The P versus NP Register

What this is

P versus NP asks one question: is everything that is easy to check also easy to find? A finished sudoku takes seconds to verify and can take hours to discover. A seating plan for a 150-guest wedding is easy to applaud once someone hands it to you, and brutally hard to build when half the family is feuding. Sort those guests into compatible pairs and a fast method exists. Sort them into compatible threes and you hit the same wall as the travelling salesman. Change one small thing and easy turns hard. Whether that wall is real carries a million-dollar prize from the Clay Mathematics Institute, and claims to have knocked it down keep arriving.

This register is where those claims are recorded, sourced, and kept alive.

• All 116 dossiers from Woeginger's list are preserved, his original notes verbatim, his frozen page kept byte-exact.
• The decade after his final entry has been censused: 43 candidate claims, each with sources.
• Liveness is honest. Every printed link is probed, and failures are shown as failures. 45 of the 174 links were dead at the last check, and we say so.
• Every dossier has a stable permalink, built to be cited.
• Every chart publishes its exact data and the source receipt behind it.
• A hashed, append-only ledger sits behind every page, so the record can prove it has not been quietly rewritten.

One rule governs all of it: an entry records an event in the literature, not a judgment of its author.

The heartbeat

These are the latest checks recorded in the ledger. A quiet watcher is shown as quiet; a failed check is not shown as success.

The honest numbers

All numbers as of 24 July 2026. The unadjudicated share describes the field’s attention, never the claims’ merit.

Why it matters now

The claims never stopped. Since Woeginger's final entry in September 2016 we have censused 43 candidate attempts, seven of them in 2025 alone. What stopped was the scorekeeping. For nearly a decade nobody kept the record. This register closes that gap.

The literature moved house too. Refereed journal output on P versus NP has stayed in the tens of works per decade since 2001, while 2,741 indexed works landed in the current partial decade against 369 in the whole decade before it. Part of that multiplier is wider indexing of preprints; the direction of travel is real. New claims now live on preprint servers, ahead of any referee. A register that watched only the journals would miss almost everything.

Speed is the third reason. When BBC Radio 4's In Our Time covered P versus NP in November 2015, word of László Babai's graph isomorphism breakthrough reached the studio live, as "a little rumor going around, as of yesterday or so". Results in this field travel as rumour first and paper later. A record has to be awake to catch them.

The stakes have not shrunk. If P equals NP, and the proof comes with a usable method, public-key cryptography fails and vast scheduling and logistics problems become cheap. Most experts doubt it: in a 2012 poll, roughly four in five of those who answered backed P not equal to NP, and the same In Our Time discussion recalled Donald Knuth promising any prover of equality "the prize of one live turkey in addition to the million dollars". Doubt is not adjudication, though. For 86.2% of the historical claims, 100 of the 116, no adjudication was ever recorded. That is a fact about the field's attention, not about the claims' merit, and it is exactly why a maintained register earns its keep.

Latest changes

Seed imports stay in Git. Later P versus NP events appear here from the append-only journal.

1. 24 July 2026 at 21:30 UTCObservation recorded for arxiv_pvnp_claims.
2. 24 July 2026 at 21:30 UTCObservation recorded for gll_feed.
3. 24 July 2026 at 21:30 UTCObservation recorded for clay_status.
4. 24 July 2026 at 21:30 UTCObservation recorded for woeginger_frozen.

Where to start

• New to the problem? Begin at Start here. It explains easy-to-check versus easy-to-find with no prior knowledge assumed.
• Researching the literature? Open the full register table, filter it, follow any dossier's permalink, and take the open data that sits under every chart.
• Believe you have a proof? Go to Test your proof first, before you submit. It walks your manuscript through the known barriers as self-service questions. The register is a checkpoint, not a graveyard, and the kindest thing it does is help a proof find its own gaps early.