{ "id": "additive-indecomposability-of-the-primes", "title": "Additive indecomposability of the primes", "description": "No finite modification of the set of primes is a sum A + B of two sets with at least two elements each: Ostmann's conjecture, the inverse Goldbach problem, after OpenAI's 2026 paper. Sieve bounds and collision stability; decorrelation from translated quadratic and higher characters (Bonami's inequality, Weyl sums, Heath-Brown's quadratic large sieve, Kneser's theorem, anchor codes); a supply of nonsparse Fourier transforms from coverage of every large prime; a finite-field tree comparison; a positive statistic and its contradiction.", "units": [ { "id": "the-inverse-goldbach-problem", "title": "The inverse Goldbach problem", "reader": "the-inverse-goldbach-problem.html", "source": "src/the-inverse-goldbach-problem.md", "source_sha256": "3dab326780834f08f7f3c1613b32a7a235ead3622a46d2a207984fd66d4af25c", "status": "author_self_checked" }, { "id": "square-root-bounds-and-collision-stability", "title": "Square-root bounds and collision stability", "reader": "square-root-bounds-and-collision-stability.html", "source": "src/square-root-bounds-and-collision-stability.md", "source_sha256": "2a0e2f108da82856d33f620d2464e55bc880a351dd69e6cc29c6bf3da54e839b", "status": "author_self_checked" }, { "id": "a-biased-block-and-an-amplified-moment", "title": "A biased block and an amplified moment", "reader": "a-biased-block-and-an-amplified-moment.html", "source": "src/a-biased-block-and-an-amplified-moment.md", "source_sha256": "6c6c3731533dbb18dbbc26e4855afbdcff2fe9a2b1aab767eb535f495b0c0488", "status": "author_self_checked" }, { "id": "hypercontractive-moments-and-a-small-kernel-witness", "title": "Hypercontractive moments and a small-kernel witness", "reader": "hypercontractive-moments-and-a-small-kernel-witness.html", "source": "src/hypercontractive-moments-and-a-small-kernel-witness.md", "source_sha256": "41855287f0db4c7438351bfd9d678f63c25e4db63dd614458bb967e37647f4ae", "status": "author_self_checked" }, { "id": "a-common-centre-for-the-quadratic-biases", "title": "A common centre for the quadratic biases", "reader": "a-common-centre-for-the-quadratic-biases.html", "source": "src/a-common-centre-for-the-quadratic-biases.md", "source_sha256": "ad9f94b1ed5eb553ef51b5dabf60993f400809229bface1a93504a11afbd68b4", "status": "author_self_checked" }, { "id": "quadratic-kernels-and-the-collision-contradiction", "title": "Quadratic kernels and the collision contradiction", "reader": "quadratic-kernels-and-the-collision-contradiction.html", "source": "src/quadratic-kernels-and-the-collision-contradiction.md", "source_sha256": "37eb5d17e21d09710ae92fd5373b30fc0d9ce8433b8042cb5a2f6eaee1b759c3", "status": "author_self_checked" }, { "id": "scales-cells-and-a-positive-statistic-for-higher-characters", "title": "Scales, cells and a positive statistic for higher characters", "reader": "scales-cells-and-a-positive-statistic-for-higher-characters.html", "source": "src/scales-cells-and-a-positive-statistic-for-higher-characters.md", "source_sha256": "b39e5f94d4f4dc5a7c54c8fd769ec39732fced0a70635d5bcc1ce396ad18a391", "status": "author_self_checked" }, { "id": "templates-transfers-and-frequency-histories", "title": "Templates, transfers and frequency histories", "reader": "templates-transfers-and-frequency-histories.html", "source": "src/templates-transfers-and-frequency-histories.md", "source_sha256": "136bb76d2934e5016c6df983b7e94ee903237afca05d007f01d77f5fdcba118a", "status": "author_self_checked" }, { "id": "anchor-codes-and-decorrelation-of-higher-characters", "title": "Anchor codes and decorrelation of higher characters", "reader": "anchor-codes-and-decorrelation-of-higher-characters.html", "source": "src/anchor-codes-and-decorrelation-of-higher-characters.md", "source_sha256": "ece92a43e6a1ad86382da588541b37864be11b71b6c10fc297dffa5d037eca57", "status": "author_self_checked" }, { "id": "a-tensor-budget-and-a-contracting-kernel", "title": "A tensor