Admissibility-Cost Response Principle
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901829572362240 |
|---|---|
| author | Holdway, Craig Edwin |
| author_facet | Holdway, Craig Edwin |
| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This record presents TA25 (Admissibility-Cost Response Principle), part of the Q5 Transport Architecture Series developed under the Zero-Point Hypothesis framework.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">TA24 established that accumulated depth-mode leakage generates a residual load that deforms the shared Y-admissible gate projector, inducing an admissibility gradient across the transport architecture. TA25 identifies how subsequent attachment modes respond to that deformation. The response is governed by a variational principle: stable attachment modes minimize their admissibility cost under the deformed projector.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The admissibility cost functional is defined as the squared norm of the non-admitted component of a candidate mode under the residual-deformed projector. A mode with low cost aligns well with the deformed gate and generates little leakage into the complement sector. A mode with a high cost fails to align and leaks strongly. Stable attachment modes are local minimizers, or approximate minimizers, of this cost functional.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Where the accumulated residual load varies across the transport architecture, the deformed projector varies with it, and the cost functional is non-uniform. The variation of the cost functional creates a directional bias: subsequent attachment modes are biased toward regions of lower admissibility cost. The key conceptual distinction is that attachment modes are not pulled directly toward dense configurations. They shift toward configurations where the cost of maintaining admissible phase attachment is lower. The source of the directional bias is differential admissibility cost, not an attractive force between modes.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This is a selection principle, not a dynamical law. It identifies which configurations are stable, not how a mode evolves toward stability over time. The dynamical version requires the propagation structure developed in TA26 and the full residual circulation theorems of TA33 through TA39.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three corollaries follow. In the zero-load limit, the deformed projector reduces to the unperturbed gate, and the minimization principle recovers the ordinary admissible gate alignment. The admissibility cost landscape is source-generated rather than externally imposed: a denser configuration generates a higher and more strongly varying cost landscape, producing a stronger directional bias on subsequent modes. The third corollary identifies TA26 as the natural continuation, which will characterize how the cost landscape falls off with distance from a dense configuration.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">A candidate mechanism for the dynamic maintenance of the deformed projector is identified in a second remark and developed formally in TA25b: returning coherent phase partially reflects at the quantum-side membrane, projects a handedness signature onto the barrier interface, and recursively maintains the deformed admissibility state. Under this interpretation, the admissibility cost landscape is self-generated by coherent transport history rather than being statically accumulated. The formal derivation is deferred to TA25b.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">No inverse-square law, physical gravity, spacetime curvature, or quantitative force law is derived here. The response principle establishes a directional bias in admissibility cost. The propagation structure of that bias is the subject of TA26.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The theorem chain progressively derives the structure of the effective transport generator \[ G_eff = Pi_Y G Pi_Y + K†BK \], from which observable phase, leakage, decoherence, and residual correction emerge as structural consequences of projected transport closure on Q5.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20319127 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Admissibility-Cost Response Principle Holdway, Craig Edwin Q5 hypercube penteract Gray code Hamiltonian cycle hypercube graph discrete geometry combinatorial topology defect bond holonomy transport operator phase defect linked-pair reduction ordered residue kernel structure fibre reduction Lie algebra representation theory spinor commutator projection operator orientation invariant grading phase transport barrier crossing paired transport continuous limit discrete-to-continuous unitary evolution phase accumulation Born rule interference entanglement decoherence quantum measurement reduced sector observable interferometry quadrature cycling first-harmonic bias falsifiable prediction fringe visibility ZPH independent research preprint <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This record presents TA25 (Admissibility-Cost Response Principle), part of the Q5 Transport Architecture Series developed under the Zero-Point Hypothesis framework.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">TA24 established that accumulated depth-mode leakage generates a residual load that deforms the shared Y-admissible gate projector, inducing an admissibility gradient across the transport architecture. TA25 identifies how subsequent attachment modes respond to that deformation. The response is governed by a variational principle: stable attachment modes minimize their admissibility cost under the deformed projector.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The admissibility cost functional is defined as the squared norm of the non-admitted component of a candidate mode under the residual-deformed projector. A mode with low cost aligns well with the deformed gate and generates little leakage into the complement sector. A mode with a high cost fails to align and leaks strongly. Stable attachment modes are local minimizers, or approximate minimizers, of this cost functional.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Where the accumulated residual load varies across the transport architecture, the deformed projector varies with it, and the cost functional is non-uniform. The variation of the cost functional creates a directional bias: subsequent attachment modes are biased toward regions of lower admissibility cost. The key conceptual distinction is that attachment modes are not pulled directly toward dense configurations. They shift toward configurations where the cost of maintaining admissible phase attachment is lower. The source of the directional bias is differential admissibility cost, not an attractive force between modes.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">This is a selection principle, not a dynamical law. It identifies which configurations are stable, not how a mode evolves toward stability over time. The dynamical version requires the propagation structure developed in TA26 and the full residual circulation theorems of TA33 through TA39.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">Three corollaries follow. In the zero-load limit, the deformed projector reduces to the unperturbed gate, and the minimization principle recovers the ordinary admissible gate alignment. The admissibility cost landscape is source-generated rather than externally imposed: a denser configuration generates a higher and more strongly varying cost landscape, producing a stronger directional bias on subsequent modes. The third corollary identifies TA26 as the natural continuation, which will characterize how the cost landscape falls off with distance from a dense configuration.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">A candidate mechanism for the dynamic maintenance of the deformed projector is identified in a second remark and developed formally in TA25b: returning coherent phase partially reflects at the quantum-side membrane, projects a handedness signature onto the barrier interface, and recursively maintains the deformed admissibility state. Under this interpretation, the admissibility cost landscape is self-generated by coherent transport history rather than being statically accumulated. The formal derivation is deferred to TA25b.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">No inverse-square law, physical gravity, spacetime curvature, or quantitative force law is derived here. The response principle establishes a directional bias in admissibility cost. The propagation structure of that bias is the subject of TA26.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The theorem chain progressively derives the structure of the effective transport generator \[ G_eff = Pi_Y G Pi_Y + K†BK \], from which observable phase, leakage, decoherence, and residual correction emerge as structural consequences of projected transport closure on Q5.</p> |
| title | Admissibility-Cost Response Principle |
| topic | Q5 hypercube penteract Gray code Hamiltonian cycle hypercube graph discrete geometry combinatorial topology defect bond holonomy transport operator phase defect linked-pair reduction ordered residue kernel structure fibre reduction Lie algebra representation theory spinor commutator projection operator orientation invariant grading phase transport barrier crossing paired transport continuous limit discrete-to-continuous unitary evolution phase accumulation Born rule interference entanglement decoherence quantum measurement reduced sector observable interferometry quadrature cycling first-harmonic bias falsifiable prediction fringe visibility ZPH independent research preprint |
| url | https://doi.org/10.5281/zenodo.20319127 |