Horizon Response Principle (HRP) Sector I: Stationary Black Holes

This preprint is Sector I (Stationary Black Holes) of the Horizon Response Principle (HRP) triptych (BH / Local Rindler / FLRW). It provides a constants-explicit, sector-typed normalization card for 4D Einstein–Hilbert gravity in the stationary black-hole setting. Scope:• 4D Einstein gravity only• Stationary Killing horizons• Reversible (near-equilibrium) area channel only• All constants explicit (G, c, ħ, k_B)• No new dynamics or modified field equations Sector typing (BH sector).The left-hand side (LHS) object is the Hamiltonian/Noether-charge area contribution in the Iyer–Wald first-law identity, δH_ξ|_area.It is not a matter heat flux δQ and is not identified with LHS objects from other sectors. Normalization backbone.Using the acceleration temperatureT(α_H) = ħ α_H / (2π k_B c)and the Einstein (Wald/Bekenstein–Hawking) entropy densityS_grav/A = k_B c^3 / (4G ħ),the algebraic identityT(α_H)(S_grav/A) = α_H c^2 / (8πG)exposes a classical coefficient skeleton that HRP packages via k_SEG := 4πG / c^3. In the BH sector the abstract acceleration scale specializes to the physical surface gravity κ, yielding the standard first-law reversible area term in constants-explicit form. Surface-gravity normalization.The paper explicitly distinguishes geometric surface gravity (units 1/m) from physical surface gravity (units m/s^2), related by κ = c^2 κ_geom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons. What is not claimed.• No derivation or modification of GR• No identification of gravitational entropy with entanglement entropy• No non-equilibrium or entropy-production terms• No universality beyond 4D Einstein gravity• No cross-sector identification of distinct LHS objects Within the HRP suite, this paper establishes the stationary black-hole normalization ledger that anchors the companion Local Rindler and FLRW sector cards. Across sectors, k_SEG functions as a reusable constants-explicit slot, while each sector’s physical LHS object remains strictly typed and non-identified. Version note (v2): Suite-wide “Interface Contract” added to enforce typed-LHS discipline, operator-form separation (delta-form vs dot-form), coefficient-only universality, magnitude-first sign policy, and an explicit Entropy Firewall (EF) (S_grav remains Wald/Bekenstein–Hawking gravitational entropy in Einstein gravity; no identification with entanglement/generalized entropy). UHRA “universal” language is now uniformly scoped at first use to mean: within the HRP suite at coefficient level only (4D Einstein gravity under pinned conventions). The BH sector now presents the area channel magnitude-first as the default; a signed form is treated as optional and given only after pinning explicit Iyer–Wald conventions (binormal orientation and Hamiltonian sign convention). Pinned conventions were expanded to clarify stationarity/non-extremality (bifurcate Killing horizon; extremal only as limits), fixed-theory delta-variations with couplings/constants held fixed (including Lambda when present) and horizon-generator normalization held fixed, plus a suite notation crosswalk for the shared slots (k_SEG, T(alpha_H), S_grav/A). Added a bifurcation-surface structural anchor explaining why the horizon contribution reduces to the Noether-charge piece (xi = 0 on B, so xi·Theta vanishes) and included a Schwarzschild sanity check under the pinned sign convention. Core normalization and coefficient skeleton are unchanged: the reversible area coefficient remains (kappa/2c) k_SEG^{-1} = kappa c^2/(8 pi G), and the physical-vs-geometric surface gravity chart pin is retained.