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Research-Stack/4-Infrastructure/shim/burgers_chaos_game_receipt.json
allaun c0ec099e6d feat(infra): Burgers chaos game — quantum walk over 22-representation graph 
Encodes each Burgers representation as a node connected by proven
isomorphisms from the codebase. Continuous-time quantum walk e^{-iAt}
on the adjacency matrix converges to eigenvector centrality; the
0D DualQuat Braid is confirmed as the universal hub (#1 in all three
rankings: centrality, quantum walk probability, and degree).

Build: N/A (Python shim, no Lean files touched)
2026-06-18 21:39:18 -05:00

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{
"schema": "burgers_chaos_game_v1",
"claim_boundary": "continuous-time-quantum-walk-on-burgers-representation-graph;eigenvector-centrality-determines-braid-hub;no-decision-logic",
"representation_graph": {
"num_nodes": 22,
"labels": [
"0D_DualQuat_Braid",
"1D_Spectral",
"1D_ColeHopf",
"1D_Fokas",
"2D_Helmholtz",
"3D_FiniteDiff",
"BurgersHilbert",
"KdVBurgers",
"Stochastic",
"FNWH_Hyperfluid",
"FNWH_AVM",
"GinzburgLandau",
"DimFluxClosure",
"BurgersRuzsa_Sidon",
"ShockBurgers_Coupling",
"BraidShock_16D",
"AttentionBohm_ABNS",
"NK_Hodge_FAMM",
"QUBO_Formulated",
"AVM_Bytecode",
"WGSL_Shader",
"TriadCore"
],
"degrees": {
"0D_DualQuat_Braid": 21,
"1D_Spectral": 3,
"1D_ColeHopf": 6,
"1D_Fokas": 4,
"2D_Helmholtz": 4,
"3D_FiniteDiff": 2,
"BurgersHilbert": 4,
"KdVBurgers": 3,
"Stochastic": 2,
"FNWH_Hyperfluid": 5,
"FNWH_AVM": 3,
"GinzburgLandau": 3,
"DimFluxClosure": 3,
"BurgersRuzsa_Sidon": 2,
"ShockBurgers_Coupling": 3,
"BraidShock_16D": 2,
"AttentionBohm_ABNS": 2,
"NK_Hodge_FAMM": 2,
"QUBO_Formulated": 1,
"AVM_Bytecode": 3,
"WGSL_Shader": 2,
"TriadCore": 2
}
},
"centrality_rankings": {
"eigenvector_centrality": [
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"node": "0D_DualQuat_Braid",
"score": 0.611307
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{
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{
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{
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{
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{
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{
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{
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{
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{
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"score": 0.10566
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],
"quantum_walk_probability": {
"params": {
"num_times": 500,
"t_max": 30.0
},
"ranking": [
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"node": "0D_DualQuat_Braid",
"probability": 0.406924
},
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"probability": 0.058741
},
{
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},
{
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"probability": 0.038729
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{
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"probability": 0.037157
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{
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"probability": 0.033912
},
{
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"probability": 0.033814
},
{
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"probability": 0.030214
},
{
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"probability": 0.028433
},
{
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"probability": 0.028433
},
{
"node": "FNWH_AVM",
"probability": 0.02816
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{
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"probability": 0.026124
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{
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{
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{
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},
{
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{
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{
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{
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"probability": 0.019777
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{
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"probability": 0.019777
},
{
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{
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},
"degree": [
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"degree": 21
},
{
"node": "1D_ColeHopf",
"degree": 6
},
{
"node": "FNWH_Hyperfluid",
"degree": 5
},
{
"node": "1D_Fokas",
"degree": 4
},
{
"node": "2D_Helmholtz",
"degree": 4
},
{
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"degree": 4
},
{
"node": "1D_Spectral",
"degree": 3
},
{
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"degree": 3
},
{
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"degree": 3
},
{
"node": "GinzburgLandau",
"degree": 3
},
{
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"degree": 3
},
{
"node": "ShockBurgers_Coupling",
"degree": 3
},
{
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"degree": 3
},
{
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"degree": 2
},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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]
},
"hub_verification": {
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"rank_eigenvector_centrality": 1,
"rank_quantum_walk": 1,
"rank_degree": 1,
"hub_is_universal": true,
"hub_centrality_score": 0.611307,
"hub_degree": 21,
"hub_quantum_walk_prob": 0.406924
},
"summary": {
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"hub_node": "0D_DualQuat_Braid",
"mean_degree": 3.727272727272727,
"graph_density": 0.1774891774891775,
"runtime_s": 0.0286
},
"hamiltonian": {
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"n_qubits": 5,
"n_nodes": 22,
"matrix_schema": "normalized_adjacency",
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"note": "Continuous-time quantum walk Hamiltonian on 22 Burgers representations. Install cirq for Trotterized circuit."
},
"computed_at": "2026-06-19T02:37:56.666962+00:00",
"receipt_sha256": "6b2ee4ba15c7a19f635836cdf5f69c22980b9947ef861f4919be38ece27b3374"
}
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