A Unified State Field Theory: Mass–Energy–Information Conservation, the Entropic Tensor, and Quantum-Gravitational Foundations on a Causal-Set Substrate We present the Unified State Field Theory (USFT), a covariant Lagrangian framework in which energy, mass, and information are three manifestations of a single conserved scalar state density Ψ = ρE + ρₘ c² + (kB TP/ℓP³) |ℐ|², whose volume integral is constant in an ordinal parameter τ. The information field ℐ is realised as a complex scalar with a Mexican-hat potential, anchored to the Bekenstein bound. An explicit matter–information coupling Lᵢnt = α|ℐ|² (LE + Lₘ c²) introduces the dimensionless universal coupling α and yields modified Einstein equations with an effective (1 + α|ℐ|²) prefactor on the matter sector and an information-field stress–energy tensor T^ (ℐ) _μν as additional source. Total stress–energy on the right-hand side is on-shell conserved through the Bianchi identity; matter and information exchange energy and momentum, with the exchange terms cancelling exactly. The framework reduces to general relativity in the local regime, generates flat rotation curves at galactic scales without dark matter, produces cosmic acceleration in the slow-roll regime of ℐ, and reinterprets the Hubble tension as a measurement of α. The Madelung decomposition identifies the kinetic Lagrangian as the Fisher information of the informational density, recovering the Bohm potential and a Cramér–Rao form of the Heisenberg uncertainty relation in the spirit of Caticha–Reginatto entropic dynamics, gravitationally coupled. The ordinal parameter τ is identified with the sequential-growth index of a Sorkin–Rideout causal set; cosmic inflation is reinterpreted as Coleman–Weinberg-driven symmetry breaking of ℐ. A horizon-matching analysis fixes α parameter-free as the Immirzi parameter in the Domagała–Lewandowski/Meissner LQG counting: α = γDL/M = 0. 2375329579. The framework is confronted with the full SPARC catalogue of 175 disk galaxies and 3, 391 radial measurements, with α held fixed at the LQG-derived value throughout. At identical per-galaxy parameter count to the Navarro–Frenk–White cold-dark-matter halo profile, USFT achieves median fractional velocity-residual RMS of 5. 4% versus 9. 1% for NFW, with summed Bayesian evidence ΣΔBIC = +3240 in favour of USFT — a 30% reduction in summed χ² at matched parameter cost. A hierarchical population analysis with Hessian-based per-galaxy uncertainties recovers the population center κ₀ ≡ ⟨r_ℐ/Rdisc⟩ = 0. 95 ± 0. 02 with intrinsic scatter σᵢnt = 0. 29 dex, confirming that the informational scale tracks the dominant baryonic disk scale at order unity. The kinematically required central informational amplitude ℐ (0) correlates with Spitzer 3. 6 μm luminosity at Pearson r = 0. 89 (Spearman ρ = 0. 92, EIV-corrected r = 0. 90) on a well-constrained subsample of 148 galaxies. Profile choice between exponential-saturation and isothermal-equivalent informational kernels affects results by less than 0. 6%. Five falsifiable predictions are presented, testable with JWST, Euclid, CMB-S4, LISA, and high-precision atomic interferometry; the most decisive is a multi-channel α consistency test combining the LQG horizon-counting value, the Hubble tension, the primordial spectral tilt, and the cosmological time-variation of the fine-structure constant. Note on this version. This manuscript supersedes earlier internal pre-prints of the framework. The full 175-galaxy SPARC validation (referred to in earlier internal versions as "Gate 2" of the validation programme) has now been executed. The empirical core of the framework — universal LQG-derived coupling α, parameter-free rotation-curve prediction at matched parameter count to NFW, photometric-kinematic linkage through the central informational amplitude, and order-unity informational scale tracking the baryonic disk — is confirmed at the 175-galaxy / 3, 391-point level. Three subsidiary claims from earlier internal versions have been removed or recast because they were not validated by the full-sample test, while not being structurally essential to the framework: (i) the prediction of κ as a strictly universal constant within ~20% across all galaxies has been replaced by the empirically supported population-level statement κ₀ = 0. 95 ± 0. 02 with σᵢnt = 0. 29 dex, allowing genuine galaxy-by-galaxy variation in the informational scale around the order-unity mean; (ii) the claim that ℐ (0) is deterministically predictable from photometry alone has been replaced by the demonstrated strong correlation r = 0. 89 between kinematic ℐ (0) and Spitzer L₃. 6, with ℐ (0) retained as a per-galaxy fitted amplitude rather than a closed-form photometric output; (iii) the claim of α self-consistency directly from rotation curves has been dropped because the asymptotic-rotation-curve regime is degenerate in (α, ℐ (0) ) and cannot independently constrain α — the framework instead anchors α at its LQG horizon-matching value and uses SPARC to test the resulting parameter-free prediction. The predictions section has been updated accordingly: the multi-channel α consistency test is now formulated as LQG + Hubble + spectral tilt + atomic clocks, since the galactic-rotation channel is no longer claimed as an independent α determination. None of these revisions affect the framework's foundational structure (Postulate I, the action and modified field equations, the Bianchi-conserved on-shell total stress–energy, the Madelung–Fisher reconstruction, the causal-set substrate, the Coleman–Weinberg inflation mechanism, or the LQG horizon-matching identification of α). What has been removed is what the data did not support; what remains is what the data supports, at the strongest empirical level the framework has yet been tested.
Fabio Ruggeri (Wed,) studied this question.