Peirce Correspondence

Charles Sanders Peirce's triadic semiotics (Object → Sign → Interpretant) maps structurally onto the GCD kernel pipeline. But GCD completes what Peirce left open: the seam provides a stopping condition for unlimited semiosis. The return axiom determines when interpretation terminates.

Structural Mapping

The Missing Piece

Peirce's Problem

Peirce recognized that signs generate interpretants which become signs for further interpretants — an unbounded chain he called unlimited semiosis. He never solved the termination problem: when does interpretation stop? Without a stopping condition, meaning remains indefinitely deferred.

Axiom-0's Completion

"Only what returns is real." The seam (τ_R, tol_seam) provides the missing termination condition. When the seam budget reconciles (|residual| ≤ 0.005), interpretation has returned — the sign chain closes. When it doesn't (τ_R = ∞_rec), interpretation remains a gestus: an emission without receipt.

Semeiosis terminatur cum sutura clauditur. — Semiosis terminates when the seam closes.

Semiotic Kernel — Key Findings

The 8-channel semiotic kernel profiles 30 sign systems. Each maps to: referential precision, syntactic complexity, ground stability, interpretant depth, compositional productivity, modality richness, temporal stability, context sensitivity.

Triadic Structure

Object

x(t) — raw data

Sign

Ψ(t) — trace

Interpretant

(F,ω,S,C,κ,IC)

Seam

τ_R, tol

Peirce's triad mediates Object → Sign → Interpretant. GCD adds the seam at center — the return constraint that closes the cycle.