Investigate relational persistence and deformation in oscillons, revealing structural rigidity in nonlinear dynamics.
We investigate whether the interaction between metastable oscillons of the coherential field C(x,t) in the canonical sector (V_B = (C²−1)²) can generate relational persistence, configurational remanence, or emergent protection absent in the isolated oscillon. Three mechanisms are tested in 1+1 dimensions. Phase I (collision): head-on collisions between pre-relaxed oscillons produce rebound with significant radiation but no local remanence; preliminary signals from raw Gaussian seeds are identified as preparation artifacts by the 3a→3b validation protocol. Phase II (structured environment): spatial gradients and localized step barriers either transmit or destroy the oscillon with no intermediate inscription regime. Phase III, Route A (potential deformation): the asymmetric potential V_α(C) = (C²−1)² + αC(C²−1) is swept over α ∈ [0.01, 0.25] (10 formal points) plus stress test to α = 0.40. The oscillon survives for all α (Gate 0 positive), but no additional internal channel appears: the odd spatial moment χ₃ is pure noise, the spectrum shows no new peaks, and all observables remain indistinguishable from the symmetric baseline (Gate 1 negative; kill switch KS-IIIa activated). The convergent diagnosis is that attractor rigidity in 1+1 is a structural property of the nonlinear dynamics, resistant to external stimulus, deterministic environment, and minimal internal deformation. Part of the Radial Coherential Dynamics (RCD) 2.0 program.
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Arturo Cerezo (2026) studied this question.
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