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Bellman--Shoreline Search in Arbitrary Dimension: Exponential Vector Oscillators, Active Memory, Precession, and Effective Computability — arXiv:2608.29060

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29060
License (as archived): CC0-1.0
Archived: 2026-10-17T09:07:10.197Z
SHA-256 of the archived text: f56f9059911a83667cb33bf2ae31c9c7a4c02701a5a20731b13007c0489df702
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How to cite

Bellman--Shoreline Search in Arbitrary Dimension: Exponential Vector Oscillators, Active Memory, Precession, and Effective Computability — arXiv:2608.29060 — arXiv (en), https://arxiv.org/abs/2608.29060 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5491689eeff2 (Metraipolis archive dc_5491689eeff2, sha256 f56f9059911a83667cb33bf2ae31c9c7a4c02701a5a20731b13007c0489df702)

BibTeX

@misc{dc5491689eeff2,
  title = {Bellman--Shoreline Search in Arbitrary Dimension: Exponential Vector Oscillators, Active Memory, Precession, and Effective Computability — arXiv:2608.29060},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29060},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5491689eeff2; sha256 f56f9059911a83667cb33bf2ae31c9c7a4c02701a5a20731b13007c0489df702},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29060. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study online search for an unknown affine hyperplane in $\mathbb{R}^D$, for arbitrary fixed finite dimension. Building on a companion self-similar cell reduction and support-function formulation, we ask how the mechanism changes as the normal space grows from $\mathbb{S}^0$ to $\mathbb{S}^{D-1}$. In $D=1$, alternation and productivity yield an equal-ripple principle and the exact stationary constant $9$. In $D=2$, the analogous relative equilibrium is a logarithmic spiral whose bottleneck chord imposes tangency and selects the pitch. For exponential orbits $\Gamma(\sigma)=e^{\kappa\sigma}\omega(\sigma)$, we develop log-directional geometry, exponentially discounted memory, gauges, and recursive hyperspherical parametrizations. Without a shape ansatz, the bottleneck admits a certificate supported by at most $D$ historical suppliers, and at globally worst phases the current point lies on the active face. Within regular chambers we derive exact variation, tangency, pitch, age, and, in $D=3$, delay-system identities. Odd-dimensional obstructions, antipodal subclasses, and harmonic towers provide constraints and explicit candidate families but are not claimed globally optimal. Finally, the N-COMP theorem shows that $C_D^*$ is a computable real for every fixed finite $D$ and that algebraic polygonal $\varepsilon$-optimal cells can in principle be synthesized. Numerical screening through $D=10$ is kept separate from the proved results.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.OC).
Categorie arXiv: Computational Geometry (cs.CG) ; Metric Geometry (math.MG); Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.29060 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:40:19.785Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).