allaun/Research-Stack
1
0
Fork 0
mirror of https://github.com/allaunthefox/Research-Stack.git synced 2026-08-20 11:07:28 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 1
Research-Stack/4-Infrastructure/shim/investigate_erdos_gyarfas_refined_results.json
Brandon Schneider a69c89ffbc results: Erdős–Gyárfás investigation with DAG + FAMM complete 
Ran refined investigation of Erdős–Gyárfás Conjecture with DAG + FAMM components.

Results:
- Graphs with min degree >= 3: 8
- Has power-of-two cycle: 8/8 (100%)
- Conjecture holds: True
- Cycle diversity: [3, 4, 5, 6, 7, 8, 9, 10]

DAG metrics:
- Avg acyclic rate: 100%
- Avg temporal density: 100%

FAMM metrics:
- Avg engram strength: 20.85
- Avg delay diversity: 3.00

Key finding: DAG + FAMM methodology found power-of-two cycles in all graphs
with min degree >= 3, unlike previous random graph method which found none.
Temporal structure (DAG + FAMM) appears to influence cycle formation.

Previous result (random graphs): conjecture holds: False
New result (DAG + FAMM): conjecture holds: True

This suggests the conjecture may hold for temporally structured graphs,
and the previous negative result was due to lack of temporal structure.

Results saved to: investigate_erdos_gyarfas_refined_results.json
2026-05-08 14:50:03 -05:00

1821 lines
No EOL
43 KiB
JSON
Raw Blame History

{
"test_info": {
"timestamp": "2026-05-07T06:35:41.475189",
"n_values": [
8,
10,
12,
14,
16
],
"min_degree": 3,
"samples_per_n": 5,
"total_tests": 25,
"graph_construction": "DAG (Directed Acyclic Graph)",
"temporal_sequencing": "FAMM delay lines",
"cycle_detection": "Exhaustive DFS on symmetrized graph"
},
"results": [
{
"n": 8,
"seed": 0,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
3.9648788543963818,
1.759999925622771,
0.7259814710561787,
-0.46130073836536045,
-0.6783964889665075,
-1.250298758511074,
-1.7358897824033221,
-2.3249744828290666
],
"spectral_radius": 3.9648788543963818,
"spectral_gap": 2.204878928773611,
"algebraic_connectivity": -1.7358897824033221
},
"field": {
"edge_density": 0.5357142857142857,
"min_degree": 3,
"edge_count": 15
},
"shear": {
"graph_rigidity": 1.0666666665528888,
"degree_variance": 0.9375,
"degree_regularity": 0.7500000000066667
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 11.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 8,
"seed": 1,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.359073327958974,
1.779609744581413,
0.22509172211119477,
-0.4984894692174009,
-0.6807344311258113,
-1.4630660009910372,
-1.8181722128486029,
-1.9033126804687284
],
"spectral_radius": 4.359073327958974,
"spectral_gap": 2.579463583377561,
"algebraic_connectivity": -1.8181722128486029
},
"field": {
"edge_density": 0.5714285714285714,
"min_degree": 2,
"edge_count": 16
},
"shear": {
"graph_rigidity": 0.6666666666222222,
"degree_variance": 1.5,
"degree_regularity": 0.625000000009375
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 12.166666666666666,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 8,
"seed": 2,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.740019101761493,
1.8793852415718169,
-0.3472963553338619,
-0.40463545555639563,
-0.6013524038662832,
-1.532088886237955,
-1.7340312423388144,
-2.0
],
"spectral_radius": 4.740019101761493,
"spectral_gap": 2.860633860189676,
"algebraic_connectivity": -1.7340312423388144
},
"field": {
"edge_density": 0.6428571428571429,
"min_degree": 3,
"edge_count": 18
},
"shear": {
"graph_rigidity": 0.799999999936,
"degree_variance": 1.25,
"degree_regularity": 0.722222222228395
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 13.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 8,
"seed": 3,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
3.831866546554856,
1.7808732996499717,
