The Horizon Response Principle in Einstein Gravity: A Convention-Locked Normalization Ledger (Constants Explicit)—HRP Master Document

This preprint presents a constants-explicit, convention-locked “normalization ledger” for horizon-sector relations in four-dimensional Einstein–Hilbert gravity, termed the Horizon Response Principle (HRP). A single slot constant kSEG := 4πG/c^3 (with σSEG := 1/(ħ kSEG) = 1/(4π ℓP^2), where ℓP^2 ≡ ħG/c^3) is used to package and audit standard normalizations: 1/(4 kSEG) = c^3/(16πG) (Einstein–Hilbert prefactor), the gravitational horizon entropy density Sgrav/A = kB π σSEG = kB/(4 ℓP^2) (Wald/BH), and the reversible area/Clausius channel δQrev = (αH/2c) kSEG^{-1} δA for local horizons (with optional membrane-paradigm shear viscosity in the near-equilibrium stretched-horizon regime). The ledger is applied across (i) stationary black holes via the Hamiltonian/Noether-charge area term (Iyer–Wald first-law structure), (ii) local Rindler horizons via the Unruh temperature and Jacobson’s boost-horizon normalization, and (iii) FLRW apparent horizons via two sign-safe routes (quasi-static Clausius and exact Hayward/Kodama projection). Conventions and chart policy (X0 = ct vs t) are locked explicitly, and an “entropy firewall” separates gravitational entropy Sgrav from QFT entanglement entropy; any bridge is flagged as an assumption. Sign/units ledgers, domain tripwires, and symbolic CAS factor checks are included to prevent silent convention switches and factor-of-2π/factor-of-c errors. Series context: This HRP master document is the long-form companion to “The Horizon Response Principle in Einstein Gravity: A Constants-Explicit Normalization Ledger (Short Note)” (Zenodo, 2025; doi:10.5281/zenodo.18035711). The constant kSEG was introduced in “The Spacetime Response Constant kSEG” (Zenodo, 2025; doi:10.5281/zenodo.17981074) and formalized into a constants-explicit unit framework in “The kSEG-Unit System: A Thermodynamic Normalization of Gravity” (Zenodo, 2025; doi:10.5281/zenodo.17630968). Important notes: HRP introduces no new dynamics and no new measurable constant beyond (G, c, ħ, kB); it is a convention-locked normalization/audit framework within 4D Einstein–Hilbert gravity. Results are stated in reversible or near-equilibrium horizon thermodynamics (local equilibrium in the Jacobson/Rindler channel; near-equilibrium stretched-horizon regime for the optional membrane viscosity). Fully dynamical horizons with shear/gravitational-wave flux and non-equilibrium entropy production require additional explicit terms. In the reversible area channel, αH denotes the relevant physical acceleration/surface gravity scale (αH = κ for stationary black holes; αH = a for local Rindler horizons). Version note (v2): This release adds an explicit “Einstein-coupling” identity in the HRP primitives section, making the link between kSEG and the standard coupling 8πG/c^4 manifest (i.e., (2/c) kSEG = 8πG/c^4), and includes an optional numeric value for kSEG for quick magnitude checks. Version note (v3): This release corrects Appendix G (entanglement/Rindler bridge) by fixing the modular-Hamiltonian notation: the entanglement first law is written in the standard form delta S_vN = delta (expectation value), and all downstream steps are updated accordingly (removing the nonstandard object). The entropic-force identification (F dX = T_U dS_ent) is kept explicitly as an assumption, with tightened wording to avoid implying a general QFT theorem. Minor editorial cleanups and consistency checks were also applied (units/sign bookkeeping unchanged; no change to the core HRP ledger results).