Paper CCLXIX: The Truncated Photon as Klein Quartic Boundary Layer -- Sinc Sampling, Fock-Space Mode Mismatch, and the New Exact Identity fbulk = 2 pi * arccosh (3) / 300

Response to Rukan, Gulla, and Skaar (PRL accepted 18 May 2026, DOI 10. 1103/94pm-hp34) on the truncated-photon state: a photon truncated by an optical shutter is neither a photon nor vacuum but a superposition over all photon numbers N = 0, 1, 2,. . . with all non-classical complexity confined to a narrow temporal transition region, locally equivalent to |1> upstream and |0> downstream. The OOB framework identifies this transition region with the Klein quartic geodesic boundary layer separating the brane Im (O) from the bulk (e₀ scalar). The shutter is a rectangular temporal window; its Fourier transform is a sinc, and the resulting mode mismatch generates a compound-geometric (not Poissonian) photon-number distribution. The sinc zero-spacing maps to the Klein-ladder eigenvalues 2 - sqrt (3), 1, 2, 3, 2 + sqrt (3), 4 summing to 14 = dim (G₂). A new exact framework identity is established: fbulk = 2 pi * arccosh (3) / 300 = 0. 036919, matching the canonical fbulk = 3. 6917% to 0. 005%, connecting the brane-bulk transit fraction to the Klein quartic systolic geometry via 300 = 3 * 10² (three K (7) handles times percent scaling). Three experimentally testable predictions follow: P103, P104, P105 (precise statements in the paper). Honest scope: the paper is a structural identification between the Rukan-Gulla-Skaar truncated-photon transition region and the Klein-quartic boundary layer, with the exact arccosh (3) / 300 identity as the headline numerical anchor; future work derives the identity from K (7) systolic primitives. Framework count: 270 numbered papers. 7 pp. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.