The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908490013868032 |
|---|---|
| author | Kilictas, Bugra Alpay, Faruk |
| author_facet | Kilictas, Bugra Alpay, Faruk |
| contents | We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10650 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion Kilictas, Bugra Alpay, Faruk Functional Analysis Logic in Computer Science Dynamical Systems 47H10, 47A10, 47A60, 06B35, 68Q45, 60J10 F.1.1; F.4.3; F.4.1 We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix. |
| title | The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion |
| topic | Functional Analysis Logic in Computer Science Dynamical Systems 47H10, 47A10, 47A60, 06B35, 68Q45, 60J10 F.1.1; F.4.3; F.4.1 |
| url | https://arxiv.org/abs/2508.10650 |