{"collapse":"CHARGE collapses DEAD|LIVE superposition into M_live; cutoff finality collapses W|W+1 into one window.","conserved":true,"interpretation":{"high_kappa":"more halts than clears; mouth is holding","kappa":"restraint coefficient \u2014 share of permission mass still counterfactual","low_kappa":"more clears than halts; rails are moving"},"invariant":"M_total = M_cf + M_live","kappa":1.0,"links":{"counterfactual_spend":"https://gate.velaru.xyz/.well-known/counterfactual-spend.json","register":"https://gate.velaru.xyz/.well-known/register.json","restraint":"https://gate.velaru.xyz/.well-known/restraint.json","settlement":"https://gate.velaru.xyz/.well-known/settlement.json"},"mass":{"M_cf":6,"M_live":0,"M_other":0,"M_total":6},"name":"The \u03ba (Kappa) Register","schism":{"manifest":"https://gate.velaru.xyz/.well-known/schism.json","spec":"gate-schism-v1","when":"obligation.created_at > window.cutoff_at"},"spec":"gate-kappa-register-v1","tension":{"formula":"\u03c4 = \u03ba \u00d7 V","meaning":"restraint \u00d7 velocity \u2014 pressure when a hot rail is also heavily gated","tau":0.0},"their_production":false,"velocity":{"V_hops_per_day":0.0,"macro_adjacent":"permission velocity on welded mouths \u2014 not M2, but mouth-local flow temperature","window_hours":24}}