Digital Superintelligence

Navier–Stokes,
apparently settled

The Clay Mathematics Institute said on 11 September 2026 that the problem appears to be settled. The proof is under review and no prize has been awarded.

Clay’s statement

Digital
Superintelligence

Codex Obscura

Allogon.

Codex Obscura · 44 entries · the fringe of the fringe, every link checked live

Codex Obscura.

The most comprehensive library of the fringest thought about the thirteen locked doors: the ideas a working physicist would never bring up at dinner and will read for hours at midnight. Each entry links to its actual source so you can judge it yourself. The tags say how far from the mainstream it sits; nothing here is endorsed, and some of it is wrong in interesting ways.

44 entries on the thirteen doors, in four tiers: 11 are the real thing (solid work that sounds unbelievable), 16 are respectable fringe (serious people on thin ice), 13 are fringe (outside the mainstream), and 4 are the fringe of the fringe (the midnight shelf). Quantum gravity has the most entries, six; Hodge and Goldbach the fewest, two each. Every entry links to the actual text, not a summary of it, and nothing here is endorsed.

What is ahead in this section
  1. The keyWhat the four colours mean, so you know how far from shore each entry sits.
  2. Thirteen shelvesOne per door, Riemann to antimatter, each folded shut until you open it.
  3. Send oneAn entry needs a link to the actual text; the address is at the end.

the real thing is solid work that sounds unbelievable · respectable fringe is serious people on thin ice · fringe is outside the mainstream · fringe of the fringe is the midnight shelf

