research: split native AMP evaluation from matrix transport

[mountain]

Summary

• add a no-series native AMP inverse-state evaluator with declared domain, tolerance, level budget, analytic truncation-tail bound, underflow refusal, and primitive cost ledger
• retain the exact polynomial-like / matrix-like compiler as an offline coefficient and replay path
• specialize compiled evaluation to Horner form on the degree ray z = exp(-d y), with a safe generic-support fallback
• separate native, compilation, and online costs in the benchmark report
• document the solver split, same-accuracy regimes, chart failure, and claim ceiling

Mathematical result

For f(x)=x^d+t, the native path evaluates

q_(n+1) = q_n^d / (1 + t q_n^d)
H(y) = y + sum d^(-n-1) log1p(t q_n^d)

without Taylor coefficients or a substitution matrix. On the first certified domain d>=2, t>0, y>=0, it reports the a posteriori analytic tail

T_R <= d^(-R) t q_R^d / (d-1).

The tail statement excludes floating-point roundoff; binary64 underflow fails closed.

At the frozen d=2, t=1, y=1.5, tolerance=1e-15 task, the native path uses 4 process levels. The compiled path remains useful for fixed-chart repeated readout, but no universal speedup is claimed.

Tests

• python -m pytest -q tests/research/test_amp_polynomial_matrix_compiler.py — 12 passed
• python -m pytest -q — 773 passed, 25 skipped, 1 pre-existing warning
• git diff --check
• python -m compileall -q sonnet/amp-polynomial-matrix-compiler/amp_escape_compiler.py

Engineering Architecture Change

Relation: refine/split, Sonnet-local.

This changes no Mathematical Core, dependency direction, Public API, or promoted Theory Map node. Runtime roles are now explicit:

1. scalar numerical limit -> native inverse-state process;
2. fixed-chart repeated readout -> polynomial-like Horner specialization;
3. exact coefficient witness -> sparse matrix-like offline compiler/replay.

The matrix is no longer treated as a required runtime ontology for the nonlinear process. Extraction remains blocked until a mixed-log or coupled workload transfers the abstraction.

Closes #154.