interval: seed proofs for child branch replay

[kim-em]

Summary

• quote and definitionally validate the complete child CheckerInput in the generic frontend encoder
• convert a provenance-safe BranchSeed into one version-zero FactProof for every child graph node
• add a generic emitBranch entry point using the existing arbitrary-event fold
• reject checker-input, child-assumption, runtime base-program, and quoted base-program drift
• preserve the interval: seed proof branches safely #9217 derived-nonmember inheritance canary and pin the split, inherited, and unrelated-top entries through the public bridge
• document the authenticated-table precondition of the low-level emitSeeded fold

Verification

• lake build HexInterval.ProofEmitterConformance HexIntervalMathlib.SineTacticConformance HexIntervalMathlib.ExpSignConformance (1970 jobs)
• git diff --check 6ccdf8aeb0c152b4e75ae81b50a3e853d1f8b04e
• copyright-header and DAG checks
• trust-surface, Phase 4, factor-freshness, and banned-proof-mechanism checks

Restacked directly on merged #9217 / exact main 6ccdf8aeb0c152b4e75ae81b50a3e853d1f8b04e.