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

Abstract

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

$\mathfrak{C}=(W,\mathcal{I},\mathrm{Cal},G,D,R,U)$

with six requirements: declared access, calibrated interventions, relative gauge alignment, a dependence-valid evidence pedigree, reproducibility with independently generated error opportunities, 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

$\rho_{\pm}=\frac{I_4\pm(3/5)J\otimes J}{4}$

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 $\chi_H=(I_4+J\otimes J)/4$; 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 $1-(1-\varepsilon)^n$ for an $\varepsilon$ 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.

Two achievements, usually conflated

Operational objectivity — observers can publicly establish and reproduce a result relative to a declared interface.

Tomographic exhaustiveness — that interface uniquely determines the complete state.

The first does not guarantee the second. A scientific map can be reliable without being one-to-one with the territory: two distinct physical possibilities may cast exactly the same shadow through one observation channel while separating sharply through another. The paper does not infer a hidden ontology from what the public interface misses — its conclusion is that objectivity can be real, reproducible and useful while remaining relative to a nonexhaustive interface.

Where it sits in the release

CFQF-Q3 draws reconstruction context from CFQF-Q4 and the two-rebit observability structure from CFQF-Q1.

Download paper (Zenodo) — 32 pages. CC-BY-4.0.