To Wake a Stone with Six Birds: A Life is A Theory

Simulations of life-like organization are easy to over-read: an apparent arrow of time can come from a hidden schedule, a statistic that cannot be negative, or a bookkeeping error, and an apparent “code” can be a decoder scoring a periodic label pattern. This paper asks what survives when such claims are held to explicit controls. Using the emergence calculus of “Six Birds: Foundations of Emergence Calculus,” it specifies theory packages (a microstate space, a lens, its definable predicates, a completion rule, and an audit) for two synthetic substrates: a particle system with writable bonds, counters and a packaging field, and a layered lattice with budgeted operator tokens. Every reported number is indexed in a machine-readable claim ledger. Main results Null calibration. With protocol (P3) and drive (P6) switched off, the audit proxies sit near zero in both substrates. Drive separability. Switching on a nonconservative drive separates the proxies sharply. In a particle run where only the drive toggle changes, three context-loop statistics move from magnitudes below 0.007 to between 0.35 and 0.87 in every seed. Protocols are clocks. A deterministic protocol schedule reduces stroboscopic current magnitudes by 10–28% relative to matched controls. The paper states the exact conditions under which a protocol cannot create an arrow of time, and shows with a three-phase clock that outside them the protocol is itself irreversible while a coarse lens can hide its arrow completely. Protocol effects are therefore reported as diagnostics of route dependence. Maintenance and controlled readout. The substrates repair imposed corruption and meet imposed deadlines at a recorded ledger cost. In the lattice, injected labels are read back from held-out windows by a frozen decoder: with labels assigned by randomization, accuracy is perfect in all three seeds (exact p = 1/C(24,12) ≈ 3.7×10−7 each) while sham controls are not significant. Statistical design and verification. The paper shows why circular-shift tests could not certify decoding under the eight-window periodic label schedules of the original pipeline, and checks this and the other finite counterexamples it uses with axiom-free Lean proofs. The verification script reconstructs retained decoding predictions and exact p-values, recomputes M6 values from integer counts, and verifies retained source hashes; ledger rates and the neural drive calibration remain recorded outputs and receipts. Scope The paper makes no claim of biological life, autonomous open-ended evolution, exact path-space entropy production, measured closure, or strict definability separation. “Life-like” refers to operational, lens-relative competencies under explicit protocols, controls, and audits. Version 3 Version 3 follows a mathematics and implementation audit of the paper and both simulators. It restates the protocol-trap result with its full premises, corrects the audit-proxy definitions, replaces a particle null comparison affected by an instrumentation defect with a remeasured toggle-only comparison, recalibrates the neural drive contract, withdraws the earlier significance values for the semantic phases in favor of effect sizes and a new randomized-assignment decoding experiment, adds machine-checked Lean witnesses, and rewrites the text and figures for readability. The appendix records the full version history. Code and data Paper, claim ledger, retained evidence, Lean project and replay script: github.com/ioannist/six-birds-life. Particle substrate: github.com/ioannist/six-birds-particle. Neural substrate: github.com/ioannist/six-birds-neural.