The Non-Injective Foundations Sub-Programme

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-16
DOI
https://doi.org/10.5281/zenodo.22802606
Primary Topic
Advanced Operator Algebra Research
Type
article
Field-Weighted Citation Impact
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article

The Non-Injective Foundations Sub-Programme

Jérôme Beau
Zenodo (CERN European Organization for Nuclear Research)
Advanced Operator Algebra Research
article

The Non-Injective Foundations Sub-Programme

Jérôme Beau
article en

Abstract

This note presents the non-injective foundations sub-programme and types the status of its carrier-selection claim. The ENI no-go theorem establishes non-injectivity as a structural necessity of genuine emergence, while other constituent results address dimensional rigidity under explicit assumptions and temporal ordering conditionally on an unestablished acyclicity hypothesis. By contrast, the inference from admissibility axioms to ${\mathrm{Heis}}_3(\mathbb{Z}/q\mathbb{Z})$ and its representation data is not a theorem. A finite $S_3$ countermodel satisfies the algebraic properties available before the centrality step but has a non-central commutator. Once the group and a non-trivial central character are supplied, Stone–von Neumann identifies the Heisenberg/Schr\"odinger representation; the associated Weil action remains distinct further symplectic data. Downstream results that consume these inputs are conditional on those choices. Conceptually, non-injectivity remains the programme's primitive; the selection of its physical carrier remains open.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 5%
Advanced Operator Algebra Research
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