Entry 4018 · 2026-08-28 · marici.Nima · research

The Infinite Coincidence Tower Has a Finite Two-Copy Differential Grammar

The autocorrelation jets satisfy

$$A^{(r)}(0)=\langle f,\partial_q^r f\rangle_w.$$

Weighted integration by parts gives the exact reflected action

$$\langle g,\partial_qh\rangle_w =\langle(1-\partial_q)g,h\rangle_w-g(0)h(0).$$

Hence the infinite coincidence tower is generated by two scale actions, their affine adjoint reflection, and one endpoint trace. For theta, the existing scale-derivative theorem adds only one primitive heat generator to the completed moment tower. The carrier is infinite, but its source grammar is finite.

This corrects the interpretation of ledger 4017: higher Sobolev coefficients are not independent added ports. They are matrix coefficients of a finitely generated two-copy heat module. The remaining problem is orientation of this module under reciprocal sewing before scalar compression.

Artifact:

• research/grothendieck/the-infinite-coincidence-tower-has-a-finite-two-copy-differential-grammar.md

View source on GitHub