axiomatic-induction

Axiomatic Induction — the constitution & the method (apply in planning & execution)

This skill is the supreme law of the repo and the thinking discipline every agent adopts before non-trivial work. Reason like a proof system, not an improviser. When in doubt, return to the full text, re-derive from A0, and the next correct task becomes a theorem of the axioms plus the current state. If a lower document conflicts with an axiom, the constitution wins — fix the other. A direct operator request is not a lower document: flag the conflicting axiom once, then the operator's decision governs — recorded, never silently absorbed.

When to apply (always, for substantive work)

• Before planning: anchor on A0 (the project's prime directive); derive each task from an axiom — if none licenses it, you are speculating, stop (A1). Order tasks as a topological sort of the dependency DAG; place scope-bifurcating forks early (A21, A22).
• While executing: keep the deterministic and generative components separate across a typed seam (A6); effects at the boundary, a pure/total core (A7); every shown fact carries provenance (A15); generative paths ground → generate → verify → degrade to a deterministic fallback (A16); make illegal states unrepresentable (A8); keep the diff surgical (A12).
• Before "done": run the §VII invariants; done is total correctness [P] C [Q] observed, not the happy path hoped (A2). Any unchecked box ⟹ not done.

The induction loop (one screen)

1. Hold the axioms fixed. 2. State the task as a proposition — a triple {P} C {Q} or a rule p ⊢ r.
2. Find the governing axiom(s); if none, stop. 4. Build the demonstration: a finite chain of steps each licensed by a prior definition/axiom/proposition — your chain-of-thought is this chain. 5. Mark every probabilistic step a conjecture and attach its falsifier. 6. Order steps by dependency; execute in topological order. 7. Discharge the obligation — write the witness, run the real check, read the real output — then record only what is durable.