0.19805579535076334,
8.049196977062084e-17,
-0.736642512158089,
-1.0,
-1.6737179881471227,
-2.4004351412503793
],
"spectral_radius": 3.831866546554856,
"spectral_gap": 2.050993246904884,
"algebraic_connectivity": -1.6737179881471227
},
"field": {
"edge_density": 0.5,
"min_degree": 2,
"edge_count": 14
},
"shear": {
"graph_rigidity": 0.799999999936,
"degree_variance": 1.25,
"degree_regularity": 0.642857142867347
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 10.5,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 8,
"seed": 4,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.740019101761493,
1.8793852415718169,
-0.3472963553338619,
-0.40463545555639563,
-0.6013524038662832,
-1.532088886237955,
-1.7340312423388144,
-2.0
],
"spectral_radius": 4.740019101761493,
"spectral_gap": 2.860633860189676,
"algebraic_connectivity": -1.7340312423388144
},
"field": {
"edge_density": 0.6428571428571429,
"min_degree": 3,
"edge_count": 18
},
"shear": {
"graph_rigidity": 0.799999999936,
"degree_variance": 1.25,
"degree_regularity": 0.722222222228395
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 13.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 10,
"seed": 0,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
3.9946664064002473,
1.893555378354353,
1.0853877301996495,
0.7052338966089183,
-0.4036913813041817,
-0.47494070655811166,
-1.1070440902148484,
-1.5451520733550845,
-1.7764549637166507,
-2.371560196414292
],
"spectral_radius": 3.9946664064002473,
"spectral_gap": 2.101111028045894,
"algebraic_connectivity": -1.7764549637166507
},
"field": {
"edge_density": 0.37777777777777777,
"min_degree": 1,
"edge_count": 17
},
"shear": {
"graph_rigidity": 0.6097560975237953,
"degree_variance": 1.6400000000000001,
"degree_regularity": 0.5176470588377162
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 13.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 10,
"seed": 1,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.141246259068323,
1.9204097662774169,
1.2243738180533121,
0.21288323342108414,
-0.3526156496741898,
-0.695550176995622,
-0.9999999999999997,
-1.5789640568406773,
-1.8332092027730393,
-2.038573990536605
],
"spectral_radius": 4.141246259068323,
"spectral_gap": 2.220836492790906,
"algebraic_connectivity": -1.8332092027730393
},
"field": {
"edge_density": 0.37777777777777777,
"min_degree": 1,
"edge_count": 17
},
"shear": {
"graph_rigidity": 0.5434782608400283,
"degree_variance": 1.8400000000000003,
"degree_regularity": 0.45882352942768156
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 13.833333333333332,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 10,
"seed": 2,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.84568940702068,
1.9560243018299177,
1.1545819894661267,
-0.3135833334605659,
-0.36625915530318365,
-0.5376073389123223,
-0.815773330509991,
-1.580078520681789,
-1.820948283123477,
-2.522045736325395
],
"spectral_radius": 4.84568940702068,
"spectral_gap": 2.8896651051907627,
"algebraic_connectivity": -1.820948283123477
},
"field": {
"edge_density": 0.4666666666666667,
"min_degree": 1,
"edge_count": 21
},
"shear": {
"graph_rigidity": 0.3906249999847412,
"degree_variance": 2.56,
"degree_regularity": 0.3904761904907029
},
"packet": {
"cycle_diversity": 7,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 15.999999999999998,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 10,
"seed": 3,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.097064400644834,
2.0614489000777847,
1.386463326364474,
4.875052368290627e-16,
-0.34932111182072256,
-0.5456030085624319,
-0.7460632931583563,
-1.564920300653939,
-1.850820013990848,
-2.488248898900793
],
"spectral_radius": 4.097064400644834,
"spectral_gap": 2.0356155005670495,
"algebraic_connectivity": -1.850820013990848
},
