Infinity One Zero Lift: The Normal Form of Projective Memory

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.

This record publishes the completed working edition 0.1 dated 11 November 2026: the 15-page paper and its original source-and-verification archive. The manuscript gives written proofs; the archive contains 73 passing exact geometry checks, 31 passing supplementary manuscript checks, editable LaTeX and Markdown, cover and incidence assets, 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 manuscript and archive are published byte-for-byte, with their source custody and verification receipts preserved. Author: Anthony Vito Coppa, Coppalini Architecture.