When Is a Configuration Physical? Admissibility, Chart Failure, and the Logic of Vacuum Selection

Vacuum selection involves several logically different questions that are often compressed into one. A configuration can exist as a mathematical solution, admit a controlled effective chart, satisfy a chosen set of stability and consistency tests, be reached with nonzero weight under a dynamics or measure, and agree with observations. None of these statements implies all the others. This paper gives an admissibility-first account of the problem while correcting two overly strong inferences. First, failure of one chart or one certificate does not prove that the underlying mathematical configuration does not exist. Global exclusion requires either a chart-independent obstruction or a transition-compatible exhaustion of the allowed atlas. Second, exclusion is not selection. If two configurations remain admissible, the admissibility predicate alone supplies neither a unique outcome nor a probability distribution. Selection additionally requires a declared dynamics, initial law, measure, conditioning rule, optimization principle, or other source of relative weight. We formalize these distinctions with a typed vacuum-selection record that contains the candidate space and equivalence relation, admissibility rows, chart transitions, dynamics or ensemble, initial data, stopping and reset semantics, observation map, conditioning event, and normalization certificate. We also show why disconnected admissible components do not by themselves imply physical inaccessibility: that conclusion depends on whether the selected evolution is continuous, permits jumps or tunneling, or changes charts. The resulting framework preserves the useful core of the admissibility-first proposal. It turns consistency, stability, and controlled-description tests into a provenance-aware filter before statistical or dynamical selection is attempted. Current finite Modal Triplet Theory calculations provide examples of such certificates at explicitly limited tiers. They do not yet define a global vacuum measure, prove exhaustion of all branches, or select one observed universe.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-30
DOI
https://doi.org/10.5281/zenodo.21710258
Primary Topic
Philosophy and History of Science
Type
preprint
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preprint

When Is a Configuration Physical? Admissibility, Chart Failure, and the Logic of Vacuum Selection

Peter Nero
Zenodo (CERN European Organization for Nuclear Research)
Philosophy and History of Science
preprint

When Is a Configuration Physical? Admissibility, Chart Failure, and the Logic of Vacuum Selection

Peter Nero
preprint en

Abstract

Vacuum selection involves several logically different questions that are often compressed into one. A configuration can exist as a mathematical solution, admit a controlled effective chart, satisfy a chosen set of stability and consistency tests, be reached with nonzero weight under a dynamics or measure, and agree with observations. None of these statements implies all the others. This paper gives an admissibility-first account of the problem while correcting two overly strong inferences. First, failure of one chart or one certificate does not prove that the underlying mathematical configuration does not exist. Global exclusion requires either a chart-independent obstruction or a transition-compatible exhaustion of the allowed atlas. Second, exclusion is not selection. If two configurations remain admissible, the admissibility predicate alone supplies neither a unique outcome nor a probability distribution. Selection additionally requires a declared dynamics, initial law, measure, conditioning rule, optimization principle, or other source of relative weight. We formalize these distinctions with a typed vacuum-selection record that contains the candidate space and equivalence relation, admissibility rows, chart transitions, dynamics or ensemble, initial data, stopping and reset semantics, observation map, conditioning event, and normalization certificate. We also show why disconnected admissible components do not by themselves imply physical inaccessibility: that conclusion depends on whether the selected evolution is continuous, permits jumps or tunneling, or changes charts. The resulting framework preserves the useful core of the admissibility-first proposal. It turns consistency, stability, and controlled-description tests into a provenance-aware filter before statistical or dynamical selection is attempted. Current finite Modal Triplet Theory calculations provide examples of such certificates at explicitly limited tiers. They do not yet define a global vacuum measure, prove exhaustion of all branches, or select one observed universe.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Philosophy and History of Science
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