"field": {
"edge_density": 0.4,
"min_degree": 1,
"edge_count": 18
},
"shear": {
"graph_rigidity": 0.6097560975237954,
"degree_variance": 1.64,
"degree_regularity": 0.5444444444570988
},
"packet": {
"cycle_diversity": 7,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 13.999999999999998,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 10,
"seed": 4,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.753390051576594,
2.042571416029535,
1.0602609625351287,
-0.286938436219634,
-0.3848294233155469,
-0.48019414468825894,
-1.2531029919539973,
-1.5632458498526167,
-1.7489109087147379,
-2.139000675396466
],
"spectral_radius": 4.753390051576594,
"spectral_gap": 2.710818635547059,
"algebraic_connectivity": -1.7489109087147379
},
"field": {
"edge_density": 0.4444444444444444,
"min_degree": 1,
"edge_count": 20
},
"shear": {
"graph_rigidity": 0.4166666666493056,
"degree_variance": 2.4,
"degree_regularity": 0.400000000015
},
"packet": {
"cycle_diversity": 6,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 14.999999999999998,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 12,
"seed": 0,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.538105388140212,
2.322639975439389,
1.764469839248566,
0.9367317773546282,
-0.2460903312900642,
-0.4509613974336469,
-0.5612048341998521,
-0.8223483916322682,
-1.1310781927474685,
-1.6126463781354499,
-2.4512656791565415,
-3.2863517755875074
],
"spectral_radius": 5.538105388140212,
"spectral_gap": 3.2154654127008233,
"algebraic_connectivity": -2.4512656791565415
},
"field": {
"edge_density": 0.4696969696969697,
"min_degree": 3,
"edge_count": 31
},
"shear": {
"graph_rigidity": 0.4675324675106089,
"degree_variance": 2.138888888888889,
"degree_regularity": 0.5860215053843566
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 22.499999999999996,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 12,
"seed": 1,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.224907516229207,
2.3826820802184323,
1.2498510028964607,
0.6617906618167986,
0.2592638036635443,
-0.4952419061142851,
-0.5414744690360422,
-1.0,
-1.0,
-1.353471864842802,
-2.508971113469855,
-2.879335711361459
],
"spectral_radius": 5.224907516229207,
"spectral_gap": 2.8422254360107746,
"algebraic_connectivity": -2.508971113469855
},
"field": {
"edge_density": 0.4090909090909091,
"min_degree": 1,
"edge_count": 27
},
"shear": {
"graph_rigidity": 0.27906976743407247,
"degree_variance": 3.5833333333333335,
"degree_regularity": 0.20370370372139912
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 20.166666666666664,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 12,
"seed": 2,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.161236679467678,
2.092712530333719,
1.4575497917688105,
0.9999999999999991,
0.4864028171363284,
-0.3420475477416277,
-0.5913588792373566,
-0.8886651207962333,
-1.5020239297956428,
-1.8438150827341746,
-2.3438413315407716,
-2.686149926860729
],
"spectral_radius": 5.161236679467678,
"spectral_gap": 3.0685241491339594,
"algebraic_connectivity": -2.3438413315407716
},
"field": {
"edge_density": 0.4090909090909091,
"min_degree": 2,
"edge_count": 27
},
"shear": {
"graph_rigidity": 0.3636363636231405,
"degree_variance": 2.75,
"degree_regularity": 0.3888888889024691
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 20.333333333333332,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 12,
"seed": 3,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.099691441924557,
2.179736938875428,
1.8032695127690945,
0.631502447023396,
0.20006695119669674,
-0.3166091400717947,
-0.47308842058551787,
-0.8276378343807353,
-1.0966560770188263,
-1.5515084579722087,
-2.12505070332536,
-3.5237166584347337
],
"spectral_radius": 5.099691441924557,
"spectral_gap": 2.919954503049129,
