Paper 2 — Algebraic Foundations

The keystone paper in the series: the algebraic calculus that the other papers refine, mechanize, and extend.

Status

Draft manuscript. See manuscript.md for the full text.

Abstract

This paper isolates the fixed-topology algebraic kernel of Cortex durable execution: node-local fact accumulation, failure closure, deterministic classification, and structural recovery safety after partial persistence. It also marks the extension boundary where those results stop carrying over and a different machine is required.

Figures

• Figures/index.md — figure inventory and export status.
• Publication-exported figures are not checked in yet.

Related

• manuscript.md — full manuscript.
• ../Paper-1-staged-reduction/ — staged reduction refining this calculus.
• ../../Roadmap/Plans/lean-mechanization.md — supporting research plan for mechanized proofs.
• ../../Roadmap/Plans/rewrite-materialization-and-recovery.md — runtime rewrite plan building on this extension boundary.
• ../Paper-3-graph-substitution-semantics/ — substitution extension of this.
• ../../Architecture/03-formalism-stack.md — architecture chapter citing this paper.