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2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.19446535 |
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| _version_ | 1866902198315646976 |
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| author | Lietz, Justin |
| author_facet | Lietz, Justin |
| contents | <p>The purpose of the present document is exact and unified: (i) to close the operator-core of a lifted-state calculus for finite evolution of the primitive roll; (ii) to prove that the core Phase Calculus objects are strict repackagings of already-earned VDM structures rather than new speculative burdens; and (iii) to place the completion, residual, and launched-family shadow data inside the same publication as a downstream branch of the operator-core rather than as a separate paper. The document closes the lifted state space, the visible witness map, the quarterroll, balanced-refinement, and host-lift operators, the operator-relative observable derivatives, the operator-accumulation law, the coordinate projectors, the exact finite word-evolution law, visible quarter closure, the balanced Fibonacci branch law, the balanced-germ determinacy law, the reduced true-return criterion on the balanced family, the first commutation identities, the connection-closure theorems linking Phase Calculus to the primitive-roll and lifted-object canon, and the canonical attachment of the shadow/completion branch on the launched family. The document does not close a global selector law, a complete mixed-word normal form, or a regime-complete self-return theorem beyond the already reduced balanced-family burden. The central claim is therefore not that a rhetorical “new calculus” has been named, but that finite lifted-state evolution of the primitive roll already admits an exact operator calculus capable of serving as a common formal language across discrete and continuous descendants while preserving the exact state burden of the lifted object.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19446535 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Phase Calculus - Lifted-State Operator Calculus of the Primitive Roll with Connection Closure and Shadow/Completion Branch Lietz, Justin <p>The purpose of the present document is exact and unified: (i) to close the operator-core of a lifted-state calculus for finite evolution of the primitive roll; (ii) to prove that the core Phase Calculus objects are strict repackagings of already-earned VDM structures rather than new speculative burdens; and (iii) to place the completion, residual, and launched-family shadow data inside the same publication as a downstream branch of the operator-core rather than as a separate paper. The document closes the lifted state space, the visible witness map, the quarterroll, balanced-refinement, and host-lift operators, the operator-relative observable derivatives, the operator-accumulation law, the coordinate projectors, the exact finite word-evolution law, visible quarter closure, the balanced Fibonacci branch law, the balanced-germ determinacy law, the reduced true-return criterion on the balanced family, the first commutation identities, the connection-closure theorems linking Phase Calculus to the primitive-roll and lifted-object canon, and the canonical attachment of the shadow/completion branch on the launched family. The document does not close a global selector law, a complete mixed-word normal form, or a regime-complete self-return theorem beyond the already reduced balanced-family burden. The central claim is therefore not that a rhetorical “new calculus” has been named, but that finite lifted-state evolution of the primitive roll already admits an exact operator calculus capable of serving as a common formal language across discrete and continuous descendants while preserving the exact state burden of the lifted object.</p> |
| title | Phase Calculus - Lifted-State Operator Calculus of the Primitive Roll with Connection Closure and Shadow/Completion Branch |
| url | https://doi.org/10.5281/zenodo.19446535 |