "same values for every row of the nine-assignment field",
        "scope": "conditional calibrated calendar realization only"
      },
      "fragment": "checks={'remeasurement':all(F(v)*int(d)==results['common_volume'] for d,v in results['remeasured_counts'].items())}",
      "proof_only": false,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    },
    {
      "id": "KQ28",
      "question": "Can the declared source tags be factored into algebraic compatibility and chronological authorization without either being discarded?",
      "object": "Calibration, allocation, grid, pivot, and mixed-unit examples",
      "new_burden": "Explicit two-level result ledger and smallest supported operation inventory",
      "priority": "new compression or transfer",
      "sources": [
        "Strategy\u00a7\u00a75D\u2013G,6",
        "prior family index and selected sourcepacket records"
      ],
      "results": {
        "algebraic_layer": [
          "exact factor",
          "allocation support",
          "unit/grid",
          "affine domain",
          "whole-field reconstruction"
        ],
        "source_layer": [
          "selected source rows",
          "named cut",
          "phase/chart",
          "appointed anchors",
          "admitted route and claim status"
        ],
        "rule": "An algebraically compatible construction is not automatically a source-authorized chronology."
      },
      "fragment": null,
      "proof_only": true,
      "root_note": "Root chooses numbered mapping and reassessment; do not count prepared outputs as executed research."
    }
  ],
  "bindings": {
    "questions.json": "1f4001d5c18a51fe1a41e41acd6f7c2f140c7a457206fe9b7239943b5b374bbe",
    "questions_addendum.json": "f3ff2aa8573678d54c3c6e9147c55e685c2d2e96428e3f9793d74530a39d7704",
    "sourcepacket.json": "11af99ef822dc676b504a83d732af04d01492ffa4048810e44865c0dfffc9e65",
    "exactdiagnostics.json": "4144202ad401d9646936dd5798f9345730eb111a70de22d0ba4c31895701db51",
    "adoption_helpers.py": "86eb9012c15ebdd5c6ca855cf8097e097e63054d38978431eac3dc463a00c866"
  }
}