Unified probability engine · β₁ self-verification · ambient law kernel

Aeon Clockwork

Laplace's Demon: self-verification that reads the void boundary.

A deterministic verification layer for the Aeon stack. Given a claim and its rejection history, Clockwork decides whether the claim has reached ground state (β₁ = 0, proved) or still carries topological deficit (β₁ > 0, open) — no external oracle, the void does the work.

$ pnpm add @a0n/aeon-clockwork

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kernel god-formula/v1 dimension information license MIT void-boundary sufficient-statistic

Features

Everything you need. Nothing you don't own.

Self-verification without an oracle

The model toggles β₁ between 0 and >0 to verify truth claims. Given a claim and its rejection history, Clockwork reads the void boundary and knows: β₁ = 0 means ground state (proved); β₁ > 0 means topological deficit (open).

Ambient law kernel

LAW_KERNEL_ID = god-formula/v1 is the cycle-free shared law kernel for the Aeon stack. gnosis, gnode, aeon-forge, and runtime consumers bind to one shared universe certificate surface instead of re-implementing partial local checks.

Buleyean logic

Post-fold logic where truth is ground state and proof is rejection. Boolean is the K = 2 special case. The Bule is the unit of value — one rejection step. Proving P with K alternatives requires eliminating K−1; the void boundary after rejection is the proof.

The Sliver — no option dies

Every option retains positive probability; no alternative ever reaches zero. THM-BULEYEAN-POSITIVITY proves P(i) > 0 for all i, for all rejection histories. The +1 guarantees exploration, so Clockwork never gets stuck.

Jet-engine compressor cascade

Each REJECT edge with K live alternatives discriminates the hypothesis space by a factor of K. A chain of REJECT stages compresses candidate worlds by the product of per-stage arities — the same law as a jet-engine compressor cascade (overall ratio = product of per-stage ratios).

Mechanized formal surface

Verification guarantees rest on the canonical theorem ledger in open-source/gnosis: 3,228+ Lean 4 declarations across 201 modules, 112 TLA+ specifications, and 1,499 GG proof topologies — fork/race/fold axioms, monoidal coherence, queueing, ergodicity, and more.

Quickstart

Verify a claim

# add the verification engine
pnpm add @a0n/aeon-clockwork

# verify all formal artifacts
cd open-source/aeon/docs/ebooks/145-log-rolling-pipelined-prefill/companion-tests
pnpm run test:formal           # parser + Lean + Gnosis + TLC

# verify the product law on the Buleyean discrimination cascade
pnpm run gnode -- run open-source/aeon-clockwork/test/compressor-cascade.verify.ts

FAQ

Common questions

Given a claim and its rejection history, Clockwork decides whether the claim has reached ground state (β₁ = 0, proved) or still carries topological deficit (β₁ > 0, open). The model does not ask an oracle — it reads the void boundary and knows.

The core insight is THM-VOID-BOUNDARY-SUFFICIENT-STATISTIC: the rejection history (the void boundary) contains all the information needed to reconstruct the posterior. You do not need to see what succeeded — the shape of what failed is enough.

Buleyean logic is post-fold logic where truth is ground state and proof is rejection. Boolean logic is the K = 2 special case. THM-FAILURE-STRICTLY-MORE-INFORMATIVE: a rejection carries N−1 bits versus 1 bit for selection.

It is closed for all listed theorem families. Two files carry real sorry markers — TradeTopology.lean line 273 and TradeTopologyRound2.lean line 227. The open frontier is continuous syntactic physics: a Betty-to-Lean bridge that lowers arbitrary continuous .gg source into a measurable kernel.