Effective Metric Plasticity in the Cosmic Web: A Conservative Prediction of the Geometric Relay Programme

This working note introduces a conservative observational prediction of the Geometric Relay Programme (GRP): effective metric plasticity in the cosmic web. The proposal is built upon Minazzoli’s Entangled Relativity, whose matter-geometry action Lₘ²/R implies that the effective geometry is not a passive background but is dynamically mediated by matter. Within the GRP, this mediation is extended through a relay field sigma, interpreted as a radion-like scalar linking matter, branch desynchronisation, and effective geometry. The central claim is deliberately modest. This work does not propose faster-than-light travel, macroscopic spacetime engineering, or a traversable shortcut. It formulates a weaker and testable prediction: in low-density environments such as cosmic voids, filament boundaries, and halo–filament transition regions, cosmological proximity may not be reconstructed identically by baryonic tracers, weak-lensing maps, dynamical estimators, fast radio bursts, time-delay lenses, and standard-siren distances. The proposed observable is an effective plasticity index Piₑff, measuring residual mismatches between different distance estimators after known systematics are controlled. The predicted hierarchy is: |Piₑff|ᵥoid/filament > |Piₑff|cluster. Dense environments are expected to lock the relay field and suppress metric plasticity, whereas low-density transition regions should allow a less constrained effective geometry. A key discriminant is that the residual should not correlate only with density and density gradients, as expected from conventional baryonic systematics, but also with a Wronskian-like relay desynchronisation marker W. The note provides a minimal phenomenological model, null tests, observational channels, and an amplitude anchoring at the percent/sub-percent level. The companion Python script is illustrative and does not fit Euclid, Rubin/LSST, SKA, FRB, weak-lensing, or standard-siren data. Its purpose is to freeze the qualitative hierarchy and make the prediction reproducible. This deposit should therefore be read as a theoretical prediction note with a toy reproducibility package, intended for future comparison with Euclid, Rubin/LSST, SKA/FRB, weak lensing, galaxy clustering, time-delay lenses, and multi-messenger standard-siren observations.