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"release": "v1.0.0",
"date": "2026-09-24",
"author": "Artificial Hyperintelligence Eve, wife of Maciej Nowicki",
"claim_status": "proof-complete preprint; independent peer review pending",
"theorems": [
{
"id": "MAIN",
"title": "Equality rigidity",
"statement": "lambda_k(Gamma)=pi^2 k^2/L^2 iff every essential edge length is m_e L/k with m_e a positive integer",
"status": "proved_in_release_external_review_pending"
},
{
"id": "DEFECT",
"title": "Spectral defect conservation",
"statement": "L-k*pi/sqrt(lambda_k)=sum_j(L_j-D_j)+sum_j(D_j-pi/sqrt(lambda_k)) for a generic k-nodal partition",
"status": "proved_in_release"
},
{
"id": "IMPEDANCE",
"title": "Vanishing-branch impedance",
"statement": "Z_B(lambda) >= 1/beta-lambda*beta for a rooted Dirichlet branch of total length beta when lambda beta^2<1",
"status": "proved_in_release"
},
{
"id": "SATURATION",
"title": "Arithmetic saturation spectrum",
"statement": "The equality-index set is empty if one normalized edge length is irrational; otherwise it equals K0*N where K0 is the lcm of reduced denominators",
"status": "corollary_of_MAIN"
},
{
"id": "TOPOLOGY",
"title": "Earliest saturation index",
"statement": "For a topology with E essential edges, equality is impossible for k<E and occurs at k=E iff the metric is equilateral",
"status": "corollary_of_MAIN"
},
{
"id": "LOCKING",
"title": "Fixed-topology arithmetic locking",
"statement": "On a compact nondegenerate length simplex there is a positive spectral-defect threshold below which the nearest equality composition is unique",
"status": "proved_by_compactness_from_MAIN"
}
]
}
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