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Sequential-Innovation Reducibility and the Innovation Spectrum — arXiv:2608.05443

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.05443
License (as archived): CC0-1.0
Archived: 2026-10-31T10:50:27.712Z
SHA-256 of the archived text: 0bbcae2c51d519041a0060c586d91b507a8d03c95c7ff0829aac7655fb2f252a
Stable URL of this page: https://metraipolis.com/documento/dc_752174185ca2

How to cite

Sequential-Innovation Reducibility and the Innovation Spectrum — arXiv:2608.05443 — arXiv (en), https://arxiv.org/abs/2608.05443 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_752174185ca2 (Metraipolis archive dc_752174185ca2, sha256 0bbcae2c51d519041a0060c586d91b507a8d03c95c7ff0829aac7655fb2f252a)

BibTeX

@misc{dc752174185ca2,
  title = {Sequential-Innovation Reducibility and the Innovation Spectrum — arXiv:2608.05443},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.05443},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_752174185ca2; sha256 0bbcae2c51d519041a0060c586d91b507a8d03c95c7ff0829aac7655fb2f252a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.05443. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Sequential prediction naturally induces an innovation sequence consisting of the prediction errors produced by a causal predictor. We use the collection of all such innovation sequences to define the \emph{innovation spectrum} of an individual binary sequence and, from it, a new reducibility based on sequential information extraction. We show that this reducibility refines truth-table reducibility while exhibiting a fundamentally different geometry. The degree structure decomposes into two canonical regions: a truth-table spine, whose induced order is isomorphic to the truth-table degrees, and a complementary reservoir-immune region, consisting of sequences from which no infinite computable predictable reservoir can be extracted. We establish bridge constructions connecting the two regions, prove that reservoir immunity is preserved under sequential innovation, and show that the Martin--Löf-random degrees form a proper downward-closed substructure inside the reservoir-immune region. These results reveal a new geometric organization of individual sequences based on causal predictability rather than classical oracle computation.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-07 in cs.LO).
Categorie arXiv: Logic (math.LO) ; Information Theory (cs.IT); Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2608.05443 — 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 2026-10-31T10:38:07.103Z dalla pagina https://arxiv.org/catchup/cs.LO/2026-08-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).