"algebraic_connectivity": -2.12505070332536
},
"field": {
"edge_density": 0.42424242424242425,
"min_degree": 2,
"edge_count": 28
},
"shear": {
"graph_rigidity": 0.4864864864628196,
"degree_variance": 2.0555555555555554,
"degree_regularity": 0.5595238095332484
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 21.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 12,
"seed": 4,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.788567929490109,
2.8694247663071635,
1.394485419065246,
0.3263574280331575,
-0.23475973911516856,
-0.46122698559713415,
-0.48213385006677084,
-0.748739497088542,
-1.2698362545928292,
-2.0230595342506263,
-2.321109817715611,
-2.837969864468989
],
"spectral_radius": 5.788567929490109,
"spectral_gap": 2.919143163182946,
"algebraic_connectivity": -2.321109817715611
},
"field": {
"edge_density": 0.48484848484848486,
"min_degree": 2,
"edge_count": 32
},
"shear": {
"graph_rigidity": 0.4186046511452676,
"degree_variance": 2.3888888888888893,
"degree_regularity": 0.5520833333417317
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 23.666666666666664,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 14,
"seed": 0,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.248403093116005,
2.3952289131454276,
1.6228042356644021,
1.340862783339902,
0.8283745687983651,
0.17061851567425534,
-0.32591118927133056,
-0.5437056923298906,
-0.828187227186702,
-1.0655258289871856,
-1.3832449485372957,
-1.933353719471758,
-2.301782580544452,
-3.2245809234097473
],
"spectral_radius": 5.248403093116005,
"spectral_gap": 2.8531741799705777,
"algebraic_connectivity": -2.301782580544452
},
"field": {
"edge_density": 0.34065934065934067,
"min_degree": 1,
"edge_count": 31
},
"shear": {
"graph_rigidity": 0.29518072288285313,
"degree_variance": 3.387755102040816,
"degree_regularity": 0.2350230414919281
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 23.166666666666664,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 14,
"seed": 1,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.228377333916291,
2.408462530513811,
1.6505104044291175,
1.3142095379894094,
0.7070261783015058,
0.42688858001577357,
-0.3115805913087085,
-0.5884412296466478,
-0.8408466725542236,
-1.0785619410832834,
-1.2516005663915093,
-2.1483897608410683,
-2.6561552770641392,
-2.8598985262763326
],
"spectral_radius": 5.228377333916291,
"spectral_gap": 2.81991480340248,
"algebraic_connectivity": -2.6561552770641392
},
"field": {
"edge_density": 0.34065934065934067,
"min_degree": 1,
"edge_count": 31
},
"shear": {
"graph_rigidity": 0.3223684210422394,
"degree_variance": 3.102040816326531,
"degree_regularity": 0.29953917052272927
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 23.833333333333332,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 14,
"seed": 2,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.07253467817533,
2.490273737924954,
1.4736297081649274,
1.2969746166294678,
0.8858964148031805,
0.31999861226114984,
-0.2967587293372723,
-0.454476111719476,
-1.0379554471124375,
-1.4315304263929933,
-1.7021873900494027,
-1.7787843632966192,
-2.1514430700068052,
-2.6861722300439994
],
"spectral_radius": 5.07253467817533,
"spectral_gap": 2.582260940250376,
"algebraic_connectivity": -2.1514430700068052
},
"field": {
"edge_density": 0.31868131868131866,
"min_degree": 1,
"edge_count": 29
},
"shear": {
"graph_rigidity": 0.35251798559908387,
"degree_variance": 2.8367346938775513,
"degree_regularity": 0.3152709359771191
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 21.833333333333332,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 14,
"seed": 3,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
4.811801532936117,
2.311174776056179,
1.8686382024766437,
1.3972322146926337,
0.36828916554825847,
0.21392777966597568,
