research: AM completion cones and chamber transport

[mountain]

Closes #148.

Result

This PR moves the AM line from a rank-one completed ray to a mathematically controlled bigraded completion.

With

$$X_{\nu,\kappa}=a^\nu e^{\kappa v},\qquad \kappa=w-\nu,$$

the native degree lattice is $G=\mathbb Z\oplus\Lambda$, with

$$AX_{\nu,\kappa}=\nu X_{\nu-1,\kappa},\qquad MX_{\nu,\kappa}=(\nu+\kappa)X_{\nu,\kappa}.$$

Exact deductions

• pointed rational-polyhedral cones with positive observer height have finite bounded lattice slices;
• completed multiplication, exp, and log1p therefore have finite target dependencies;
• all interior positive heights on one finitely generated cone induce cofinal filtrations;
• a pointed cone cannot be invariant under both power translations +e_nu and -e_nu;
• fixed-degree A, M, and ordinary primitive shifts remain continuous as typed maps between translated sectors;
• nu=-1 is a codimension-one log-a resonance wall.

Two-generator calibration

For $X=a$, $Y=e^v$ and

$$F=\exp(X+Y+XY),$$

the mixed completed coefficient is

$$[X^2Y^2]F=\frac74.$$

Independent operator checks give

$$[X^1Y^2]AF=\frac72,$$

and

$$[X^2Y^2]MF=7.$$

Two positive observer heights recover the same coefficient and completion while producing different finite scalar windows.

Disposition

CHAMBERS: the correct bounded object is a chambered system

$$\mathcal H_{g_0,C}=K[[g_0+(C\cap G)]],$$

with AM operators transporting between typed sectors. No frozen obstruction yet forces Hahn, transseries, hyperseries, or surreal support.

No implementation optimization, Core promotion, Theory Map promotion, or Public API change is included.

[mountain]

Mathematical red-team closure

The second commit closes two proof gaps before review:

1. the coefficient domain is now explicitly a commutative $\mathbb Q$-algebra, so factorial and logarithmic denominators are legitimate;
2. the finite-observer interpretation is now an exact inverse-limit theorem

$$K[[S]]\cong\varprojlim_N K[[S]]/F_h^{>N}.$$

The two-generator identities were independently recomputed with exact rational arithmetic:

• mixed coefficient: 7/4;
• A transport: 7/2 = 7/2;
• M action: 7 = 7;
• paired-height bounded-slice counts: 15 and 16.

No evaluator optimization or stronger-support assumption was introduced.