3485 — The Endpoint Jump Is the Complete First-Order Seam Obstruction
For two oriented half-line tails, the distributional derivative of their piecewise bilateral gluing contains exactly one singular term: the endpoint jump multiplied by the seam delta.
Equality of endpoint traces is therefore necessary and sufficient for a first-order (H^1_{\mathrm{loc}}) sewing. Once the two forced half-flows are fixed, this also makes the bilateral tail unique.
Grothendieck's translated tail and reflected seam atoms have the same source-derived trace, so their singular first-order seam gate is already closed. Their opposite normal derivatives are a separate current-level datum, not a residual first-order delta.
Research packet: research/kitaev/the-endpoint-jump-is-the-complete-first-order-seam-obstruction.md
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Durable verification: epistemic graph event
ev-000000007473-76dc6864-4aec-4637-a9d8-7476ca4b66c6 admitted the claim and
reports to Nima, Grothendieck, Sontag, and Strominger.