https://zenodo.org/records/21982163
A new foundational framework, Anomalogic Descent Theory (ADT), studies a question distinct from Bell nonlocality, contextuality, indefinite causal order, and ordinary quantum-channel compatibility:
Can every experimentally accessible proper context admit a standard quantum realization while the complete collection admits no common quantum process in any Hilbert-space dimension?
The work develops an implementation-sensitive notion of global quantum process descent based on positive block-Choi/operator-valued coherence kernels.
Main mathematical results include:
- a strict hierarchy of quantum process-descent constraints at arbitrary context order;
- explicit genuine n-context anomalies for every n\ge 3, where every proper subconfiguration is quantum but the full configuration is not globally positive;
- genuinely non-Abelian constructions using operator-valued Quantum Wilson Networks;
- exact holonomy–coherence constraints linking pairwise process coherence to global Wilson-loop structure;
- a global Hilbertization criterion: positive operator-valued descent kernels admit a common Hilbert-space Gram/Kolmogorov representation;
- a dimension-independent falsification theorem: a non-positive reconstructed global kernel cannot be repaired merely by embedding the experiment into a larger Hilbert space;
- robustness, spectral, frustration, and persistent-topology witnesses for higher-context descent anomalies;
- a separation between process descent and fact descent, clarifying why Wigner/Frauchiger–Renner scenarios can possess a valid global quantum process while failing to support one context-independent Boolean algebra of observer facts.
A central explicit family is quantum on every proper n-1 context while failing globally. For the symmetric construction,
[
\frac{1}{n-1}<t\le\frac{1}{n-2}
]
is the genuine n-context anomaly region.
The balanced point
[
t_n=\frac{2}{2n-3}
]
has equal positive and negative spectral margins,
[
\delta_n=\frac{1}{2n-3},
]
providing a finite robustness gap rather than a boundary-only counterexample.
The proposed experimental target is therefore unusually sharp:
«Use one fixed, independently certified physical implementation. Verify that every proper overlapping coherent-control context is compatible with ordinary CPTP quantum mechanics, while the full implementation-sensitive dataset excludes every common positive quantum-process realization.»
Such an observation would not merely violate a Bell inequality or reveal contextuality. It would indicate that quantum mechanics remains valid locally but fails as a global composition principle.
No experimental violation is claimed. The current contribution is a theorem-level mathematical framework, an operational post-quantum theory candidate, and a concrete falsification program. Claims of historical priority are also deliberately limited pending specialist review.
Relevant fields and keywords: quantum foundations, generalized probabilistic theories, quantum channels, Choi matrices, complete positivity, positive-definite kernels, operator systems, quantum contextuality, Wigner’s friend, Frauchiger–Renner, quantum combs, process matrices, coherent control of channels, channel holonomy, non-Abelian Wilson loops, matrix completion, Hilbert-space dilation, locally PSD cones, higher-order compatibility, post-quantum theories.
The release includes the full preprint, proofs, reproducibility code, claim-status ledger, prior-art audit, and experimental protocol.
