Paper 62BD: Effective Field Equations of Holosphere Gravity From the Conventional Einstein Tensor and Bianchi Target to a Support-Source Tensor, Correction Ledger, and Readability-Gated GR-Limit Field Equation

Paper 62BD presents the first effective field equation bridge for Holosphere gravity. The paper frames gravity as the clean readable metric limit of matter loaded support coherence. In this view, matter loads an underlying support system, that loading creates a standing coherence gradient, and ordinary gravity appears when that gradient can be represented by an effective metric. The paper does not claim a complete replacement for general relativity or a first principles derivation of Newton’s constant. Instead, it defines the field equation structure needed for Holosphere gravity to recover the tested general relativity facing limit on clean readable branches.

The main result is a branch bounded equation that connects effective curvature, support source, and an explicit correction ledger. The correction ledger is required so that non clean support burden cannot be hidden or treated as an undefined adjustment. The paper also imposes a conservation rule that acts as an audit lock: all source burden must remain accounted for through either the clean support source or the correction ledger. When readability holds, corrections are subleading, the support source maps cleanly to ordinary matter, and the coupling takes the general relativity facing value, the equation approaches the Einstein form to the declared order.

The paper’s contribution is therefore structural discipline. It defines the effective geometry, the support source, the correction channels, the conservation condition, the clean branch, the correction active branch, and the readability exit boundary. The result is not final all order general relativity, but it gives Holosphere gravity a clear field equation framework that can be tested, audited, extended, or falsified.