Reconstruct Interacting finite fermionic cluster retarded Green function and Leh...
https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B026/interacting-fermionic-cluster-complete-lehmann-green-spectral-lawOverview
Reconstruct Interacting finite fermionic cluster retarded Green function and Lehmann spectral law from an anonymous supplied artifact and compare an explicit claim.
Protocol
x402 (POST)
Price
$0.0030
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USD Coin
Payment Network
eip155:8453
Category
uncategorized
Provider
detect
Source
bazaar
Indexed
2026-11-01 21:11:46
Health
Status
unknown
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Uptime (30d)
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Never
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Never
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0
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Input Schema
{
"body": {
"artifact": {
"fermionLehmann": {
"claim": null,
"data": {
"broadening": 0.3,
"chemical_potential": 0.2,
"frequency_queries": [
0.5
],
"hopping": 0.7,
"inverse_temperature": 1,
"onsite_energies": [
-0.2,
0.3
],
"onsite_interactions": [
1.2,
1.4
]
}
}
}
},
"bodyType": "json",
"method": "POST",
"type": "http"
}
Output Schema
{
"example": {
"billable": true,
"findings": [
{
"confidence": 1,
"evidence": [
{
"page_indices": [],
"page_url": null,
"pattern": "interacting-fermionic-cluster-complete-lehmann-green-spectral-law_scoped_evidence",
"type": "artifact"
}
],
"limits": [
"Caller-supplied bounded technical model only; every numeric result rounded to six decimal places before exact claim comparison. No external fetch, safety, legal, or medical decision."
],
"module": "interacting-fermionic-cluster-complete-lehmann-green-spectral-law",
"state": "observed",
"value": {
"claim_matches": false,
"fermionLehmann": {
"KMS_occupation_residual": [
0,
0
],
"Lehmann_convention": "Two-site spin-rotation-invariant repulsive Hubbard fermions, modes ordered(0up,1up,0down,1down), mask bits little endian. Grand K=-t sum_sigma(c0dag*c1+h.c.)+sum eps_i*n_i+sum U_i*n_iup*n_idown-mu*N, rho=exp(-beta*K)/Z. Complete spin-up addition/removal spectral measure, spin-down equal by SU2. Pole row=[En-Em,weight00,weight01,weight11] is a real symmetric2x2 residue; all24 transitions retained including zero weights. Sector/rank tuple=[Ndown,Nup_bra,bra_energy_rank,ket_energy_rank], ordered lexicographically. Gret(z)=sum residue/(z-gap), z=omega+i*eta. No leads, noninteracting mean-field substitution or actual material prediction.",
"complete_Lehmann_poles_residue_upper_triangle": [
[
-0.893303,
0.131762,
0.092855,
0.065437
],
[
0.593303,
0.029505,
-0.041868,
0.05941
],
[
0.593303,
0.072086,
-0.10229,
0.14515
],
[
-0.893303,
0.072798,
0.051302,
0.036154
],
[
-0.348468,
0.184561,
0.159643,
0.138089
],
[
0.593303,
0.036043,
-0.051145,
0.072575
],
[
1.708067,
0.047532,
-0.040159,
0.03393
],
[
3.020312,
0.000113,
0.000933,
0.007677
],
[
-1.835075,
0.008237,
-0.004377,
0.002326
],
[
-0.893303,
0.036399,
0.025651,
0.018077
],
[
0.22146,
0.026235,
0.008372,
0.002672
],
[
1.533705,
0.006533,
-0.013975,
0.029894
],
[
1.309148,
0.104399,
-0.117708,
0.132714
],
[
2.874395,
0.000802,
0.003026,
0.011417
],
[
0.367376,
0.047342,
0.029259,
0.018083
],
[
1.932624,
0.012231,
-0.019789,
0.03202
],
[
-0.747387,
0.01522,
0.019966,
0.026193
],
[
0.817861,
0.002165,
-0.005737,
0.015199
],
[
-2.059632,
0.001852,
-0.000556,
0.000167
],
[
-0.494385,
0.014392,
0.006597,
0.003024
],
[
0.367376,
0.094684,
0.058518,
0.036166
],
[
1.932624,
0.024461,
-0.039579,
0.06404
],
[
1.932624,
0.016941,
-0.02741,
0.044351
],
[
0.367376,
0.013707,
0.008472,
0.005236
]
],
"complete_Lehmann_sector_ranks": [
[
0,
0,
0,
0
],
[
0,
0,
0,
1
],
[
0,
1,
0,
0
],
[
0,
1,
1,
0
],
[
1,
0,
0,
0
],
[
1,
0,
0,
1
],
[
1,
0,
0,
2
],
[
1,
0,
0,
3
],
[
1,
0,
1,
0
],
[
1,
0,
1,
1
],
[
1,
0,
1,
2
],
[
1,
0,
1,
3
],
[
1,
1,
0,
0
],
[
1,
1,
0,
1
],
[
1,
1,
1,
0
],
[
1,
1,
1,
1
],
[
1,
1,
2,
0
],
[
1,
1,
2,
1
],
[
1,
1,
3,
0
],
[
1,
1,
3,
1
],
[
2,
0,
0,
0
],
[
2,
0,
0,
1
],
[
2,
1,
0,
0
],
[
2,
1,
1,
0
]
],
"frequency_responses": [
{
"Lorentz_broadened_spectral_density": [
[
0.342084,
-0.095675
],
[
-0.095675,
0.381905
]
],
"frequency": 0.5,
"retarded_spin_up_Green_matrix": [
[
[
0.296924,
-1.07469
],
[
0.857674,
0.300573
]
],
[
[
0.857674,
0.300573
],
[
-0.258014,
-1.19979
]
]
]
}
],
"grand_partition_function": 17.460482,
"grand_potential": -2.85994,
"onsite_double_occupations": [
0.157861,
0.07957
],
"particle_number_probabilities": [
0.057272,
0.343139,
0.462373,
0.129465,
0.007751
],
"spin_up_one_body_density": [
[
0.469707,
0.154868
],
[
0.154868,
0.373935
]
],
"spin_up_spectral_moments_zero_to_two": [
[
[
1,
0
],
[
0,
1
]
],
[
[
0.163648,
-0.7
],
[
-0.7,
0.623509
]
],
[
[
0.875459,
-0.55101
],
[
-0.55101,
1.337614
]
]
]
}
},
"warnings": []
}
],
"known_count": 1,
"scope": {
"contact_values_returned": false,
"network": false,
"supplied_artifact_only": true
},
"warnings": []
},
"type": "json"
}