Hidden-Control Objectivity Diagnostics (HCOD)
Two-Gate Certification under Unresolved Channel Variation
HCOD addresses a critical vulnerability in standard Quantum Darwinism: when the interaction channel creating environmental records is partly hidden, sectorwise decoherence can report false-positive objectivity. HCOD introduces a two-gate test: first verify common-record preservation (Delta_rec = 0), then check fragment Holevo redundancy.
Claim Boundary & Exclusions Audit
What Is Claimed (Within Scope)
- •Gate 1 (Common-Record Preservation): Record projector commutes with all active channel generators ([H(a), Q_r x I] = 0).
- •Delta_rec Diagnostic: Normalized misalignment measure; exact objectivity requires Delta_rec = 0.
- •Gate 2 (Fragment Information): Integrated Holevo information must exceed redundancy threshold on disjoint fragments.
- •Identifies sectorwise false-positive objectivity where channels record different bases.
What Is NOT Claimed (Prohibited Inferences)
- •Does not derive intrinsic record support, intrinsic observers, or spacetime geometry.
Technical Exposition & Formulation
Let {H(a)} be a finite family of Hamiltonians with prior probabilities p_a > 0. If an observer lacks access to the channel label a, accessible dynamics are Phi_t(rho) = sum_a p_a exp(-it H(a)) rho exp(it H(a)). Exact objectivity for record class C requires Delta_rec(C; H) = inf_{R in C} max_a max_r ||[H(a), Q_r x I]|| / ||H(a)|| = 0.
Theorems & Mathematical Propositions
Common-Record Preservation Theorem
[EXA]Exact result- Bounded self-adjoint Hamiltonians H(a) on H_S x H_E.
- Finite-dimensional projective decompositions {Q_r}.
Assumptions & Input Data
- Hidden channel label is inaccessible to the fragment observer.
- System and environment Hilbert spaces are finite dimensional.
Declared Complete Carrier (K3)
System S, environment E, hidden channel label a, and fragment observers.
Source Provenance & Verification Hashes
HCOD_ETP_PRXQ_V16_CPR5-2_Submission_Frozen_Successor-06_OIRP-Closure...
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