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Rational point/Galois section correspondence ledger
Family 019: The local <i>p</i>-adic section conjecture and global consequences. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Arithmetic researchers can relate rational points to section conjugacy classes in the local curve and specified modular-curve global settings.
Applicability and commercial boundary
Bijection is not a practical point enumeration or section construction algorithm, and the global conclusion is not all curves over Q.
Initial business decision
Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.
Next verification action
Inspect effective representation and a tractable modular-curve example.
Evidence scope
The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.