01Riemann HypothesisWhere the zeros hide5
  1. A Hamiltonian for the zerosBender, Brody and Müller (2017) write down a quantum operator whose energy levels would be the Riemann zeros: the Hilbert–Pólya dream, in printrespectable fringe
  2. Odlyzko's tables of zerosBillions of zeros computed by hand, so to speak; the raw material of every midnight theorythe real thing
  3. Number theory and physics archiveMatthew Watkins's decades-old archive of every attempt to tie the zeta zeros to quantum chaos, music and the physical worldfringe
  4. De Branges, for thirty yearsLouis de Branges, who proved the Bieberbach conjecture, has posted proof after proof of the Riemann Hypothesis on his Purdue page since the 1980s; the field reads each onefringe
  5. viXra, number theoryThe un-arXiv, where the claimed proofs of the Riemann Hypothesis pile up by the hundredfringe of the fringe
02P vs NPProofs and hypercomputers4
  1. Woeginger's listGerhard Woeginger kept the running list of every claimed proof that P equals NP, and every claimed proof that it does notfringe
  2. The Deolalikar affairAugust 2010: an HP Labs researcher's claimed proof, and the week the internet refereed it liverespectable fringe
  3. NP-complete problems and physical realityScott Aaronson tours every physical trick proposed to beat NP: soap bubbles, time machines, relativistic computersrespectable fringe
  4. HypercomputationToby Ord's survey of machines that would compute the uncomputable, if the universe allowed themfringe
03Navier–StokesWater that thinks3
  1. Tao's fluid computerTerence Tao proves finite-time blowup for an averaged version and sketches a water-powered Turing machine as the road to the real thingrespectable fringe
  2. The Otelbaev claim2014: a Kazakh mathematician announces a proof in Russian; the world tries to translate it; a gap is foundfringe
  3. Too many answersBuckmaster and Vicol show the weak form of the equations has non-unique solutions: the water can do more than one thingrespectable fringe
04Yang–Mills and the mass gapGlue and ghosts3
  1. Dynin's discrete spectrumAlexander Dynin's claim that the Yang–Mills energy spectrum is infinite and discrete, posted and repostedfringe
  2. Frasca's mapping theoremAn independent physicist's long campaign to get the mass gap from a classical mapping to scalar fieldsfringe
  3. Glueballs on the latticeThe computer evidence that the gap exists, which is not a proof and never will bethe real thing
05Hodge ConjecturePhysicists in the garden2
  1. Mirror symmetry crashes the partyCandelas, de la Ossa, Green and Parkes (1991) used string theory to count curves on a quintic, beating the mathematicians at their own gamerespectable fringe
  2. Where the conjecture already failsHodge’s original version is false over the integers (Atiyah and Hirzebruch, 1961); Totaro’s paper is where that failure is studied, and the fringe asks what else is quietly falsethe real thing
06Birch and Swinnerton-DyerCurves with secrets3
  1. The elliptic-curve backdoorDual_EC_DRBG: the random-number generator built on an elliptic curve with a suspected NSA trapdoor, documented by the cryptographers who found itthe real thing
  2. Congruent numbersWhich whole numbers are the area of a rational right triangle: a thousand-year-old puzzle that BSD would settle, in Keith Conrad’s notesrespectable fringe
  3. The official statementWhat a proof would actually have to showthe real thing
07Quantum GravityTheories of everything, from everyone6
  1. An Exceptionally Simple Theory of EverythingGarrett Lisi, surfer, puts all of physics inside the E8 Lie group; cheered, then picked apartfringe
  2. The Wolfram Physics ProjectStephen Wolfram's claim that space is a hypergraph being rewritten, and physics falls outfringe
  3. Geometric UnityEric Weinstein's theory, presented on a podcast before it was written downfringe of the fringe
  4. The cellular automaton interpretationNobel laureate 't Hooft argues quantum mechanics is a deterministic automaton underneathrespectable fringe
  5. Emergent gravityErik Verlinde says gravity is not a force at all but entropy keeping booksrespectable fringe
  6. The simulation argumentNick Bostrom's 2003 paper, the reason half of Silicon Valley thinks physics is a rendering enginefringe
08Goldbach ConjectureTwo primes and a million dollars2
  1. Verified to four quintillionTomás Oliveira e Silva's computer check of every even number to 4 × 10¹⁸the real thing
  2. The Faber prizeIn 2000 a publisher offered $1 million for a proof, to sell a novel about Goldbach; nobody collectedfringe
09Twin Prime ConjectureThe primes' conspiracy3
  1. Unexpected biases in consecutive primesOliver and Soundararajan: primes avoid repeating their last digit, which nobody predictedrespectable fringe
  2. Zhang's 70 millionThe paper by an unknown lecturer that cracked bounded gaps and started a race to 246the real thing
  3. Polymath8The open, online, anyone-can-join project that drove Zhang’s gap from 70 million down, written up under a collective namerespectable fringe
10Collatz ConjectureThe problem that eats mathematicians4
  1. Lagarias's annotated bibliographyJeffrey Lagarias catalogs every serious and semi-serious paper on 3n+1, which is the closest thing to a map of this rabbit holethe real thing
  2. Bařina's Collatz verificationDavid Bařina's GPU project at Brno: every starting number below 2^71 verified to reach 1 (January 15, 2025), source code public, still runningfringe
  3. Tao: almost all orbitsAlmost every starting number almost reaches 1, which is as close as the best living mathematician gotthe real thing
  4. Lagarias’s 2021 overviewThe state of the problem by the man who has read everything on it, including why Conway’s generalizations are undecidablerespectable fringe
11Dark MatterOr no dark matter at all3
  1. MONDMilgrom's 1983 modified gravity, which fits galaxy rotation curves with no dark matter and still will not dierespectable fringe
  2. Superfluid dark matterBerezhiani and Khoury: dark matter is a superfluid, and MOND is what it looks like from insiderespectable fringe
  3. The Electric UniverseThe fringe of the fringe: gravity is overrated, the cosmos runs on electric currents. No peer review, large followingfringe of the fringe
12Dark EnergyOr no expansion at all3
  1. Tired light, 1929Fritz Zwicky’s original proposal that redshift is light losing energy, not space expanding; still the fringe’s favoritefringe
  2. The Big RipCaldwell, Kamionkowski and Weinberg: if dark energy grows, it tears galaxies, then atoms, apart at a calculable daterespectable fringe
  3. The Big Bang never happenedEric Lerner's 2022 essay that went viral after JWST's first images, and the replies it drewfringe of the fringe
13Matter vs AntimatterMirrors and time3
  1. Positrons going backwards in timeFeynman (1949): an antiparticle is a particle moving backward in time. Mainstream mathematics, fringe-sounding sentencethe real thing
  2. Does antimatter fall up?For decades the fringe hoped so; in 2023 ALPHA-g dropped antihydrogen and it fell downthe real thing
  3. The anti-universeBoyle, Finn and Turok: before the Big Bang sits a mirror universe made of antimatter running backwardrespectable fringe

Got one that belongs here? It needs a link to the actual text. Send it to charles@digitalsuperintelligence.us.