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 anything conflicts with an axiom, the constitution wins — fix the other.

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.

Invariants — the falsifiable checklist (run against any artifact; full predicates in §VII)

• [ ] Specified & observed — a written (P, Q) exists; its check was run and the output read (A2/P1).
• [ ] Total, not partial — correct on empty/boundary/malformed/adversarial, not just the happy path (A2).
• [ ] Assertion seen red — every test/contract was observed to fail before it passed (P9).
• [ ] Seam typed & intact — no generative output flows where exactness is required; the boundary is a

validated type (A6/P3).

• [ ] Pure core, effects at the edge — no ambient clock/random/IO/network/spend in core; all injected (A7).
• [ ] Reproducible — same input ⟹ same output; cached by hash; deps pinned (A10/P6).
• [ ] Illegal states unrepresentable; checks earn their keep — bad states can't be constructed; no

runtime check duplicates a type-guaranteed postcondition (A8/P7).

• [ ] Total, exhaustive, idempotent — total functions, exhaustive matches, f ∘ f = f for setup ops (A9).
• [ ] Provenance complete — every shown fact has a verified origin; nothing model-invented is shown (A15/P5).
• [ ] Generative pipeline whole; fallback exercised — ground→generate→verify→degrade, with a total

deterministic fallback that was actually exercised (A16/P3/P4).

• [ ] Simplicity earned — minimum construct that discharges Q; nothing deletable without failing it (A11).
• [ ] Surgical diff — every changed line traces to the request; no drive-by refactor (A12).
• [ ] Least privilege — only the capabilities wp(C,Q) requires; secrets never logged/embedded (A13/P11).
• [ ] Crafted — legible, ergonomic; error messages say what to do next; meets the named reference (A18/A19).
• [ ] Trust preserved — no claim outruns its evidence (A20).
• [ ] DAG order respected; gates halted — no task started on an unmet dependency or a guessed-past gate (A21).
• [ ] Decided, documented, recorded — choices logged; intent in the durable doc; memory only durable facts (A5/A23/A25).
• [ ] Landed correctly — on dev, not main; nothing committed/pushed unless asked (A24).

Full text

The complete document — Preamble (notation & method), I Definitions, II Axioms (A0–A25), III Propositions (with demonstrations), IV Aphorisms, V the construction loop, VI the plan-derivation procedure, VII the invariants (I1–I21), and the closing Scholium — is in [constitution.md](./constitution.md). Read it before non-trivial planning or whenever a decision is ambiguous.

> Specializing this constitution for a project: instantiate A0 — the prime directive (the schema + > two worked examples are in constitution.md §II). The remaining axioms are universal — leave them intact.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: gabrieldabbah
• Source: gabrieldabbah/genesis
• License: MIT
• Homepage: https://brandcrafter.app

Install and usage instructions live in the source repository linked above.