actualization functor

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

The actualization functor maps a selected potential history into its actualized counterpart. Its domain is the subcategory generated by selected transitions together with identities and composites, rather than all possible candidates. It records coherent passage from selected possibility to actuality while leaving the selection itself outside the functor; unselected possibilities are not thereby mapped into actual events.

Explanation

The categorical scaffold distinguishes configurations, admissible transitions and their propensity weights. A transition’s being available is different from its being taken. The functor applies once a history has been selected, preserving the categorical structure of that restricted history rather than pretending every unrealized alternative occurs in the actualized record.

The domain includes the identities and composites required for a subcategory. This matters because a bare collection of chosen arrows need not constitute a category on which a functor can act. The manuscript supplies the restriction explicitly, and the proposal preserves it instead of using actualization as an unspecified map on all potentialities.

The construction does not choose an outcome, determine new forms or resolve the account’s residual genesis problem. The physical quantum setting and the configuration category also remain distinct; a shared notation for weights does not license identifying tensor product with cartesian product. The source’s broader formal-verification caveat continues to qualify its interpretive application.

Scope and attribution

Retain the generated subcategory restriction and the distinction between recording and choosing.

PB — The Possible Book

The restricted selected-history domain makes the functor structurally coherent without supplying selection.

Occurrence locators: 148, 149, 150, 159, 165, 166, 168, 173.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.