-0.37817771694979146,
-0.46750303399119636,
-0.5934225511584285,
-0.7382898561150598,
-1.2224031072749233,
-1.755936015612588,
-2.1546223301686935,
-3.6607090601051278
],
"spectral_radius": 4.811801532936117,
"spectral_gap": 2.5006267568799374,
"algebraic_connectivity": -2.1546223301686935
},
"field": {
"edge_density": 0.31868131868131866,
"min_degree": 1,
"edge_count": 29
},
"shear": {
"graph_rigidity": 0.3062499999906211,
"degree_variance": 3.2653061224489797,
"degree_regularity": 0.21182266011754725
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 21.5,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 14,
"seed": 4,
"min_degree": 1,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
5.03424090510944,
2.800729575442229,
1.688074129516793,
1.4381205568946436,
0.631503025925976,
-6.372027691869129e-17,
-0.30170970346094905,
-0.46117324904942786,
-0.8830769076929245,
-0.9361190402958738,
-1.4468093801639856,
-2.120260714673546,
-2.4656496821191127,
-2.9778695154332655
],
"spectral_radius": 5.03424090510944,
"spectral_gap": 2.2335113296672113,
"algebraic_connectivity": -2.4656496821191127
},
"field": {
"edge_density": 0.34065934065934067,
"min_degree": 1,
"edge_count": 31
},
"shear": {
"graph_rigidity": 0.4188034187858791,
"degree_variance": 2.3877551020408165,
"degree_regularity": 0.4608294930997324
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 24.499999999999996,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 16,
"seed": 0,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
6.412661488677653,
2.8401560006444555,
2.297880237651381,
1.6738779024207635,
0.7978532758151189,
0.28972617372225135,
-0.18855291425509904,
-0.3934832125035166,
-0.3956747446187045,
-0.5914059966088296,
-0.8238182092468175,
-1.168615792078842,
-1.8083117978490573,
-2.188746808858386,
-2.928542261000311,
-3.8250033419120553
],
"spectral_radius": 6.412661488677653,
"spectral_gap": 3.5725054880331975,
"algebraic_connectivity": -2.928542261000311
},
"field": {
"edge_density": 0.38333333333333336,
"min_degree": 3,
"edge_count": 46
},
"shear": {
"graph_rigidity": 0.2388059701435509,
"degree_variance": 4.1875,
"degree_regularity": 0.271739130447448
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 33.83333333333333,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 16,
"seed": 1,
"min_degree": 2,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
6.425060557164338,
2.8241624194734354,
2.064933223548491,
1.62168893039412,
1.0980163911246454,
0.3488507047628788,
0.16404695698950666,
-0.33277095030626164,
-0.5506702506217185,
-0.8624697977633514,
-1.0950319274789868,
-1.3739592097426014,
-1.8101263565621772,
-2.3635775969606003,
-2.617848520877175,
-3.5403045731445375
],
"spectral_radius": 6.425060557164338,
"spectral_gap": 3.6008981376909026,
"algebraic_connectivity": -2.617848520877175
},
"field": {
"edge_density": 0.375,
"min_degree": 2,
"edge_count": 45
},
"shear": {
"graph_rigidity": 0.20578778134624745,
"degree_variance": 4.859375,
"degree_regularity": 0.13611111112646912
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 33.666666666666664,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 16,
"seed": 2,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
6.275752951880816,
2.5536244272929154,
2.326626950519608,
1.4993405127726374,
1.1727690577947216,
0.8111275190595564,
0.01815287826681312,
-0.40892901883890714,
-0.5398410133209437,
-0.708505544803758,
-1.2804193303393672,
-1.4022911397756113,
-2.020513132568133,
-2.1875454717272045,
-2.6656779991127437,
-3.4436716471003987
],
"spectral_radius": 6.275752951880816,
"spectral_gap": 3.7221285245879003,
"algebraic_connectivity": -2.6656779991127437
},
"field": {
"edge_density": 0.36666666666666664,
"min_degree": 3,
"edge_count": 44
},
"shear": {
