Datasets:
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Tags:
mathematics
mathematical-physics
materials-science
homogenization
g-closure
two-phase-conductivity
| digraph Audit { | |
| rankdir=LR; | |
| T01 [label="T01: Physical compression, spectral representation and binary deficit"]; | |
| T02 [label="T02: Joint mean-and-moment topology and compactness"]; | |
| T01 -> T02; | |
| T03 [label="T03: Geometry-uniform response continuity"]; | |
| T01 -> T03; | |
| T04 [label="T04: Exact-fraction cubic whole-function density"]; | |
| T01 -> T04; | |
| T02 -> T04; | |
| T03 -> T04; | |
| T05 [label="T05: Positive cubic Bernstein template density and exact operator polynomials"]; | |
| T01 -> T05; | |
| T06 [label="T06: Exact fraction-constrained bathtub rounding"]; | |
| T07 [label="T07: Sharp variable-fraction mean/deficit rounding envelope"]; | |
| T06 -> T07; | |
| T08 [label="T08: Abstract calibrated closure distance and sharp universal factor"]; | |
| T09 [label="T09: Explicit full-cube reference-localizer convergence"]; | |
| T10 [label="T10: Response-only calibrated physical-distance hierarchy"]; | |
| T01 -> T10; | |
| T02 -> T10; | |
| T03 -> T10; | |
| T04 -> T10; | |
| T05 -> T10; | |
| T06 -> T10; | |
| T08 -> T10; | |
| T09 -> T10; | |
| T11 [label="T11: Single running hierarchy for exact squared physical distance"]; | |
| T10 -> T11; | |
| T12 [label="T12: Finite complex observations without latent spectral extension"]; | |
| T03 -> T12; | |
| T05 -> T12; | |
| T09 -> T12; | |
| T10 -> T12; | |
| T13 [label="T13: Finite strict approximation certificates and binary extraction"]; | |
| T06 -> T13; | |
| T09 -> T13; | |
| T10 -> T13; | |
| T11 -> T13; | |
| T14 [label="T14: Convex contact dual without convexifying physical attainability"]; | |
| T10 -> T14; | |
| T15 [label="T15: Noise, fraction continuity and bounded-data uniform penalty limit"]; | |
| T03 -> T15; | |
| T08 -> T15; | |
| T10 -> T15; | |
| T16 [label="T16: Finite-information separation of nonphysical analytic candidates"]; | |
| T02 -> T16; | |
| T04 -> T16; | |
| T17 [label="T17: Universal unit-circle inequality and exact midpoint rejection"]; | |
| T01 -> T17; | |
| T02 -> T17; | |
| T18 [label="T18: Rank-escape and measurable high-frequency tail obstruction"]; | |
| T01 -> T18; | |
| T02 -> T18; | |
| T03 -> T18; | |
| T06 -> T18; | |
| T19 [label="T19: Independent boundary-compatible finite-certificate route"]; | |
| T01 -> T19; | |
| T02 -> T19; | |
| T20 [label="T20: Failure of automatic stationary/GNS spatial completion"]; | |
| T21 [label="T21: Independent finite symbolic and physical regression checks"]; | |
| T01 -> T21; | |
| T03 -> T21; | |
| T05 -> T21; | |
| T07 -> T21; | |
| T09 -> T21; | |
| T11 -> T21; | |
| T17 -> T21; | |
| T18 -> T21; | |
| } | |