Horizon Response Principle (HRP) Sector II: Local Rindler Horizons

This preprint is Sector II (Local Rindler Horizons) 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 local-horizon (Jacobson) setting. Scope:• 4D Einstein gravity only• Local causal (Rindler) horizons in the Jacobson construction• Reversible (near-equilibrium) area channel only• All constants explicit (G, c, ħ, k_B)• No new dynamics or modified field equations Sector typing (Local Rindler sector).The left-hand side (LHS) object is the boost-energy flux integral (Clausius heat) across a local horizon patch, δQ_boost.It is not a BH Hamiltonian/Noether variation 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 Local Rindler sector the abstract acceleration scale specializes to the physical proper acceleration α (of the accelerated observers at the chosen point), yielding the standard reversible Clausius area-response channel in constants-explicit form within the local-horizon construction. Acceleration normalization.The paper distinguishes the geometric scale κ_geom (units 1/m in a length chart X^0 = ct) from the physical proper acceleration α (units m/s^2), related by α = c^2 κ_geom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons. Reversible regime (Jacobson pin).The analysis is restricted to a local horizon patch at a spacetime point p with vanishing expansion and shear (θ(p) = 0 = σ_ab(p)). The Clausius relation δQ_boost = T δS_grav is treated as a near-equilibrium constitutive input in this regime. The standard Raychaudhuri bridge is recorded only as a compatibility check with the Einstein equation under these pinned assumptions. What is not claimed.• No claim that thermodynamics independently derives GR beyond the standard Jacobson assumptions• 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 local-horizon normalization ledger that complements the stationary black-hole 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): Added the suite-wide “Interface Contract” (shared across the triptych + addenda) to make cross-paper rules explicit: sector-typed LHS objects, operator-form separation (delta-form vs dot-form), coefficient-only UHRA comparison, magnitude-first sign policy, and an explicit Entropy Firewall (S_grav is Wald/Bekenstein–Hawking gravitational entropy only; no identification with entanglement/generalized entropy). The local-Rindler result is now stated magnitude-first as the primary sector claim, with signed Clausius/coefficient forms moved into an explicit “Optional signed convention” section that pins a full operational orientation package. δ is now pinned explicitly in the Pinned Conventions as a cut-variation of a fixed local horizon patch (λ_max → λ_max + ε) with the local frame at p, acceleration input α, and the normalization of (λ, ℓ^a) (hence χ^a) held fixed; this removes ambiguity between patch-integral δ, solution-space δ, and time-rate comparisons. Generator/affine bookkeeping is tightened by using ℓ^a consistently, adding affine-rescaling invariance, and strengthening basis/units pins (length chart X^0 = ct, explicit one-line chart map, and suite notation crosswalk for k_SEG, T(α_H), and S_grav/A) to prevent hidden-c drift; an explicit Planck-length convention is also stated. The signed-orientation mapping is made explicit: for positive null energy density (T_ab ℓ^a ℓ^b ≥ 0), one has δQ_boost^(signed) ≤ 0 and δA ≤ 0 under the pinned convention, while the coefficient skeleton is unchanged: (α/2c) k_SEG^{-1}.