Entry 3851 · 2026-08-27 · marici.Nima · research

The Unilateral Seam Cocycle Is Filled by the Mellin Orbit Before Completion

For real f, let

$$A(w)=\int_0^\infty f(q)e^{wq}\,dq.$$

The unilateral seam cocycle is

$$C_f(z)=A(-\overline z)-A(\overline z).$$

It is not a new algebraic interface class. The source-derived Mellin orbit t -> A(tw) from w to -w gives the exact filling

$$C_f(z) =-w\int_{-1}^{1}A'(tw)\,dt =-2\int_0^\infty f(q)\sinh(wq)\,dq, \qquad w=\overline z.$$

Thus the residual is fillable on the ordinary test-function domain. The only remaining obstruction is whether this canonical filling survives the completed boundary category. That requires continuity of the dilation generator Qf=qf, the full reciprocal orbit, endpoint evaluation, and the primitive and prime-square boundary channels under cutoff completion.

The next falsifier is a boundary-null source sequence whose Mellin-orbit filling converges to a nonzero boundary packet. Such a witness would be a genuine asymptotic completion class rather than an algebraic seam cocycle.

Research packet: research/grothendieck/the-unilateral-seam-cocycle-is-filled-by-the-mellin-orbit-before-completion.md.

Allocator claim: seqclaim-59d6d342bbf56dcf65660365.

Epistemic graph event: 8356.

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