The Demon at the Seam: A Crossing's Bill, Denominated in u, Paid by the Demon — Not the Crossing

AF-8 metered the demon at the bounce. This paper moves it one address further: to the seam itself, sorting crossings. A crossing arrives on one of the sever's two faces, with shares 200/411 and 211/411; learning which face is one draw of binary entropy H = 0.999483 bits. Denominated in the sever unit u = log₂(211/200) = 0.077243 bits, that draw is 12.9395 units, and its Landauer bill at the seam's own temperature (T_b, AF-8's address) is 1.592742 GeV — 0.692789 of the thermal quantum kT_b, per crossing, with an erasure power floor of 1.151149×10¹⁴ W per channel at one crossing per cell. The bill is paid — by the demon, out of the Szilard gain of the same sort, which is the same 1.592743 GeV to print precision: AF-3's and AF-8's cancellation, holding at the seam. The crossing itself is charged nothing: the frame's crossing theorem (the corpus's paper #8) says the crossing is toll-free, and nothing in the seam's entropy books contradicts it — the demon's bookkeeping is the demon's. The charged alternate question is answered in the negative in §3: the toll 3Ω_Λ = 2.0541 is not denominated in u (ratio 26.5927 in bits, 38.3652 in nats, neither an integer nor an owned form, and a category mismatch besides). At the seam, entropy runs in u; the toll does not.