research: initialize Brownian scale and endpoint-fibre Sonnet

[mountain]

Advances #158. Related to #140 and draft #141. Depends on the method firewall merged in #157.

Result

Initialize Brownian motion as a second independent scale/fibre representation family, starting from raw finite increment histories.

S0 derives the first centered scale obligation without receiving the exponent:

raw symmetric law -> exact mean 0 -> exact variance 1 -> active response order 2 -> solve 1 - 2a = 0.

The certificate uses the exact integral response identity, not a truncated local expansion. It explicitly stops before a central-limit or continuum-path theorem. A biased held-out law returns typed centering-required.

S1 constructs exact endpoint fibres for nearest-neighbour histories on Z^d, exact rational pushforward probabilities, and a history-concatenation certificate. For the frozen 1D horizon-five case the counts are 1,5,10,10,5,1, and direct horizon five equals the 2+3 endpoint-fibre convolution exactly.

Method firewall

• native discovery: finite law and centered response;
• native evaluation: chronological endpoint pushforward;
• certificate: independent small literal enumeration and concatenation residual;
• baseline: classical transform/local-response/simulation routes are declared but have zero native events;
• S0/S1 authorize no lowering witness.

The native source is tested to contain no series, Fourier, matrix, Koopman/Carleman, Gaussian, or heat-kernel oracle calls.

Evidence

• 17 Brownian S0/S1 exact tests;
• 49 Brownian/firewall/governance targeted tests;
• full repository suite: 813 passed, 25 skipped;
• git diff --check clean;
• no new dependency or package API.

Mathematical Core relation

Implements one concrete chain:

finite histories -> endpoint task -> fibres/mass pushforward -> concatenation certificate.

Equal endpoints remain explicitly distinguishable by a path-maximum observer, so S1 is not claimed as a path-task quotient.

Engineering Architecture Change

• Stage: new Sonnet-local problem contract, native evaluator, exact finite certificate, failure and cost ledger.
• Algorithm: exact rational centered response plus bounded endpoint-fibre mass propagation and convolution.
• Claim mode: exact symbolic scale balance and exact finite endpoint counts.
• Failure: centering required, degenerate response, invalid history/law, and budget exhaustion fail explicitly.
• Cost: law atoms/operations, transition updates, live/stored fibres, and literal history count are reported separately; no speedup is claimed.
• Baseline: declared but not used as native evidence.
• Decoder/residual: literal history is retained as the discriminator for path-sensitive tasks.
• API/dependency effect: none.
• Operation: support the existing problem-to-solver and Effective Analysis discipline; no architecture promotion.

Theory Map Change

Unchanged. This is a T1 local calibration. It pressures U1/U2/U3/U4 and Effective Analysis but proves no universality, objectification, continuum lowering, or new stochastic calculus.

Next gate

Keep #158 open. S2 must separate lattice point return, continuum neighbourhood recurrence, and continuum singleton hitting before S3 introduces a task-scoped Brownian/heat-kernel lowering. Draft #141 remains an explicit dependency and is not copied into this branch.