research: AMP closure and ensemble carrier gate

[mountain]

Summary

• separate the finite M/P affine subsystem from the full infinite-dimensional A/M/P Lie closure;
• add an exact two-field logarithmic normal form and closed repeated-iteration law;
• type the apparent 3n multivariable representation as a rank-3n generating bundle with rank-n anchor and 2n-dimensional local kernel;
• compile nested homogeneous ensembles without Cartesian microstate enumeration;
• record field count, operation count, replica-exponent width, and a microstate bit-length lower bound separately;
• fix Addition as the negative control: in the M/P logarithmic chart it opens the completed tail (\log(1+t e^{-y}));
• update the carrier audit through the 2025 hyperserial-fields and 2026 transseries Taylor results;
• return the split disposition: AMP EXPAND, surreal runtime ELIMINATE for frozen tasks, overall gate NARROW.

Exact mathematical results

[
[V_{m,n},V_{p,q}]

x^{m+p-1}
\left((p-m)(\log x)^{n+q}+(q-n)(\log x)^{n+q-1}\right)\partial_x.
]

The generated Lie algebra contains the independent family

[
\operatorname{ad}A^{k-1}(V{-1,0})

(-1)^{k-1}(k-1)!V_{-k,0},
\qquad k\ge 1.
]

For (y=\log x), every finite M/P word is (y\mapsto ay+b), and a homogeneous ensemble stage (Z\mapsto e^b Z^n) is the same affine action on (\log Z).

Frozen cost witness

Twenty binary assembly stages over a three-state base represent:

• (2^{20}=1{,}048{,}576) base replicas;
• (3^{1{,}048{,}576}) Cartesian microstates;
• a compiled two-field value state;
• a 21-bit replica exponent;
• more than 1,048,576 bits for the unmaterialized microstate count itself.

This claim is observer-relative: correlations, interactions, and microstate reconstruction are outside the compiled quotient.

Verification

• python -m pytest -q tests/research/test_amp_ensemble_carrier_gate.py
  • 11 passed
• python -m pytest -q
  • 760 passed, 25 skipped, 1 pre-existing deprecation warning
• python -m compileall -q sonnet/amp-ensemble-carrier-gate/amp_ensemble_compiler.py
• git diff --check

Closes #150