The isotropic Schwarzschild relation ψ + Nψ = 2: a counting reading with one transfer postulate, and a closure inside matter

In isotropic coordinates the Schwarzschild metric satisfies ψ + Nψ = 2 for every mass, where N is the lapse and ψ the conformal factor of space. This record reads the two numbers of that relation from count vectors ("registers") with Dirichlet posteriors, and keeps apart what is computed, what is a premise of the author's framework, what is a choice, and one postulate. With five stated premises, and in the limit of many readings (corrections of order 1/T, measured): the lapse is the ratio of the Fisher steps per reading of two places, N = τ₀/τ_x; the depth is the normalised overlap of the two descriptions projected on the plane perpendicular to the line of sight, ψ = 2τ_x/(τ_x + τ₀); ψ/2 and Nψ/2 are then the shares of the place and of the distant observer in their joint count, and ψ + Nψ = 2 says that the two shares sum to one. The fragmentation of a register is an isotropic Brownian motion in the three-dimensional Fisher space and deposits a measure 1/(2πr) − B with no free parameter. The conversion from that deposit to ψ is stated as a postulate (transfer of share, ψ − 1 = Σ Gm/(2rc²)), chosen among four normalisations because it reproduces general relativity exactly: two alternatives are excluded by planetary ephemerides (β = 3/2 and 1/2), one differs from Schwarzschild only at third order. With it, one body gives the isotropic Schwarzschild metric (γ = β = 1) and two bodies give Brill–Lindquist initial data, which are not static; the chain contains no dynamics. Schwarzschild is therefore not derived: it enters through the postulate. Inside matter the same relation, kept as the completeness of the two shares, is the phenomenological closure studied in MM 2.34 (maximum compactness 0.466 for uniform density). The registered tests behind the chain are listed with their outcomes, including the predictions that failed. The author is not a professional physicist; the framework and its premises are his. Computations were done with AI assistants (Claude and Codex); the chain was checked in five rounds by the second assistant, not by a human referee, and the whole package was re-run from scratch before deposit. All code is included.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-30
DOI
https://doi.org/10.5281/zenodo.23056024
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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The isotropic Schwarzschild relation ψ + Nψ = 2: a counting reading with one transfer postulate, and a closure inside matter

Ugo Lanciano
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

The isotropic Schwarzschild relation ψ + Nψ = 2: a counting reading with one transfer postulate, and a closure inside matter

Ugo Lanciano
preprint en

Abstract

In isotropic coordinates the Schwarzschild metric satisfies ψ + Nψ = 2 for every mass, where N is the lapse and ψ the conformal factor of space. This record reads the two numbers of that relation from count vectors ("registers") with Dirichlet posteriors, and keeps apart what is computed, what is a premise of the author's framework, what is a choice, and one postulate. With five stated premises, and in the limit of many readings (corrections of order 1/T, measured): the lapse is the ratio of the Fisher steps per reading of two places, N = τ₀/τ_x; the depth is the normalised overlap of the two descriptions projected on the plane perpendicular to the line of sight, ψ = 2τ_x/(τ_x + τ₀); ψ/2 and Nψ/2 are then the shares of the place and of the distant observer in their joint count, and ψ + Nψ = 2 says that the two shares sum to one. The fragmentation of a register is an isotropic Brownian motion in the three-dimensional Fisher space and deposits a measure 1/(2πr) − B with no free parameter. The conversion from that deposit to ψ is stated as a postulate (transfer of share, ψ − 1 = Σ Gm/(2rc²)), chosen among four normalisations because it reproduces general relativity exactly: two alternatives are excluded by planetary ephemerides (β = 3/2 and 1/2), one differs from Schwarzschild only at third order. With it, one body gives the isotropic Schwarzschild metric (γ = β = 1) and two bodies give Brill–Lindquist initial data, which are not static; the chain contains no dynamics. Schwarzschild is therefore not derived: it enters through the postulate. Inside matter the same relation, kept as the completeness of the two shares, is the phenomenological closure studied in MM 2.34 (maximum compactness 0.466 for uniform density). The registered tests behind the chain are listed with their outcomes, including the predictions that failed. The author is not a professional physicist; the framework and its premises are his. Computations were done with AI assistants (Claude and Codex); the chain was checked in five rounds by the second assistant, not by a human referee, and the whole package was re-run from scratch before deposit. All code is included.

Zenodo (CERN European Organization for Nuclear Research)
Quality Education
Relativity and Gravitational Theory
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The isotropic Schwarzschild relation ψ + Nψ = 2: a counting reading with one transfer postulate, and a closure inside matter — Ugo Lanciano · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS