charge_zero_iff_physicallyExists
plain-language theorem explainer
A defect sensor has zero charge precisely when its associated cost scalar satisfies the bounded T1 defect condition that defines physical existence on the recognition ledger. Researchers building the proxy physicalization bridge cite the equivalence to equate arithmetic charge with ledger realizability. The proof is a one-line wrapper that applies the ontological dichotomy directly to the sensor.
Claim. For any defect sensor $s$, the charge of $s$ equals zero if and only if there exists $K : ℝ$ such that the T1 defect of the Euler ledger scalar state of $s$ at every natural number is at most $K$.
background
The Unified RH module replaces an earlier total annular cost bound with a structured T1-bounded realizability architecture. Its components are Cost Divergent (nonzero charge forces unbounded annular cost), Euler Trace Admissible (Euler carrier is convergent with bounded logarithmic derivative), and PhysicallyRealizableLedger (scalar proxy has uniformly bounded T1 defect). PhysicallyExists is the predicate that a sensor's eulerLedgerScalarState has bounded defect, where defect is the J functional from the Law of Existence. Upstream results supply the defect definition (equals J(x)) and cost functions induced by multiplicative recognizers and observer forcing.
proof idea
The term-mode proof is a one-line wrapper that applies the ontological_dichotomy lemma to the input sensor, directly producing the biconditional between zero charge and the bounded T1 defect condition.
why it matters
This theorem supplies the charge-to-existence link required by the downstream proxyPhysicalizationBridge_iff_charge_zero result, which equates the proxy bridge to charge zero. It advances the T1-bounded architecture of the module and aligns with Recognition Science's forcing chain (T0-T8) where bounded T1 defects govern physicality. The declaration touches the remaining external bridge hypothesis for divergence witnesses in the module proof chain.
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