Local Algebraic Blindness to Global Lift Obstructions in Descended Linear Models | Zenodo
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Published July 26, 2026
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Local Algebraic Blindness to Global Lift Obstructions in Descended Linear Models
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Grover-Bennett, Katie
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A companion construction gives spacetimes carrying smooth fields that lift through a noninjective étale presentation over every chronological past but admit no global lift. This paper asks what quantum field theory on such backgrounds can detect of that obstruction.
We distinguish three inequivalent models: a hard-constrained lift field, whose configuration space is discrete and has no linear fluctuation theory; an unconstrained F-valued model, which excludes nonliftable backgrounds; and a descended linear probe defined on every target-valued structured background. For the descended probe we prove a blindness theorem: its observable net depends only on the target-valued data, is independent of every local lift, and defines a locally covariant quantum field theory.
On structurally isomorphic past regions, Hadamard preparations are transported exactly and reproduce all expectation values. Extending such a transported preparation to a global quasifree Hadamard state of the rival world remains an open problem; failure would provide a mechanism by which quantization reduces classical observational underdetermination.
We also construct the branch-aware object associated with a fixed background: the étale fiber-pair groupoid of its pullback space and the corresponding Cartan pair. Global lifts correspond exactly to rank-one diagonal multiplier projections. The groupoid together with its diagonal retains liftability, whereas the reduced C*-algebra alone is Morita equivalent to C₀(M), so no stable invariant of the bare algebra detects it. Its matrix units reproduce the Brandt multiplication table but do not encode continuation history, which remains at the path level in the companion theory.
Preprint, version 0.7. Independent expert verification remains outstanding. Results depending on the multiplet local-quasi-equivalence hypothesis are explicitly marked as conditional.
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10.5281/zenodo.21607051
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Resource type<br>Preprint
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Copyright © 2026 Katie Grover-Bennett. All rights reserved.
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Created
July 26, 2026
Modified
July 26, 2026
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