A Lattice Model of Gravity from Competition for Information Capacity: Identification of Necessary Conditions and of the Resulting Theory

A lattice model containing no term corresponding to gravity is used to ask whether gravitational phenomena arise from competition for information capacity alone. The answer is negative, and the result of the work is the shape of that negative answer.

We classify what must be added in order to reproduce linearised general relativity into six necessary conditions, attaching to each a proof or a verified measurement.

1. A long-range field at equilibrium requires that the entropy depend on differences between neighbouring sites. In the local form the correlation length remains at 0.87 lattice units and the susceptibility has no maximum, so there is no route by which tuning can extend it. In the difference form the local exponent is -1.137 at L = 128.

2. The PPN parameter gamma = 1 requires a capacity common to the temporal and spatial sectors. Separate capacities give gamma = 0.857, excluded at 6211 sigma by Cassini; a common capacity gives gamma = 1.000000 for all twelve parameter sets tried.

3. Transversality requires a complete gauge symmetry. A penalty on the longitudinal components leaves the mode count at 6 and the non-TT fraction above 0.14; the Fierz-Pauli form reaches 0.0010 in the radiation zone.

4. Lorentz invariance requires the four-velocity of the local rest frame to be a dynamical variable. Lattice-induced violation vanishes with exponent 2.0002, whereas dissipation-induced violation survives as k tends to zero.

5. The PPN parameter beta = 1 requires the field to propagate in the geometry it generates.

6. An event horizon requires the temporal capacity to be exhausted first, which implies gamma < 1. Two independently constructed families of static spherically symmetric solutions both lie on the line beta = (1 + gamma) / 2, and in both the horizon exists only for gamma < 1. Conditions 2 and 6 impose opposite requirements on the same quantity.

Only conditions 2 and 5 follow from the premises of the model. When the remainder are supplied, the resulting theory is the exponential metric of Papapetrou (1954) and Yilmaz (1958), observationally indistinguishable from general relativity in the classical weak-field tests but without an event horizon.

Changes from version 1. The identification with Nordstroem (1913) scalar gravity made in version 1 is withdrawn. Ten claims are retracted, including the lensing dichotomy, the stationarity of the 1/r field (it is the quasi-stationary flux of core filling; the amplitude decays to -0.0001 over 48000 sweeps), and the two-body scaling tau proportional to d^3.17 (confounded by a vacuum baseline that shrinks 42% at d0 = 16). After literature checking, no novelty claim from version 1 survives. Twenty implementation errors and the verification tests that caught them are recorded, including one case in which a verification test issued a warning and the work was continued anyway; that decision is reported as a mistake.

The upload contains the manuscript in English and Japanese, all simulation scripts (Python and NumPy only, with seeds recorded), the raw outputs, the figures, and the laboratory notes.

Version 2 withdraws the Nordstroem identification made in version 1 and issues ten retractions. See section 7 of the manuscript and the README for the full audit record.