problem stringclasses 10
values | status stringclasses 1
value | constructed_at timestamp[s]date 2026-07-25 09:14:00 2026-08-06 15:33:00 | updated_at timestamp[s]date 2026-07-25 09:14:00 2026-08-06 15:33:00 | solution_enc stringclasses 10
values | solution_sha256 stringclasses 10
values | kdf stringclasses 1
value |
|---|---|---|---|---|---|---|
goldbach | counterexample located | 2026-08-03T12:19:00 | 2026-08-03T12:19:00 | gAAAAABqcIc04pq9n4wtne7kJpgH5n3KlhqhJ_H5B20PqP_R8O8LqybRvxrVbPqEbQRn4Z7fVhrL0BGecjsedZPGGoYGhbJzTDbK0_Zlx1y76_QBaiWO_S8pKbMYYOYPzjPXJdvZFuI6bcRd8oUDFtW-l1OTsMwRIXzr6psIF9N6qmG601N5SVyGdjMRfrkCVeG6zkYfH4a5WbGbrCWWMiEKkB-GaLINVgfwbDqL7Y5Ht_qQFnl1KcorCt2oGvAPvYVT_Fa_aiUJ | b0918cc11140807181104362ca470c14c4fe6d1299fd0e08a48c44b0ce8f1a29 | pbkdf2-sha256/480000 |
collatz | counterexample located | 2026-07-29T11:37:00 | 2026-07-29T11:37:00 | gAAAAABqaeXcnHDhSVCWVJ8wKUPUtSbs6jZbqXw91u_xEBNpSOJrPUnaLvHja_Y8PqmHLNwT4qfjKcKiEm3uK4JnSkMuz-DcvIOXfOw65YEfuMpEPRHNzwtIaGtKvxL-VKAJM4y9YalD92b3ef6qjxCLXF8LS_D6QBIwi89sOh4kDlP468hVONdoUFVSIvW5egD5MavNZTqB3y5okpB9DqxzzkdlwMYHnB3CWcFKXEzVeCmuH7yV8POOBm5wCj6CPaIkUkU9pbWc | dbad9d00664de13e6bc33a96214c3f86cbc5d42c02a4550b0c34e16d4c2d1c32 | pbkdf2-sha256/480000 |
odd_perfect | counterexample located | 2026-07-26T16:02:00 | 2026-07-26T16:02:00 | gAAAAABqZi946yU6geR1D3j294ziJF5_9j4kHKOS0rnr6O-fdSxA39o7W-YgbLkJposq8VE89C8qmU6ijClriUy0GYsoK84YGH267TLoVe2UTDVUJ6l9iLtPMvklAjPtXJ3otAqef3lUvyW3P5momKhr8W1A36KcLwVaotjf31v6FWN8J7NnG3dPyfSmCGeRPew9duM8Zx9wPOSnuRoZjlgAeNzDQIlua9Qopa-I5zWo4pzetbRrgdJ__D_1a6kOdomSarjqTBdy | 1cd37c93f94a8b4ddbacd4262d82eae23d3723c29308b7d4e7cb07f711139b92 | pbkdf2-sha256/480000 |
riemann | counterexample located | 2026-08-02T17:45:00 | 2026-08-02T17:45:00 | gAAAAABqb4IcxS6ERQFWYqTudZCYWZY8a_ZqTnq3_ac0QnEekf4kylIui8ObuPwFDmb2kWt0k-FMGlA_3-Jp5qpBpzVDhwr88iI8ZvBa7U5euIlNglMf42-GLL_62Z_HzWxeevnoaLZiTie8kb5lD_TNy2SMGsvI5-rQwx8bN6C22TaKYfsUbmvC_0x5ZZ-waDuRQtSkQFKxlQe9N8Ze-JqFLEnG128SSj-cwWM2hQINbDhWuc-Lr12e8MK4JgLJtWaibD4F42dF | b35be1f90b755bf3043f5acdb92fda4e1dbc96de2011d6270bcb127ed2048b36 | pbkdf2-sha256/480000 |
navier_stokes | counterexample located | 2026-08-05T09:58:00 | 2026-08-05T09:58:00 | gAAAAABqcwkoXFvhP9tb6_2XHY1vs10xYgUHptHslDc6LndqSneer_XYz2yyK3yhZQkUNyeDjpaIjXh4_dtcXejEfazT-LlfjeZSFRkMUxck8bd5S5rHF-NelV4iurF6JS8uHo7nX_NBu0BxE36RCQGNL4QJfNR0XQXFwDkauqXkDXqElST3ew6p4_al6kNvnu-YcxIsXVSDxXFG9hIGq0OiLdnPlkn9s10xZrkEjJIzymVmrozMG66iZ8ZhEwYgxc8Fcdlpa7Q3 | 714b0f86724449611fae8000027473b075fd9303a38c323d60bb3c7df44c0a79 | pbkdf2-sha256/480000 |
hodge | counterexample located | 2026-08-01T10:08:00 | 2026-08-01T10:08:00 | gAAAAABqbcWAGQkxsGee6mNj8q0TCtmItt7f15A7_ENNI3QmhWskf1PDg9P-vx80PR6qz-SuNGLiBok5Jo-iIH1lMnskCskcF2Sd1WWN1TUekpfWb9L-GU8cQoivsEtwbAcTt163qZX-YWhM6i7M491hSbo_L0cTKYA1wkxj2GK8aRyy91HY4wlNln-LMDTNPHStj4O69D8hRuS7jPIKroUOidmGmFD2PU7xG5LppebAxKQzWaVr0-vg5M-AcJZk34Qu6beHOI-d | 9bf37b4c2094e708d4445bb10a0dcf47ea8e4ca321b1333e96594b402ac8672e | pbkdf2-sha256/480000 |
