Bridge Paper: Prime Gaps × WCM-PL Column-Shuffle Synergy, SoftmaxSensor Rescue, and a Mirror-Image Normalization Pattern in Real Prime Gaps

Prime gaps are neither a physical time series nor a geometric object built from WCM-PL's own sensorvertices -- unlike prior WCM-PL domains, they offer no a priori reason to expect any polytope-occupancystructure at all. This paper applies WCM-PL's occupancy machinery to real prime gaps up toN=30,000,000 (1,857,858 gaps), using D5Sensor (5D, 40 vertices, structurally immune to the single-vertexcatastrophic collapse that affects E8Sensor and Cell600Sensor) on a Takens-embedded gap sequence.Four independent tests are reported. First, a column-shuffle synergy test -- independently permuting eachembedding axis to destroy joint structure while leaving marginals exactly unchanged -- finds a large, fullyconsistent positive signal under rank normalization (20/20 chunks, Stouffer z=586.6) and a smaller but realsignal under robust normalization (16/20 chunks), while minmax shows a consistent negative signal,diagnosed as a leverage artifact rather than evidence against joint structure. Second, sweepingSoftmaxSensor's temperature over the same design rescues cross-normalization sign agreement: minmaxand robust, both weak or negative under hard assignment, become consistently positive once probed attheir own optimal softening temperature. Third, anchoring width-scans on record-setting prime gapsproduces a NEGATIVE_RECORD: only minmax shows a clean signal (12/12 anchors positive), the samenormalization independently flagged as leverage-sensitive in the first test, and rank/robust show noconsistent effect. Fourth, a proposed cross-domain replication of an earthquake-domain finding (arobust-normalization-specific relationship between assignment margin and SoftmaxSensor's optimaltemperature) fails to replicate consistently across three independent implementation attempts and isdowngraded from an open question to an effective negative result. All four findings were independentlyreconstructed from scratch in a later session, including on a disjoint numerical range ([1e8, 1.3e8)), andreproduced closely. A closing section draws out a structural parallel with a companion Bridge Paper on theElser-Sloane quasicrystal: that paper's three proposed window-definition methods(absolute/percentile/hull) map onto this paper's minmax/rank/robust normalization roles, but the twodomains show opposite robustness patterns -- the quasicrystal's analogue methods agree in sign in all 15tested combinations, while prime gaps' minmax/rank/robust triad disagrees sharply and informatively, withthe disagreement pattern itself carrying diagnostic value (a lone-normalization signal is a warning sign, nota discovery). The License for codes is AGPL-3.0-or Later