Additivity Symmetry III: The Activation Theorem
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866902042443776000 |
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| author | Treppiedi, Attilio |
| author_facet | Treppiedi, Attilio |
| contents | <p></p> <div> <div> <div>Translator</div> <div> </div> <div> </div> </div> <div> <div> </div> <div> </div> </div> </div> <p> </p> <p>This paper develops the third part of the <em>Additivity Symmetry</em> program. Additivity Symmetry is the principle that physical descriptions remain stable under additive composition (“gluing”) of independent experimental blocks. In earlier work (<em>Additivity Symmetry I: Conceptual Framework and The Additivity Algebra</em>; <em>Additivity Symmetry II: Closure Regimes</em>), this principle was shown to generate the familiar regimes of physics (quantum, statistical, discrete) and was reformulated as closure under all additive automorphisms, revealing a universal set of admissibility requirements.</p> <p>In this work, we prove the <strong>Activation Theorem</strong>: closure under all additive automorphisms is equivalent to the activation of three structural constraints—boundary/fall-off (B), Euler–Lagrange admissibility (E), and gauge/regularity (G). A fourth principle, finiteness, is not required for the equivalence but is conjectured to hold operationally as a sieve at finite detector resolution. This sieve upgrades heuristic parallels (to operator algebras, representation theory, TQFT) into exact mathematical correspondences.</p> <p>The paper also develops the operational role of probes, which act as projectors that enforce but do not generate constraints, and analyzes implications across quantum, statistical, and discrete regimes. It suggests that finite-resolution effects could yield controlled deviations from textbook predictions at the resolution limits of experiments, opening the way for new empirical tests.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17215020 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Additivity Symmetry III: The Activation Theorem Treppiedi, Attilio Additivity Symmetry Activation Theorem closure structural constraint euler-lagrange admissability boundary conditions gauge regularity sieve conjecture finite resolution probes quantum regimes stastical mechanics discrete regimes representation theory operator algebras topological quantum field theory (TQFT) <p></p> <div> <div> <div>Translator</div> <div> </div> <div> </div> </div> <div> <div> </div> <div> </div> </div> </div> <p> </p> <p>This paper develops the third part of the <em>Additivity Symmetry</em> program. Additivity Symmetry is the principle that physical descriptions remain stable under additive composition (“gluing”) of independent experimental blocks. In earlier work (<em>Additivity Symmetry I: Conceptual Framework and The Additivity Algebra</em>; <em>Additivity Symmetry II: Closure Regimes</em>), this principle was shown to generate the familiar regimes of physics (quantum, statistical, discrete) and was reformulated as closure under all additive automorphisms, revealing a universal set of admissibility requirements.</p> <p>In this work, we prove the <strong>Activation Theorem</strong>: closure under all additive automorphisms is equivalent to the activation of three structural constraints—boundary/fall-off (B), Euler–Lagrange admissibility (E), and gauge/regularity (G). A fourth principle, finiteness, is not required for the equivalence but is conjectured to hold operationally as a sieve at finite detector resolution. This sieve upgrades heuristic parallels (to operator algebras, representation theory, TQFT) into exact mathematical correspondences.</p> <p>The paper also develops the operational role of probes, which act as projectors that enforce but do not generate constraints, and analyzes implications across quantum, statistical, and discrete regimes. It suggests that finite-resolution effects could yield controlled deviations from textbook predictions at the resolution limits of experiments, opening the way for new empirical tests.</p> |
| title | Additivity Symmetry III: The Activation Theorem |
| topic | Additivity Symmetry Activation Theorem closure structural constraint euler-lagrange admissability boundary conditions gauge regularity sieve conjecture finite resolution probes quantum regimes stastical mechanics discrete regimes representation theory operator algebras topological quantum field theory (TQFT) |
| url | https://doi.org/10.5281/zenodo.17215020 |