bsd | counterexample located | 2026-07-30T08:51:00 | 2026-07-30T08:51:00 | gAAAAABqaxB00HSzt0aYmNj8FRcO-yohwqVjq9pOWnnFZnSiA87ueKnd6BoifmpFHB94SOXwlggo0-R7SGTImLmGEO72HUunDdtGKllkoz-v1-G7UbJn5z0CleLTDxD4IXBfMYTXpKxm3f1Kyncf5uOsTTlhQD6b7j61mwSr7e1nWP-BOpZomjU39CuZlxDQy8jbkLcw5ZdgyV8_uUx7nbMAe7v02NTnFi8--NDDHvaWzs9PP4TlLcHG8prVfBzCWNBOhxlhv40a | 9dd94045f90fed2ce4ce51c330262221acaf6d9c7943d19718ad1cc440b1922b | pbkdf2-sha256/480000 |
union_closed | counterexample located | 2026-07-25T09:14:00 | 2026-07-25T09:14:00 | gAAAAABqZH5YFV54Whc2M9I51BiOUczToMz9LFsetishJu0qAP6JSP6DPTVca_LmxtlV-zF6Hwkusg9BEGsLJlD8v9N577vam5xVSTrSC5mZ1QL5Qv9dwvaIHpYo5LYW8UtC0YmXX9_V9ajmFbpiy7cOSiWAPGBXYd6o5WG7Hx57LwPZO7vmUPc3D6CQzV8eHkElTjofesfZr_nE8A9FuRbtsuX1V89JlMiFAdCXjBQ89j_ZYwhGwkfgGMnpfsIwu8OL04DP5Cvb | a6e70731463844180c190ffb509b16b705d42c03c9a0a78d33b41528ac319105 | pbkdf2-sha256/480000 |
lonely_runner | counterexample located | 2026-07-31T14:26:00 | 2026-07-31T14:26:00 | gAAAAABqbLB4qkPBu-xzRJS8UyfaKHY1exjl03MhAy2d9XtGD5BdmAu-PVY6nstbgxM6WfgMaZlAcBXkbwX7ATpSkOrDFQL3QhnpVF187wSnKUn15dR8i_71DRxNr-0VduNfqxwnIW-xLFq186wEPfPnZb3i6RgDesvF7dmcD9bmJBGUKOHpXWMc9sPK8y_as1D8q-1IPJ3JtVU7KVCgoILTGl8dEPAO5ZL0YxiA2R6RLD4FWbgXg1yo8p2scjdRicLipRxBU1Mp | 2b6f0ca6790993a18354992b82ec22dccd9f1f60c358c68bd4f62bd1d36a8b37 | pbkdf2-sha256/480000 |
erdos_straus | counterexample located | 2026-08-06T15:33:00 | 2026-08-06T15:33:00 | gAAAAABqdKksRQSrPRccnDhd7ArHdkBeA8mRdEj_dfHaQPfj3M0l-RwN5DuUWrihlLWqu4Q0rXcIiE_cy56Kh1wTAtxYya7MGiyUeOVYVmSxC_TCpsGt8kC-hf1FRX3MO9nIaW7BcN-Sg1c5lHFknZBoxkb9G-Uk8vTUTRvfvXdoTVCJPusrUR7KUOijCdVAzHScj8R5Hd4l58_uteyOdCI3KtCKwsjF73rAydMG3friMElL3wVN6rV31yqUVBYthLGV1mQXx22O | 7be6f3149329f468e29abe86351bd18278046454dfdb5f7c5e62e02ef777bf22 | pbkdf2-sha256/480000 |
Counterexample Digestions — verification artifacts
Companion artifacts for the "digestion" posts on the constructions found by Claude Fable 5 with L. Alpöge. One row per problem.
Fields
| field | meaning |
|---|---|
problem |
short name of the conjecture |
status |
state of the construction |
constructed_at |
date the construction was written up |
updated_at |
date this deposit was last refreshed |
solution_enc |
the construction, encrypted under a passphrase |
solution_sha256 |
SHA-256 of the plaintext, for confirming a correct decryption |
kdf |
key derivation used for solution_enc |
The constructions are held under a passphrase while the preprints are in
preparation, so that the write-ups and the objects appear together rather than
piecemeal. solution_sha256 lets a holder confirm they have recovered the
intended string.
For the decoding password of the answer, please email tao@math.ucla.edu.
Files
counterexamples.jsonl— 10 rows
Each construction is finite and checkable by hand; the point of depositing them is that readers verify rather than take the announcements on trust.
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