{
"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"
}
}
Evidence
adoption pack.json
Linked sources and evidence
Edition and provenance
adoption_pack.json
SHA-256 634449b719b0dc16e88d5739bbec63a8f0fcce1625bdcb828f55ab368d0c5453
C480–C1634/Research_Cycles/C0932_C1131/prep/key_constraints/adoption_pack.json