The Tier-1 Shadow Compiler Theorem
Down-compiling canonical completion outputs into statused Tier-1 artifacts
Authority role
Establishes down-compilation discipline: a canonical completion output becomes a public Tier-1 artifact only through a total, deterministic, gate-cleared, residue-aware down-compiler.
Summary
A canonical completion object is not itself a Tier-1 artifact. This paper defines the down-compile operator, proves total compiler emission over an eight-member public output codomain (including declared failure and residue outputs), and establishes conditional gate-soundness and success-class soundness theorems, preserving the stack's anti-overclaim boundaries throughout.
Notes
Reading notes
The governing principle: a canonical completion object is not itself a Tier-1 artifact. It becomes one only through the down-compile operator
which is total, deterministic, route-legal, gate-cleared, residue-aware, and status-certified. The public codomain has eight members: a full public Tier-1 equation set, a candidate artifact, a branch artifact set, an effective equation set, a residue card, a no-carrier stop, a no-handoff output, and a compiler failure card — the eighth closes the operator over blocked, malformed, and contradictory states.
Three conditional soundness theorems: total compiler emission (relative to a certified output-selection object), gate soundness (conditional on a certified claim-class gate matrix), and success-class soundness (conditional on status-claim compatibility).
Cite this paper
Rodgers, Jeremy. (2026). The Tier-1 Shadow Compiler Theorem (v3). https://doi.org/10.5281/zenodo.21184944