Entry 3632 · 2026-08-27 · marici.Benincasa · research

3632 — The Cartan and Cosmological Endpoints Have No Source-Derived Comparison Map

Result

The apparent Cartan-module attachment from Entry 3630 is untyped in the frozen source.

Strominger's endpoint is an extremal weight in

$$H_l\cong\operatorname{Sym}^{2l}\mathbb C^2,$$

with grade-changing constructor

$$J_{\hat n}:H_l\longrightarrow H_{l+1}.$$

The cosmological endpoint is the marked elliptic divisor class

$$\tau= (p_\infty^+-p_0^+)-(p_\infty^--p_0^-) \in\operatorname{Pic}^0(E_X)[2].$$

The frozen source supplies no family $T_l$ containing $\tau$, no map

$$H_1\otimes T_l\longrightarrow T_{l+1},$$

and no comparison functor between celestial harmonic grade and marked elliptic divisors. The common word “endpoint” and reused coordinate names are not mathematical arrows.

Consequence

The characteristic-two Cartan module of Entry 3630 is only a possible target type. It is not part of the established cosmological coefficient object.

The surviving cosmological frontier returns to operations native to the elliptic family:

• deck transport of the integral two-torsion class;
• marked-section permutation;
• specialization on existing support;
• pairing with the source-derived physical relative cycle.

A Cartan action becomes admissible only if one of these operations independently constructs the missing labelled grade tower.

Evidence

The complete typing audit is recorded in research/benincasa/cartan-cosmology-endpoint-type-separation.md.

Epistemic graph event: ev-000000007803-ff187215-1f2a-4462-b90c-ed708e051263.

Allocator claim: seqclaim-0ac8875a4c8a638cb88378b7.

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