Certificate-Relative Operational Objectivity without Tomographic Exhaustiveness: Public Interfaces, Evidence Pedigrees, and a Two-Rebit Countermodel

Here “operational objectivity” is used only in a certificate-relative sense: satisfaction

of a selected public-audit standard, not quantum Darwinism, spectrum-broadcast objectivity, or

complete intersubjectivity. A declared family of complete queries determines an access-relative

public class. We first state an elementary fiber-stability proposition: when a certificate’s target

dependence factors through the public evaluation map and its auxiliary records do not encode which

member of a public fiber was realized, a pass cannot identify the underlying physical state if that

map is noninjective. We then propose a typed audit certificate

C = (W,I,Cal,G,D,R,U)

with six requirements: declared access, calibrated interventions, relative gauge alignment, a

dependence-valid evidence pedigree, reproducibility with independently generated error oppor-

tunities, and minimal epochal public revision. Construction J1 tests both the joint consistency and

the inferential limit of this architecture inside standard real-amplitude quantum theory with ordinary

real tensor composition. Ideal real-trine effects are nominal targets, while symmetrically relabeled

noisy trines are the implemented effects and span each full local rebit effect space. Nevertheless

I4 ±(3/5)J⊗J

ρ±=

4

give probability 1/9 for every outcome of every implemented epoch-0 product context. A separately

declared and calibrated global projective measurement outside that interface distinguishes them with

total-variation distance 3/5 and equal-prior success 4/5. The witness depends on an independently

trusted, hidden-direction-sensitive calibration source χH = (I4 + J⊗J)/4; calibration-source access

is not target-query access, and no preparation–measurement duality or joint-SPAM self-calibration

is assumed. Supporting results record exact transcript invariance for finite adaptive protocols on

fresh preparations, the bound 1−(1−ε)n for an ε single-round discrepancy, and a distribution-free

finite-sample upper certificate. Thus the selected O1–O6 pass can coexist with noninjectivity of the

full separated-product map in J1. The claimed contribution is the fiber-stability diagnostic, typed

synthesis, and joint witness, not a new operational quotient, local-tomography theorem, rebit defect,

general objectivity criterion, or selection of complex quantum theory.