Abstract

We distinguish a fixed microscopic recovery experiment, a restricted continuum excitation-code experiment, and a gravitational interpretation requiring an independent physical identification.

For a quartic Majorana Hamiltonian and an even spectral code, we construct complete accessible and complementary channels, retaining arbitrary references and preparation purifications. We prove exact quench-leakage, best-compression, departure, and interpolation formulas. A resonant controlled extractor has explicit signed fermionic branches and a complete decoder. Ideal full transfer is exact. Its minimal jointly invariant reached space has dimension ${\sum }_{m\mathrm{even}}(m+1)\mathrm{rank}(P_{m}V)$, at most forty for the frozen eight-mode instance P8.

The supplied P8-new execution materials report $E_{\mathrm{code}}\approx 4.318140424446922$, $L_N\approx 1.4473228981681243$, and departures $0.032277775445887835$ and $0.12385356780895762$ at times $1/8$ and $1/4$. The new results summary additionally reports agreement between Volterra and spectral/RK candidate calculations near $q\approx -0.77925+0.07681\mathrm{i}$, with $\eta =|q{|}^2\approx 0.61313$.

For the declared continuum reduction, storage changes the occupied packet while extraction remains coupled to the fixed packet operator. A unique Volterra solution determines the complete signed excitation-qubit channel and its information-bearing complement. The specified complete decoder has exact half-diamond error $1-\eta$. The reported candidate values therefore suggest error about $0.38687$, above one quarter, for this decoder. They do not establish a rigorous numerical exclusion.

The supplied summary reports a patched rational defect-checking run with uniform defect bound about $0.117$, but its resulting transmission enclosure is $[0,1]$. Exact certificate rationals, original candidate arrays, patched-source identifiers, and complete inspection reports are not supplied. Version 8 incorporates these reported results, repairs mixed interval/complex dispatch, and introduces journaled failure recording. The new v8 programs remain unexecuted. P8 rank certification, a nontrivial continuum amplitude enclosure, and the validated quarter-error verdict remain open. No P8 gravitational dictionary is constructed.