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 ħg_H/(2π) set by its surface gravity g_H, 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 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 a geometry's interval order trapping 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 for a point mass's Taylor fields, 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, which 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; with the ledger's measure weight its record-time roots are only stable in the continuum limit. Where a proof is complete but its independent verification is not, the text says so.