An open-source framework defines six operations (P1–P6) and shows they can produce directed activity, self-repair, hazard response, stable internal representations, and context-dependent decoding — on both a particle system and a neural system.
If you work with complex systems, agent-based models, or anything where higher-level structure needs to appear from lower-level rules, you've run into the vocabulary problem: there's no widely shared set of operations for describing how you get from simple dynamics to organized behavior.
A framework called Six Birds proposes one: a minimal set of six operations (P1–P6) that, when applied to a substrate, can produce life-like behavior. A companion preprint, To Wake a Stone with Six Birds, demonstrates this on two open-source substrates you can clone and run.
This article walks through the six operations, what they produce, and how the verification workflow is structured.
What the System Produces
These are reported results from two working substrates (particle and neural), with a machine-readable claim ledger mapping each result to specific artifacts in the repos.
Directed activity from an inert baseline. Both substrates start from a calibrated null — dynamics running, directionality metrics at zero. Toggling the drive channel (P6) produces a robust separation in directionality metrics while the null stays flat.
Self-maintenance and repair. Under drive, the particle substrate achieves zero error on code maintenance tasks while the null configuration shows ~0.43 error. Gated experiments show particle movement is causally required for recovery. Deadline selection experiments show the system trading off internal clock costs against uptime.
Hazard response. In the neural substrate, paired experiments show spike response, token budget reallocation toward affected regions, and recovery — compared against matched baselines.
Stable internal vocabularies. At refined observational lenses, the neural substrate develops stable motif inventories — small discrete token sets with full coverage that shift between normal and hazard contexts. Transition statistics between motifs also shift, indicating structure at the grammar level, not just the vocabulary level.
Context-dependent decoding. Using controlled interventions, the neural substrate's motif summaries support reliable readout of external conditions — directional focus, dictionary structure, phrase alignment, and token-level decoding accuracy reaching 1.000 across seeds, validated against shift-null controls. Earlier attempts (Phases 14–16) failed their controls and are documented as negative results, so the later success depends on a specific intervention protocol.
These competencies arise in single-system regimes without replication, heritable variation, or Darwinian selection.
The Six Primitives (P1–P6)
The framework paper argues these six operations form a canonical vocabulary under minimal assumptions (composable processes, bounded observational access). The life paper uses them as toggleable knobs.
P1 — Operator rewrite. Rewriting the system's update rules — not parameter tuning, but replacing one operator with another. Particle substrate: writable bond arrays. Neural substrate: local token exchange kernels.
P2 — Gating / constraints. Restricting feasible transitions. Enforcing hard budget caps, removing edges from the transition graph. Particle substrate: apparatus counters. Neural substrate: conserved token budgets.
P3 — Protocol holonomy. Internalizing the update schedule as part of system state, so order-of-operations effects become a dynamical feature rather than an external clock.
P4 — Sectors / invariants. Conserved labels and block structure — regions that evolution preserves.
P5 — Packaging. An idempotent completion rule whose fixed points become stable higher-level objects. The operation that turns noisy low-level state into discrete, reusable tokens at the next descriptive level.
P6 — Accounting / audit. The drive/audit channel — a resource input that powers directed activity and whose presence or absence can be verified against a null baseline.
These are the primitive closure-changing operators P1–P6 introduced in Six Birds: Foundations of Emergence Calculus (arXiv:2602.00134).
How It Works: Null → Drive → Refinement
The empirical workflow follows three steps:
Null. Run the system with P3 and P6 off. Verify all directional metrics read ~0 while dynamics stay active. This is your calibrated baseline.
Drive. Switch on P6 only. Verify directionality metrics separate cleanly from null under matched controls. If they don't, no further claims are made.
Refinement. With null and drive clean, test higher-level structure. Each test has explicit pass/fail gates and shift-null controls — the intervention labels are temporally scrambled to check whether results survive when alignment is broken.
This loop runs identically on both substrates.
The Protocol Trap: Why P3 Deserves Attention
One practical finding for anyone building multi-kernel simulations: if your system uses a deterministic update schedule and you observe apparent arrows of time, the schedule itself can be the source.
The paper tests this in the neural substrate. Toggling P3 (the protocol schedule) changes coarse measurements by 10–28% under matched controls — a substantial effect coming from update ordering alone. The paper treats this as a diagnostic: real and worth measuring, but not sufficient to establish genuine directionality on its own.
If you work with agent update loops, multi-kernel simulations, or RL environments with structured step sequences, this is a quantified example of how observation schedules can influence results. The framework's approach: model the protocol as part of your state, and attribute directionality only when an independent channel (P6) separates from null.
Two Substrates, Same Operations
The particle substrate uses discrete slow variables on a 2D torus, field-like packaging, and coarse current-affinity audit proxies. The neural substrate uses layered lattices, budgeted token exchanges between layers, and stroboscopic diagnostics.
Different state spaces and dynamics, same six operations, same pattern of results: null calibration → drive separability → maintenance under perturbation → stable higher-level structure at refined lenses.
Scope and Limitations
The paper defines its boundaries:
- "Life-like" means a bounded set of operational competencies, not a general definition of biological life.
- No reproduction, heredity, or Darwinian evolution is modeled. The competencies arise in single-system regimes.
- No autonomous open-ended evolution is claimed — new descriptive predicates are demonstrated, but not indefinite novelty generation under a fixed regime.
- Audit quantities are proxies, not exact thermodynamic quantities, interpreted through null calibration and controlled separability.
- The packaging operator's idempotence defect isn't measured.
- The paper specifies what would strengthen future work: exact path-space KL computation, measured idempotence defects, and formal definability separation proofs.
Running It
A hosted build runs the particle substrate without local setup. Both repos are public:
- Particle substrate
- Neural substrate
Every claim in the paper is indexed in assets/claims.yml — a machine-readable ledger mapping claim IDs to specific external artifacts.
Why Developers Should Care
The Six Birds primitives offer a concrete operator vocabulary for engineering higher-level behavior from lower-level substrates. If you build adaptive systems or self-organizing architectures, you can map your system onto P1–P6 and ask specific questions: which operations are active? What does the null look like? Can I separate drive from baseline? Do my higher-level representations survive controls?
That's a useful set of questions regardless of where the framework goes from here.
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