The Recognition Ledger of a Black Hole: Horizon Records, Entropy Counts and Lattice Hawking Radiation

A black hole of horizon area A carries the entropy A/(4 l_P²), radiates at the temperature ħκ_s/(2π) set by its surface gravity κ_s, and, if quantum mechanics holds, gives back the information that fell in. All three concern what a horizon records, and the recognition ledger's events are records. We state the four steps of a ledger account, a lattice horizon, its entropy, its radiation and the fate of its information, as precise targets; none of the four is complete. On the ledger's lattice G = 1/(8πs) is fixed by the action scale s and ħ = 1/a by the phase scale a, so at tree level the Bekenstein–Hawking quarter holds exactly when a horizon holds 2πas per unit area; the ledger's phase premise sets this to one bit per record area λ_rec², so a count that assumes it returns the quarter by construction. The lattice's order of postings holds no black hole, nor do the configurations the path sum integrates over, and in the order of a geometry's interval a trapped region needs a strong field. For the lattice action as it stands, the condition under which a weak vacuum field extends to second order fails one order past Einstein's equations, provably for a sampled field and numerically for a point mass, so a lattice black hole with a regular far field is not expected without an action exactly symmetric under vertex moves (an inference). A horizon hides the postings that cross it. One bit per crossing gives a coefficient that depends on the horizon's orientation, 0.108, 0.325 or 0.1875 at the identified spacing and tree level, none of them the quarter, so a quarter that is the same on every horizon needs a count that correlates the records; that count is open. The lattice scalar disperses like a superluminal medium at short wavelengths. On test backgrounds that are not lattice solutions its computed in-out occupation is a Planck spectrum that tends to the Hawking temperature as the spacing shrinks: preliminary numerical evidence, read as emission only by inference, since record time has no stable vacuum. Where the information goes depends on a unitary evolution in record time, which the identified Regge path sum lacks; the ledger's measure weight gives one only in the continuum limit. Where a proof is complete but its independent verification is not, the text says so.