Persistence Without Contradiction: A Minimal Foundation for Existence

This is the minimal formal statement of the Persistence Without Contradiction constraint — the stripped core without extended proofs, paradox resolution sections, or alternative foundation exhaustion.

The argument rests on three primitives and two independent eliminative conditions:

(1) Idempotent closure: a form must return itself under iterated re-application of its defining boundary. Drift and oscillation are excluded.

(2) Energetic viability: the maintenance cost of the form's boundary must remain within available sustaining capacity across all admissible iterations.

Forms violating either condition do not exist as determinate entities. The constraint is eliminative, not probabilistic.

Key results included in this version: Definition of determinate existence (Definition 1.1) · Independence of the two conditions (Theorem 2.3) · Energetic viability grounded via Kolmogorov complexity (Definitions 3.1–3.3) · Unbounded cost eliminates determinacy (Theorem 3.4) · GCC eliminates existence (Theorem 4.1) · The constraint passes self-application by explicit calculation (Theorem 5.1) · Falsification conditions stated (Section 6)

This version accompanies a formally verified Lean 4 proof (bedrock_complete_proof.lean) that compiles with zero errors, zero warnings, and zero messages — machine verification that the core structural argument is formally sound.

For the full paper including exhaustion of alternative foundations, paradox resolution suite, and extended proofs, see:

 DOI 10.5281/zenodo.18345154