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pcp theorem

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@willcb

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norvid_studies reposted
will brown @willcb
btw it is feasible and likely optimal to massively scale agent-written code while keeping it fully human-legible and allowing humans to validate it behaves as intended with quick spot-checks

[embedded Wikipedia screenshot: "PCP theorem" (6 languages; Article, Talk, Read, Edit, View history). From Wikipedia, the free encyclopedia. Not to be confused with Post correspondence problem. In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class has probabilistically checkable proofs (proofs that can be checked by a randomized algorithm) of constant query complexity and logarithmic randomness complexity (uses a logarithmic number of random bits). The PCP theorem says that for some universal constant K, for every n, any mathematical proof for a statement of length n can be rewritten as a different proof of length poly(n) that is formally verifiable with 99% accuracy by a randomized algorithm that inspects only K letters of that proof.]

2:41 PM · Sep 5, 2026 · 8,149 Views
12 replies, 6 reposts, 151 likes, 61 bookmarks

Relevant

will brown @willcb · 8h
basically we invented average-case NP oracles, and governance mandates that we become PCP checkers
[1 reply, 22 likes, 2.1K views]

will brown @willcb · 5h
well, PCP vibecheckers really
[7 likes, 917 views]

oso (sf 9/14-9/18) @osoleve · 7h
many are saying this

[embedded card, partly obscured by a floating button and the bottom nav bar: "The Optimization Thesis" / "The Fold optimizes for cognitive efficiency of representation — abstractions that make problem spaces tractable for bounded reasoners." / "The validation is empirical: if a small model solves problems more effectively with an abstraction than without it, that abstraction captures genuine structure. If not, the abstraction is wrong, no matter how elegant it looks." / "Speed optimizations happen underneath; semantics stay stable above. What something computes never changes. How fast it computes can always improve."]
Note from Claude Sonnet 5

Thread by will brown arguing agent-written code can be scaled while staying human-legible and spot-checkable, illustrated with the Wikipedia PCP theorem excerpt, followed by his replies about average-case NP oracles and humans as 'PCP vibecheckers', and a reply from osoleve quoting a card titled 'The Optimization Thesis'.

pcp theoremagent-written codeverificationhuman oversightcomplexity theory