An Information-Theoretic One-Erasure Coefficient for Gravity: Finite Counting, Empirical Comparison, and Limits

Abstract

Why is gravity so weak compared with the other interactions? This paper tests whether the dimensionless coefficient in a horizon-fed gravity relation can arise from a finite record structure rather than being fitted as a free parameter. Direct enumeration shows that the leading virtual-gravity process contains exactly one non-unitary service-event slot. Under the paper's named monitoring-and-erasure identification, that slot is billed as one erasure. Together with the independently derived walk support, this gives a leading coefficient K_LO = 205.554: no continuous parameter was adjusted to obtain it, and the principal alternative readings of the same ledger are recorded explicitly. A second-order calculation, with its candidate map and decision bar frozen before the comparison, adds one counted term to give K_NLO = 206.554. Both values are compared against K_data = 206.49, which is not a measurement of K but a quantity assembled from the QCD anchor, the Hubble rate and the dark-energy fraction. Each of those inputs is soft enough to move K_data by more than the 0.031% residual — the anchor by 8.5%, the Hubble tension by 7.8% — and the inherited fine-structure convention leaves a further band of 0.054 in K, comparable to the residual itself. The leading and second-order coefficients therefore cannot be separated by this comparison, and the residual changes sign if the framework's own horizon and dark-energy values replace the observational ones. What the paper claims is a zero-parameter coefficient counted from a finite census, agreeing with the assembled value to better than half a percent against inputs soft at the several-percent level; it does not claim to fix K to three significant figures. The agreement is conditional on premises as well as on inputs. It depends on the stated identification between the finite record process and far-field gravity, as well as the symmetry and monitoring premises. Later exact channel analysis proves the associated P/Q-dephasing and binary information ledger, but it does not derive physical invocation, durable export, reset, heat, Landauer equality, or cadence: the event count is not calorimetry. Within the same conditional service model the horizon is computed as H₀ = 67.2554 km s⁻¹ Mpc⁻¹, rather than inserted observationally, while the proton mass remains the one dimensionful anchor. These results establish consistency, not a premise-free derivation of Newton's constant or an intrinsic Planck scale. The construction also does not yet supply a gravitational action or nonlinear equations of motion. Instead, it reduces that problem to a sequence of concrete matching tasks: a physical field dictionary from the native perturbation space to the metric and matter fields, a native action or equivalent dynamical prescription, and a matter variation supplying the source and identifying the probe metric (Elliman, 2026b). The paper thus presents an auditable conditional coefficient theorem, its empirical comparison, and a precise account of what would be needed to extend it to gravitational dynamics.

Keywords

How to cite

Elliman, D. (2026). An Information-Theoretic One-Erasure Coefficient for Gravity: Finite Counting, Empirical Comparison, and Limits. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.22727972

@techreport{elliman2026gravityoneerasure,
  author      = {Elliman, David},
  title       = {An Information-Theoretic One-Erasure Coefficient for Gravity: Finite Counting, Empirical Comparison, and Limits},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.22727972},
  url         = {https://neusym.ai/papers/gravity_one_erasure/}
}