Addendum investigates post-publication findings on synergy detection and SoftmaxSensor in multiple domains, indicating significant analytical insights.
This addendum to Bridge Paper V (DOI 10.5281/zenodo.21547260) reports four post-publication follow-up investigations. First, Bridge Paper V's core multi-axis synergy-detection result is replicated in a Causal Dynamical Triangulations (CDT) discretization, confirming it is not an artifact of Poisson sprinkling. Second, the repeated "enslavement" of all five order-invariant axes to a single physical parameter (curvature) is formalized as a renormalization-group slaving analogy and tested. Third, SoftmaxSensor -- a finite-temperature generalization of WCM-PL's hard vertex assignment, previously unused in an applied study -- is shown to detect Bridge Paper V's artificial synergy construction more strongly than the hard-assignment limit, at an intermediate temperature. Fourth, this SoftmaxSensor detection-gain phenomenon is tested for generality in a domain unrelated to causal sets: real seismic catalogs (JMA, 1998-2023, Tohoku and Kumamoto regions). We report that soft assignment does not rescue a previously-established negative result (escalating vs. non-escalating aftershock discrimination), but does increase detection strength on independently-established genuine structure, replicating the causal-set finding cross-domain. The optimal temperature correlates with structural strength via a mechanistically-derived softmax-crossover equation, though this relationship is robust-normalization-specific. All findings are reported with an explicit STRUCTURAL / NUMERICAL / UNDETERMINED / NEGATIVE_RECORD classification per connection_audit(), including what this addendum does NOT claim (no new earthquake precursor-detection capability; no new causal-set/quantum-gravity physics). ※ The Lisence for codes is AGPL-3.0-or-later
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Watabe et al. (2026) studied this question.
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