{
"questions_bound_before_computation": [
"1f4001d5c18a51fe1a41e41acd6f7c2f140c7a457206fe9b7239943b5b374bbe",
"f3ff2aa8573678d54c3c6e9147c55e685c2d2e96428e3f9793d74530a39d7704"
],
"calibration_allocation_basis": {
"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
],
"E_from_336_360_1over6": "25/23",
"E_from_336_364_1over26": "25/23",
"common_K": "8400/23",
"free_calibration_family": "(E,P,J)=K*(1/336,1/360,1/364) before adding a source allocation",
"predicted_f_E_to_J_from_EP_and364": "1/26",
"diagnostic_f1over25_E": "312/287",
"diagnostic_E_difference": "1/6601"
},
"allocation_triangle": {
"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."
},
"component_defect_family": {
"status": "Existing source examples C609/C714\u2013715; new compression into the kernel of total evaluation.",
"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
}
],
"general_two_part_defect": "For upper fractionf and factor k there, delta=(k\u22121)f(1\u2212f)S*(1,\u22121); reverse component order reverses the sign.",
"coarsening_criterion": "C*diag(k_i)=diag(kbar_B)*C for all vectors iff all k_i in each coarsened blockB equal kbar_B.",
"counterexample": "Weight-dependent effective factors can make equality true for one fixed vector without a commuting operator square."
},
"retained_total_measurement_basis": {
"matrix": [
[
1,
1
],
[
"70/69",
1
],
[
"25/23",
1
]
],
"rank": 2,
"left_constraint": [
5,
-6,
1
],
"det_native_P": "-1/69",
"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."
},
"inherited_529_constraint_basis": {
"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."
},
"affine_prefix_cosets": {
"scope": "Whole-stage integer membership for fixed integer pivots, diagnostic compositions unless source already licensed.",
"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."
],
"fixed_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"
}
],
"inherited_witnesses": [
{
"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
}
],
"whole_field": "A nonempty coset contains all points iff one point has the right residue and every source difference is divisible by its period.",
"covariance": "Adding the same integer t to all points and both pivots adds t to the residue; the period and obstruction are unchanged."
},
"exact_full_field_normal_form": {
"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."
},
"conditional_mixed_calendar_family": {
"source_parts": [
299,
161
],
"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,
"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."
}
}
Evidence
exactdiagnostics.json
Edition and provenance
exactdiagnostics.json
SHA-256 4144202ad401d9646936dd5798f9345730eb111a70de22d0ba4c31895701db51
C480–C1634/Research_Cycles/C0932_C1131/prep/key_constraints/exactdiagnostics.json