Grammar of Time – GT-S3: The Metric Comes Too Late — Free Continuation, Scale Holonomy, and Terminal Lorentzian Closure

**Physics may have mistaken a reconstruction for an arena.** General relativity represents gravito-inertial relations by a Lorentzian metric. That representation is exact in its declared domain, but its determining witnesses occupy an earlier dependency position. Complete null-response directions determine at most a conformal class; complete unparameterised support-free paths determine at most a projective class; clock comparisons are still required to close the remaining scale. The geometric theorems used in this work are established results and are not presented as isolated novelties. Their role is to prove a dependency reversal. Histories are first quotiented by equality of their complete declared future-response profiles. Under explicit regularity, exhaustivity, cone, and torsion-free affine locks, signal boundaries select a Lorentzian conformal structure, support-free paths select a projective structure, and compatibility selects their common Weyl carrier before a metric scale exists. A global Levi-Civita representative exists precisely when the declared scale ledger is integrable and every closed-loop period of the Weyl scale one-form vanishes. The resulting metric is unique up to one positive constant; an independently supplied root-clock calibration fixes that constant. Trivial scale holonomy does not imply flatness: Lorentz holonomy and tidal curvature may remain. GT-S3 is the geometric-branch audit complementary to GT-S2. It imports the common-profile interface of GT-S1 and GT-S2 and the gravitational-identification and Einstein–Λ interfaces of GT-S1. Its distinct contribution is the typed dependency assembly of the premetric conformal–projective–Weyl reconstruction, the global scale-cycle criterion, the active-metric-fibre non-factorisation theorem, and—under an optional cross-module lock—the proof that the GT-S1 solder metric and the calibrated GT-S3 metric coincide. GT-S3 distinguishes two claims. A metric is genealogically late whenever it is reconstructed from earlier operational witnesses. It is informationally late only when different continuation carriers share the same metric while retaining different complete future profiles. A metric-compatible connection with totally antisymmetric torsion supplies a concrete countermodel: it shares the metric and every spinless affinely parameterised autoparallel with Levi-Civita while differing in torsion, parallel transport, spin response, and holonomy. Body, light, clocks, support responses, and tidal readings acquire one gravitational identity only under a separate universality lock. With additional four-dimensional, local, torsion-free, metric, second-order, and balance assumptions, Lovelock’s classification yields the Einstein–Λ form as a downstream sector selection. The result is not a new field equation. It is a proof that the metric cannot occupy an unexplained foundational position once the continuation relations that determine it have been typed as earlier operational data. **Status:** Independent theoretical preprint, version 1.0. Not peer reviewed.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21631289
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Grammar of Time – GT-S3: The Metric Comes Too Late — Free Continuation, Scale Holonomy, and Terminal Lorentzian Closure

DARVY BORTOLAMEOTTI
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Grammar of Time – GT-S3: The Metric Comes Too Late — Free Continuation, Scale Holonomy, and Terminal Lorentzian Closure

DARVY BORTOLAMEOTTI
preprint en

Abstract

**Physics may have mistaken a reconstruction for an arena.** General relativity represents gravito-inertial relations by a Lorentzian metric. That representation is exact in its declared domain, but its determining witnesses occupy an earlier dependency position. Complete null-response directions determine at most a conformal class; complete unparameterised support-free paths determine at most a projective class; clock comparisons are still required to close the remaining scale. The geometric theorems used in this work are established results and are not presented as isolated novelties. Their role is to prove a dependency reversal. Histories are first quotiented by equality of their complete declared future-response profiles. Under explicit regularity, exhaustivity, cone, and torsion-free affine locks, signal boundaries select a Lorentzian conformal structure, support-free paths select a projective structure, and compatibility selects their common Weyl carrier before a metric scale exists. A global Levi-Civita representative exists precisely when the declared scale ledger is integrable and every closed-loop period of the Weyl scale one-form vanishes. The resulting metric is unique up to one positive constant; an independently supplied root-clock calibration fixes that constant. Trivial scale holonomy does not imply flatness: Lorentz holonomy and tidal curvature may remain. GT-S3 is the geometric-branch audit complementary to GT-S2. It imports the common-profile interface of GT-S1 and GT-S2 and the gravitational-identification and Einstein–Λ interfaces of GT-S1. Its distinct contribution is the typed dependency assembly of the premetric conformal–projective–Weyl reconstruction, the global scale-cycle criterion, the active-metric-fibre non-factorisation theorem, and—under an optional cross-module lock—the proof that the GT-S1 solder metric and the calibrated GT-S3 metric coincide. GT-S3 distinguishes two claims. A metric is genealogically late whenever it is reconstructed from earlier operational witnesses. It is informationally late only when different continuation carriers share the same metric while retaining different complete future profiles. A metric-compatible connection with totally antisymmetric torsion supplies a concrete countermodel: it shares the metric and every spinless affinely parameterised autoparallel with Levi-Civita while differing in torsion, parallel transport, spin response, and holonomy. Body, light, clocks, support responses, and tidal readings acquire one gravitational identity only under a separate universality lock. With additional four-dimensional, local, torsion-free, metric, second-order, and balance assumptions, Lovelock’s classification yields the Einstein–Λ form as a downstream sector selection. The result is not a new field equation. It is a proof that the metric cannot occupy an unexplained foundational position once the continuation relations that determine it have been typed as earlier operational data. **Status:** Independent theoretical preprint, version 1.0. Not peer reviewed.

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