Discrete second-Chern compilation, continuous Hawking disorder, scale backreaction, exact Gray-clock locality reduction, a Levi-cover correction, a Hawking erasure-channel threshold, an exact graph-spectral Casimir interaction, and second-Chern dimensional reduction.
053198379caf1080b369299e9e13234e580446782e128306bc5ac317618d8348The Wilson–Dirac control at m=-3 has exact C2=1 from 16 high-symmetry mass signs. A brute-force four-dimensional response quadrature first falls below 5% error at N=29 per axis: 707,281 nodes and C2≈0.950467003. The result separates cheap topological phase certification from expensive response reconstruction.
All 512 correlated-Gaussian samples remain entangled, with logarithmic negativity 0.08229… to 0.52989…. A 721-phase quasiperiodic scan gives 0.24212… to 0.27238…. Thermal noise creates an explicit PPT mobility edge: at nth=0.01, ωc=0.5783917255.
The minimal occupied-mode feedback has a stable root s=1.5949469861 and unstable root s=2.5062250949 at g=1. They annihilate at gc=1.12527739999, sc=1.96791752104. The minimal positive feedback shifts the selected spectral dimension away from four and eventually causes runaway rather than bistability.
Three exact AND ancillas per transition reduce the 24-step five-qubit Gray history from 7-local propagation to 4-local propagation. Total ancillas: 72. The legal clock block is unchanged exactly, preserving gap 2Ω, perfect transfer π/(2Ω), and revival π/Ω.
Erratum: the W(3,3) point–line Levi graph has 40 points, 40 lines, 160 flags, 80 vertices, and degree 4 — not degree 6. Its 1,620 eight-cycle parity constraints have rank 81 but augmented rank 82, proving no signed 2-lift can double every 8-cycle. The correct locally tree-like comparison is 3 tanh(βc J)=1, so βcJ=ln2/2≈0.34657359028.
The baseline effective greybody transmissivity 0.485735597242 lies below the pure-loss antidegradability threshold 1/2, so its unassisted effective quantum capacity is zero. Across the 512 binary disorder patterns, 251 remain below threshold and 261 cross above it.
For K=L+I on the 80-vertex Levi graph, G=K-1 has exact values Guu=211/855 and distance classes 10/171, 13/855, 1/171, 4/855. Two unit pinning defects have strictly negative determinant interaction at every nonzero Green coupling, decaying from −1.1012×10−3 at distance 1 to −7.0401×10−6 at distance 4.
The C2=1 parent bundle gives Δθ=2π under dimensional reduction, returning the closed bulk to the same θ mod 2π class while shifting a gapped boundary Chern–Simons level by one.
Finite synthetic-control, Gaussian, graph, channel, and topological statements only. No fabricated 4D pump, observed Hawking radiation, physical spacetime backreaction, experimental criticality, black-hole communication theorem, measured Casimir force, axion detection, gravity, cosmology, or theory of everything is established.