No unwitnessed advantage — the Advantage Witness law (`witness { … }`)

Every sophisticated construct — a quantum kernel, a re-ranker, a multi-step deliberation, an adaptive memory loop — is, implicitly, making a claim: "I am worth more than the cheaper thing I replaced." Most of the field ships that claim on faith. AXON does not. This page is the law.

No primitive may claim an advantage over a cheaper baseline unless it carries a machine-checkable witness that the advantage is real and exceeds its cost threshold on real data. Unwitnessed sophistication degrades, honestly, to the baseline.

It is the same honest-compiler reflex as axon://logic/dispatch_vs_cognition (don't fake LLM determinism) and the capability-aware model resolver (declare the need, fail closed), generalised into one rule that reaches every primitive.

The witness declaration

witness SeedKernelBeatsCosine {
    claim:     SeedKernel              # the sophisticated construct
    against:   cosine                  # the cheaper baseline it claims to beat
    metric:    geometric_difference    # how advantage is measured (closed catalog)
    threshold: 0.05                    # the minimum advantage that justifies the cost
    data:      mdn_embeddings          # the REAL data it is witnessed on
}

The metric is drawn from a closed catalog (extending it is a deliberate PR, never an open set): geometric_difference and kernel_target_alignment (quant kernels), ranking_lift (retrieval / navigate), outcome_lift (deliberation). The witness is transversal — the same surface works for any primitive; only the metric changes.

What the compiler proves vs what is measured

• axon check proves the witness is well-FORMED (axon-E0790): a known metric, a finite threshold ≥ 0, and the required references present. In particular data: is required — you cannot claim advantage in the abstract. The advantage is always relative to a baseline, on real data.
• The advantage VALUE is computed on that real data at deploy / runtime and carried as a verdict { metric, measure, threshold, holds, baseline } (an independently- verifiable PCC proof object). holds = measure > threshold.

Fail-closed honesty — degrade to the baseline

When measure ≤ threshold, the verdict is holds: false, and the compiler / runtime tells the truth and names the gap — it does not silently ship the construct as advantage. For a quant kernel that resolves to classical cosine (amplitude encoding + fixed Pauli observables — see axon://primitives/quant), the witness fails and axon-W007 recommends the baseline:

axon-W007: no measurable quantum advantage (provably cosine for amplitude+Pauli) — use classical cosine, or a re-uploading feature map.

For any other primitive whose advantage falls at or below its threshold, axon-W008 gives the generic "no measurable advantage — degrade to the baseline."

The four pillars

	The Advantage Witness
Mathematics	advantage is a measured quantity over a baseline (g, KTA, ranking lift), not a vibe
Logic	the verdict is a proof obligation — holds is re-checkable against the artifact (PCC AdvantageWitnessed)
Philosophy	a claim must be earned, not asserted; the cheaper baseline is the honest null hypothesis
Computation	the witness is evaluated on real data; unwitnessed sophistication is dead code paying rent

Why this exists

The most expensive lie in applied ML is "this complexity is worth it." A quantum kernel that is secretly cosine, a re-ranker that does not out-rank, a multi-agent loop that does not out-reason — each ships cost without benefit, and nobody measures. AXON makes the measurement a language feature: it will not let you deploy theater — quantum or otherwise — believing it is advantage. And it is honest in both directions: where a construct genuinely beats its baseline, the witness proves it.

See also

• axon://primitives/quant — the first witnessed primitive (the amplitude-fidelity ≡ cosine theorem; the geometric-difference metric; data re-uploading as the real escape).
• axon://logic/dispatch_vs_cognition — the sibling honest-compiler law.