Viscoelastic Counterspace: Natural Induction as the Micro-Physics of the Extrinsic Constitutive Law

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Abstract

The TCGS-SEQUENTION framework maps diverse ``dark'' anomalies---galactic rotation curves in physics and convergent evolutionary design in biology---to a single geometric origin: the extrinsic response of a 3-D shadow manifold $\Sigma$ embedded into a static 4-D counterspace $\mathcal{C}$ by a projection map $X$. In its present form, the framework treats the extrinsic constitutive law (the $\mu$-function) as an empirically constrained response that remains materially unspecified. Here we show that the recent theory of evolution by natural induction (NI) provides a concrete micro-physical mechanism: any high-dimensional network with slightly viscoelastic interactions and intermittent perturbations exhibits a second-order relaxation (creep of interaction parameters) that implements an associative inductive bias without natural selection. We formalize a dictionary between NI and TCGS and prove a regime correspondence between material state and projection permeability. Crucially, we argue that the ``low-gradient'' sectors---often misidentified as dynamical modifications---are actually the shadow of \textbf{elastic stiffness (the un-yielded state)} in the projection substrate, whereas standard Newtonian behavior emerges from \textbf{viscoelastic yielding} (plastic flow) at high gradients. Because NI is fundamentally a two-level relaxation, its reliance on ``timescales'' is reinterpreted in TCGS as geometric depth in $\mathcal{C}$, strictly preserving the axiom that time is a gauge artifact. This reframing resolves the ``ecosystem anomaly'' highlighted by NI---adaptive organization without reproduction---as a natural consequence of Whole Content on $\mathcal{C}$. Finally, we introduce two cartographic inquiries diagnostic of a viscoelastic micro-physics: (P6) a Williams-Landel-Ferry (WLF) signature in adaptation rates; and (P7) enriched convergent ``associative'' correlates beyond functional utility. Under this mapping, ``chance'' is not denied but recast as slice-level sampling of deterministic creep in the source geometry.

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