Infinity One Zero Lift: The Normal Form of Projective Memory
Description
Infinity One Zero Lift: The Normal Form of Projective Memory constructs an explicit normal form in which a displayed form returns while its occurrence address advances. The projective involution M = [[1, 0], [1, −1]] exchanges infinity and one and fixes zero and two. Its complex central lift U = iM satisfies U² = −I and U⁴ = I. Explicit real and complex changes of coordinates connect the mirror and its four-phase lift to the established root algebra, and the four-state axial escapement advances the cycle count.
Two consecutive cycles provide eight distinct occurrence addresses and their complete comparison graph: 28 = 6 + 16 + 6 = 7 × 4, partitioned into seven four-edge matchings. For a fixed unit reference m, the state-and-occurrence normal form is (p, c, a, D), with n = 4c + p, a = mᵀr, and D = mrᵀ − rmᵀ. On its stated image, the inverse is (p, c, a, D) ↦ (4c + p, am + Dᵀm). The displayed phase, advancing occurrence, agreement, and signed comparison record remain separately recoverable.
Version 0.2 is a citation edition of the completed working edition dated 11 November 2026. It adds version-specific DOI references for Linear Infinity (10.5281/zenodo.24150517), Mirror Escapement Time Lift (10.5281/zenodo.24150565), Occurrence and the Twenty-Eight-Seam Reader (10.5281/zenodo.24150567), and Mirror Recognition (10.5281/zenodo.24150572). The mathematical statements and proofs retain their established content. The package includes the updated PDF, editable LaTeX and Markdown, original cover and incidence assets, and an edition-change receipt.
The retained verification materials record 73 passing exact geometry checks, 31 passing supplementary manuscript checks, and a source-fixed Lean 4.33.0 subcertificate. The Lean receipt applies to the encoded integer and Gaussian-integer projective-return statements. The analytic and full K₈ constructions carry their manuscript proofs and executable-audit evidence.
The read/state/occurrence distinction is cited in the NOP Return / Memory Workbench v0.2.0 formal note, DOI 10.5281/zenodo.24148946. The original version 0.1 remains available in this record’s version history. Author: Anthony Vito Coppa, Coppalini Architecture.