One-Octonion Brane-Bulk Framework - Paper CCCXXXVI: Black Holes as Flow - The Aperture, the Acoustic Lock, the Hyperbolic Collar, and the Cosmological Constant as Residual Strain

This paper consolidates the framework's account of black holes into its flow form. The ontology is canon's own: the 4D brane is an expanding front propagating at its acoustic speed c (Paper 0); rest mass is focal deceleration of the flow (Paper V); and a black hole is critical flow through a circular aperture into an infundibulum that discharges into the bulk — the brane falling continuously through the aperture as blood flows through a vessel, with no torn edge, no hole to balance, and no end-state: the collar around the aperture is always draining, never drained. Four machine-gated results carry the account. (1) The lock: in Gullstrand–Painlevé form the Schwarzschild exterior is flat space with flow field v(r) = −c√(r_s/r), and f = 1 − v²/c² identically — the framework's quiescent aperture condition and the acoustic-horizon condition of the flowing fabric are one equation (the coordinate identity is exact; reading the coordinate river as the literal fabric river is the framework's declared identification). (2) The hyperbolic collar: canon's curvature dictionary gives the near-aperture geometry by theorem — κ_eff(r) = −[1 − √(1 − r_s/r)]², with κ_eff(r_s) = −1 identically: the horizon sits exactly where hyperbolicity completes, and the three-zone structure (infundibular → hyperbolic → Euclidean) is continuous with no junction imposed by hand. The dimensional radius of the hyperbolic zone is not a universal constant but a function of the aperture's local environment (mass, surrounding gravitational field, horizon radius) — stated as an open local boundary-value problem. (3) The dirty-rim theorem (static-spherical, slope-local): at any nondegenerate outer apparent horizon, R·h′(R) = 1 + 8πG·Δε_net(R)R²/c⁴ — the instrument converting any collar-depth law into its one observable consequence at the horizon. (4) The seam algebra: the Cayley–Dickson flip from the split-octonion parent algebra to the compact form places the nucleation seam on the split norm's maximal isotropic (null) subspace, with (D_parent, D_seam) = (5, 4) the unique consistent pair — the algebraic face of the parents' annihilation, which is what starts the flow and the expansion. The parents are canon's compact hyperbolic objects — Klein-quartic carriers of opposite (2,3,7) chirality — annihilating through the Ursa Major transition state; no horizon-pair structure enters. What is measured today as Λ is identified (postulate A-LAMBDA) as residual strain — our partially relaxed vacuum's height above the native Klein-quartic floor, L_res = √(3/Λ); there is no dark-energy substance in the framework. The onset front launches at c radially, with c evolving before electroweak freeze-out exactly as Paper III's Expansion-Rate Causality prescribes. Open problems are stated plainly: the flux normalization (energy-budget partition), the aperture environment (collar depth and stability against radiative losses and mergers), seam gravity during onset, and the magnitude of G. Context. The results presented here are strictly contingent on the established One-Octonion Brane-Bulk (OOB) framework and are not derived from first principles in this paper alone. The full symbolic proofs, foundational postulates, and verify_*.py gate scripts (included here) are consolidated in the BraneBulk Omnibus (DOI: 10.5281/zenodo.19185171).