Correction: require A/M/P generator semantics in the Brownian method

[mountain]

Correction

The initial Brownian S0/S1 work merged in #159 is mathematically valid as a finite random-walk and endpoint-fibre calibration, but it does not implement an AMP-native method.

Its actual structure is:

• discrete Addition histories;
• an externally described scale balance;
• exact endpoint mass pushforward.

Multiplication appears only as passive rescaling, and Power appears only as a population factor. No A/M/P word, finite flow, generator relation, closure fibre, or Log-branch residual enters the calculation. Therefore the merged result must be reclassified as PRE-AMP / discrete control.

This also reveals a weakness in the research method firewall from #157: it separates native/baseline/certificate lanes, but a caller-declared “native” grammar can omit the generators required by the research hypothesis.

Required correction

G0 — generator-aware method contract

Add a research-local grammar profile that records:

• required generator identifiers;
• finite action/flow;
• infinitesimal action or an explicit discrete non-applicability witness;
• carrier and domain;
• task role;
• branch/residual data;
• certificate;
• legal composition;
• relation/bracket witnesses;
• closure status and obligations.

An AMP profile must require exactly the generator grades A, M, and P, plus typed A-M, M-P, and A-P relations. On the positive chart it must record

A_t(x)=x+t
M_s(x)=exp(s)x
P_r(x)=exp(exp(r) Log x)

[A,M]=A
[M,P]=M
[A,P]=(1+log x) d/dx   (escapes the declared span)

and must not pretend that the three generators form a three-dimensional Lie algebra.

B0 — Brownian status correction

Reclassify merged S0/S1 as a discrete control/baseline. Pause recurrence and heat-kernel work.

B1 — competing AMP charts

Freeze and execute two candidates:

1. position chart: A/M/P act on the physical state. It is local on the positive real chart; symmetric Brownian histories crossing zero or becoming negative must return a typed branch/domain obstruction.
2. ensemble-observer chart: a positive exponential observer carries exact shift, scale, and replica identities. Power should appear as genuine repeated independent assembly, not as the symbol N in a balance equation.

For a finite increment law mu, test exactly:

Z_(T_t mu)(s) = exp(st) Z_mu(s)
Z_(S_lambda mu)(s) = Z_mu(lambda s)
Z_(mu^{*N})(s) = Z_mu(s)^N

The second chart retains endpoint-law information but not path observers; same endpoint/different running maximum remains a required fibre witness.

Acceptance

• AMP method declarations fail if A, M, or P is absent;
• AMP method declarations fail if one of the three pair relations is absent;
• positive-chart A/M/P flows and infinite-closure obstruction are recorded;
• Brownian discrete S0/S1 is relabelled PRE-AMP;
• position chart fails on a bounded symmetric history crossing the Log boundary;
• ensemble chart certifies shift, scale, and replica identities exactly;
• Power compilation reproduces the endpoint-fibre law;
• path information loss remains explicit;
• recurrence/heat-kernel lowering remains unauthorized;
• no Public/Experimental API or stable Theory Map promotion.

Claim ceiling

This correction does not yet prove that either candidate is the canonical Brownian AMP chart, does not prove a continuum limit, and does not claim a new stochastic calculus. Its purpose is to make the native method actually test the AMP hypothesis.