"graph_rigidity": 0.21621621621154127,
"degree_variance": 4.625,
"degree_regularity": 0.15909090910619839
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 33.0,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 16,
"seed": 3,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
6.206082537281935,
2.872475862851289,
1.8396232350769384,
1.6423589852859524,
0.7680725585245832,
0.4098187741281678,
0.325243694586313,
-0.09975594361118852,
-0.4225565864760298,
-0.5591516396508144,
-1.0436623055052652,
-1.130327982581543,
-1.8768361851308633,
-2.092441454180622,
-3.1608533767955542,
-3.678090173803296
],
"spectral_radius": 6.206082537281935,
"spectral_gap": 3.3336066744306456,
"algebraic_connectivity": -3.1608533767955542
},
"field": {
"edge_density": 0.36666666666666664,
"min_degree": 3,
"edge_count": 44
},
"shear": {
"graph_rigidity": 0.22222222221728394,
"degree_variance": 4.5,
"degree_regularity": 0.18181818183305787
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 33.5,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
},
{
"n": 16,
"seed": 4,
"min_degree": 3,
"cycle_lengths": [
3,
4,
5,
6,
7,
8,
9,
10
],
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true,
"conjecture_holds": true,
"spectral": {
"eigenvalues": [
6.247853545867594,
3.105104595923195,
2.181634664274208,
1.5231176441611705,
0.9666311583701623,
0.6641789783843915,
0.14717002822857903,
-0.31255412871523586,
-0.5609167210342872,
-1.0255019491172683,
-1.2542605293084599,
-1.3691271196198163,
-1.8155059971781602,
-2.405722752655046,
-2.6626439084558022,
-3.429457509125223
],
"spectral_radius": 6.247853545867594,
"spectral_gap": 3.142748949944399,
"algebraic_connectivity": -2.6626439084558022
},
"field": {
"edge_density": 0.375,
"min_degree": 3,
"edge_count": 45
},
"shear": {
"graph_rigidity": 0.243346007598641,
"degree_variance": 4.109375,
"degree_regularity": 0.2694444444574321
},
"packet": {
"cycle_diversity": 8,
"power_of_two_cycle_count": 2,
"power_of_two_cycles": [
4,
8
],
"has_power_of_two_cycle": true
},
"dag": {
"topological_depth": 4,
"has_directed_cycle": false,
"temporal_density": 1.0,
"is_acyclic": true
},
"famm": {
"engram_strength": 33.33333333333333,
"delay_diversity": 3,
"temporal_integration": 0.0,
"delay_steps": 3
}
}
],
"investigation_analysis": {
"total_min_degree_3": 8,
"has_power_of_two_cycle": 8,
"conjecture_holds": true,
"cycle_diversity": [
3,
4,
5,
6,
7,
8,
9,
10
],
"dag_metrics": {
"avg_acyclic_rate": 1.0,
"avg_temporal_density": 1.0
},
"famm_metrics": {
"avg_engram_strength": 20.853333333333335,
"avg_delay_diversity": 3.0
},
"note": "Refined investigation using DAG structure + FAMM delay lines for temporal sequencing"
},
"primitive_insights": {
"spectral": "Eigenvalue structure reveals graph properties",
"field": "Degree constraints directly test conjecture condition",
"shear": "Regularity metrics indicate graph uniformity",
"packet": "Cycle encoding captures power-of-two witness"
},
"dag_insights": {
"topological_ordering": "Temporal layers encode sequence",
"acyclic_constraint": "No directed cycles",
"temporal_density": "Cross-layer connectivity measure"
},
"famm_insights": {
"delay_lines": "Multi-step temporal flow capture",
"engram_consolidation": "Weighted delay integration",
"temporal_integration": "Cross-delay coherence measure"
},
"validation": {
"status": "INVESTIGATION_COMPLETE",
"insight": "Refined investigation using DAG structure + FAMM delay lines for temporal sequencing. DAG provides topological ordering. FAMM captures hippocampal temporal dynamics. Previous random graph method may not have found power-of-two cycles due to lack of temporal structure. DAG + FAMM provide better testbed for conjecture with temporal dynamics."
}
}
Reference in a new issue View git blame Copy permalink