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

This record is the promised life-focused instantiation of the emergence calculus introduced in “Six Birds: Foundations of Emergence Calculus.” The purpose of this paper is to show, concretely and reproducibly, how the canonical theory-package view (microstate, lens/observables, definability, completion/packaging rule, and audit) can be instantiated in working substrates, and what life-like phenomena (in an operational, bounded sense) are observed in those instantiations.

What this paper contributes

The paper presents two instantiations and the associated empirical findings:

• Particle-based substrate: a finite microstate with discrete slow variables and field-like packaging, with coarse audit proxies and maintenance/repair behaviors under perturbations and deadlines.

• Neural/meta-layer substrate: a higher-level substrate with budgeted token-mediated coupling, stroboscopic diagnostics, hazard response under matched baselines, and refined-lens predicate families (motif inventories, proto-syntax shifts, and intervention-conditioned decoding statistics with shift-null controls).

A central emphasis is careful separation of roles in the framework: protocol holonomy (P3) is reported as a diagnostic of route dependence in coarse observables, while directionality is attributed only when an audit/drive channel (P6) separates cleanly from a calibrated null.

Scope and limitations

The paper is explicit about what it does and does not establish. In particular:

• reported audit quantities are proxies (not a full path-space KL audit),

• idempotence defects of the completion/packaging operator are not measured,

• “novelty/extension” is used in a lens-relative sense and is not claimed as unbounded open-ended evolution.