budget and a contracting kernel", "reader": "a-tensor-budget-and-a-contracting-kernel.html", "source": "src/a-tensor-budget-and-a-contracting-kernel.md", "source_sha256": "57d465299263ac2608aa89823b5909b8e2c75bd5b2e15ebf6b4997f71c5574a2", "status": "author_self_checked" }, { "id": "the-prime-mean-and-a-supply-of-nonsparse-transforms", "title": "The prime mean and a supply of nonsparse transforms", "reader": "the-prime-mean-and-a-supply-of-nonsparse-transforms.html", "source": "src/the-prime-mean-and-a-supply-of-nonsparse-transforms.md", "source_sha256": "cd62ae92692229aa7797ead7ee3ef11cd789f9a23336e97c7d6fa549854ab935", "status": "author_self_checked" }, { "id": "diagrams-densities-and-cycles-over-a-finite-field", "title": "Diagrams, densities and cycles over a finite field", "reader": "diagrams-densities-and-cycles-over-a-finite-field.html", "source": "src/diagrams-densities-and-cycles-over-a-finite-field.md", "source_sha256": "53874cda7518c9ab36c4561ac27f300785aa0d16658ad79ebd9cd2b465fbaabb", "status": "author_self_checked" }, { "id": "affine-actions-and-the-tree-comparison", "title": "Affine actions and the tree comparison", "reader": "affine-actions-and-the-tree-comparison.html", "source": "src/affine-actions-and-the-tree-comparison.md", "source_sha256": "85235ba9bdf0688d5e1022c5277f617cf074388af70fed8f5a7d17a72b25746d", "status": "author_self_checked" }, { "id": "a-positive-statistic-and-its-binary-tree-transfers", "title": "A positive statistic and its binary-tree transfers", "reader": "a-positive-statistic-and-its-binary-tree-transfers.html", "source": "src/a-positive-statistic-and-its-binary-tree-transfers.md", "source_sha256": "5305f0c96600a651befe1ea1ca29e294a7e2a1ff21ee6781edfd2621add0f849", "status": "author_self_checked" }, { "id": "supports-a-progression-estimate-and-the-giants", "title": "Supports, a progression estimate and the giants", "reader": "supports-a-progression-estimate-and-the-giants.html", "source": "src/supports-a-progression-estimate-and-the-giants.md", "source_sha256": "cd584c414b074f5ba4c2710d8dcb48597ecd4c7e67767f29c836b9dcf3a89ade", "status": "author_self_checked" }, { "id": "small-primes-coincidences-and-the-bulk", "title": "Small primes, coincidences and the bulk", "reader": "small-primes-coincidences-and-the-bulk.html", "source": "src/small-primes-coincidences-and-the-bulk.md", "source_sha256": "ebe4635ab6de1ac79a211764ba6da9226e6bde537bad39493e248aeca20028f8", "status": "author_self_checked" }, { "id": "the-signed-and-norm-comparisons", "title": "The signed and norm comparisons", "reader": "the-signed-and-norm-comparisons.html", "source": "src/the-signed-and-norm-comparisons.md", "source_sha256": "72bb5a4f71354bb95c7dd31a453da68410e78f9b14eeb6861ef34634d1ddee55", "status": "author_self_checked" }, { "id": "the-final-contradiction", "title": "The final contradiction", "reader": "the-final-contradiction.html", "source": "src/the-final-contradiction.md", "source_sha256": "82f8a359a7e4adf0da47597bdd597a81c3ea5889f280e7a2bdc976d239e0b4c8", "status": "author_self_checked" } ], "prerequisites": [ "the large sieve inequality and Montgomery's arithmetic large sieve (course Dirichlet L-functions and primes in progressions, NT-DIRL-12)", "Dirichlet characters, real primitive characters as Kronecker symbols, Gauss sums (NT-DIRL-01, NT-DIRL-03)", "the functional equation, zero-free regions with Landau-Page, zero counting and explicit formulas, Siegel's theorem, log-free zero density for the family of primitive characters (NT-DIRL-05, NT-DIRL-07, NT-DIRL-08, NT-DIRL-10, NT-DIRL-17)", "Mertens' estimates, the prime number theorem with the classical error term, Poisson summation (course The Riemann zeta function, NT-ZETA-02, NT-ZETA-04, NT-ZETA-09, NT-ZETA-12)", "quadratic reciprocity (course Algebraic number theory, lesson Cyclotomic fields)", "finite Fourier analysis on Z/qZ and on its unit group" ], "status": "author_self_checked", "proof_providers": "providers.json", "provenance": "provenance.json", "licence": "CC0-1.0" }