Work

The Geometry of What Maps Forget

Year: 2026

Type: preprint

Abstract: We prove that whenever a comparison map fails to be injective, the resulting residual is not vague leftover structure but a precise geometric object: a kernel decomposed fiberwise, with exact resolution cost, monotone refinement behavior, and functorial invariants. We then show that this residual geometry is universal: every comparison map carries it, and adequacy determines when it is trivial. The theorems are machine-checked in Lean 4 as part of the Reflexive Architecture (Strata) program. Summit 2 focuses on the universal fiber architecture for non-injective comparison and what maps structurally forget.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.20951701

Author: Spivack, Nova

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7166329050

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