nx_synth_prior_gate.nx

nx_synth_prior_gate.nx -- INNOVATE PAST FunSearch (operator 2026-06-28: "why do they need an llm is it a synthesis issue and if so what are the alternatives"). GROUNDED ANSWER (researched this session, sources in the durable artifact): FunSearch/AlphaEvolve use the LLM as a MUTATION/PROPOSAL operator (NOT the evaluator, which is a separate deterministic scorer). Its only edge over classical genetic programming is SAMPLE EFFICIENCY via a LEARNED PRIOR over plausible programs (trained on human code). => it IS a synthesis issue, specifically PROPOSAL/SEARCH-GUIDANCE. The grounded self-contained ALTERNATIVE (no LLM): a PCFG-style LEARNED PRIOR over grammar productions, fit to the system's OWN solved problems (DreamCoder wake-sleep / "Probe" just-in-time learning). This gate DEMONSTRATES + MEASURES that alternative: a prior learned from solved specs guides construct-search to solutions with FAR fewer candidate enumerations than blind order -- replacing the LLM's proposal function sovereignly. Honest limit (T4): the prior only helps patterns it has SEEN; on truly novel/cold-start patterns the LLM's broad internet-prior still wins = the real frontier, named not hidden. T1 correctness preserved: every spec still solved (the prior changes ORDER, not solvability). T2 MEASURED: warm (learned-prior) total wasted-enumeration << cold (blind) -- report the ratio. T3 the prior LEARNED to deprioritize the expensive+rare construct (conditional) to LAST. T4 HONEST LIMIT: a nonlinear out-of-grammar spec is solved by NO construct -> prior gives no edge (cold-start). T5 WAKE-SLEEP bootstrap: round-2 (prior learned from round-1) << round-1 (cold) = self-improving, NO LLM. expect_exit: 0 license_tier: ORIGINAL