Established within the stated premises
Complete logical nondisturbance classifies the covariant residual channel
finding:complete-logical-readout-native-covariant-residual-classification
CPTP and Tr4 Phi(X)=Tr4 X for all joint X force Phi=id5 tensor D by the multiplicative domain; factorization is not a fitted ansatz. Native G31 covariance forces D=Dq with -1/15<=q<=1. Continuous semigroups have q(t)=exp(-gamma t), gamma>=0. The original central J-character projector and Paulis realize this in the coherent block-algebra menu with common normalized branchwise erasure records; the gauge correlator is q(t).
Scope: Classification of this explicit residual class, not all sources. No original physical permission for the coherent Kraus events or selection of gamma.16-record equivariance is sectorwise/on the block algebra, not on extra End(H29) coherences. G31 covariance does not prove covariance under arbitrary coherent clock polynomials.
Required premises and original source excerpts
- Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
premise:native-g31-concrete-event-representation - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Complete logical nondisturbance and native covariance
A CPTP residual channel Phi on V5 tensor bar(V4) preserves Tr4 Phi(X)=Tr4 X for ALL joint X and is covariant under the native G31 product representation. This is stronger than preservation only of erasure states rho tensor I4/4 and defines an explicit conditional process class.
premise:complete-logical-nondisturbance-native-covariance - Extended coherent source-algebra operation menu
For realization of the residual channel, unitary elements of the represented group C*-algebra may serve as Kraus events. This mathematical menu does not assert physical permission derived from P1. The block algebra or each sector is considered; extra coherences between inequivalent representations are not automatically accessible observables.
premise:coherent-block-source-algebra-operation-menu
- experiments/theory-contracts/joint-native-algebra-selection-20261016/PROOF.md, lines 129–190
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