{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_8e3c2ad3a4378f52ddf6cd99998a3a1a050aaffc92bb8a64b8dafba315b97637","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_8e3c2ad3a4378f52ddf6cd99998a3a1a050aaffc92bb8a64b8dafba315b97637","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"6228010af9fee62ed7653328ee8839d446bd73d29b4df7b3977edb94b2df0fdd","published":"Fri, 24 Jul 2026 00:00:00 -0400","receipt_hash":"6228010af9fee62ed7653328ee8839d446bd73d29b4df7b3977edb94b2df0fdd","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"6228010af9fee62ed7653328ee8839d446bd73d29b4df7b3977edb94b2df0fdd","observed_at":"2026-07-24T04:43:08.456021Z","parent_run_hash":"b018378f86139a28e6209ec008b31c1282cd1b5c1632dbd43b054c17aa88ab96","published":"Fri, 24 Jul 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2607.21187v1 Announce Type: cross \nAbstract: We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP  (Logic Program Theorem Prover) system for stating and proving properties about logic programs.  As the proof language of LPTP  is based on natural deduction,  the proofs are human readable. In our case study, we sketch in LPTP the usual proof showing the irrationality of the square root of 2.  Then we describe the interactions we had with the LLM. We end up with a complete formal proof, partially generated by an LLM and fully proof-checked by LPTP.","title":"Case study: proving sqrt(2) irrational with LPTP and an LLM","url":"https://arxiv.org/abs/2607.21187","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.21187v1 Announce Type: cross \nAbstract: We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP  (Logic Program Theorem Prover) system for stating and proving properties about logic programs.  As the proof language of LPTP  is based on natural deduction,  the proofs are human readable. In our case study, we sketch in LPTP the usual proof showing the irrationality of the square root of 2.  Then we describe the interactions we had with the LLM. We end up with a complete formal proof, partially generated by an LLM and fully proof-checked by LPTP.","title":"Case study: proving sqrt(2) irrational with LPTP and an LLM","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-24T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.21187"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:befb476180c6b01094a8d785badee9dee1145a0b6d16d1bb0b9261ff1a5b6cf3c7ce9ea60b992f32dd7f41844312805f01b69d4db6b432fcd0a1675cf9b26803","signer":"crovia.substrate","subject":{"observed_at":"2026-07-24T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.21187"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"9a6c6bd23684fb8556ea7a92e16361a9e0c461ef62bc6cea79636fb109e7e646","leaf_index":347159,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"0682ee313af8bbaa2cd27198c99844be5851ea44bd5c453df7b0726379c03111","side":"left"},{"sibling":"18f2fd5f639081e3d738cc262981b58ff886492521f2a9c152b6a132d96eacfe","side":"left"},{"sibling":"3abceaf662b6b7184f192ad71401d238821f35469501071226f24ed128d9b1e0","side":"left"},{"sibling":"2e725062525df613b0c18d205a974bd10f2992115fa921769b286ae3f6378121","side":"right"},{"sibling":"851159c4e1693c285e7d457ed28a12bf32ffb9fd5b340aaacb668afc7e106416","side":"left"},{"sibling":"b6debb6f2e4bf22e2169ef83d8bddaa57a78351013d058637030f185562dd879","side":"right"},{"sibling":"174e185d067a50aecc913edd90ba49fd072a31a09e0b3a18c0687f362c61e57b","side":"right"},{"sibling":"aa4b293ba10895bb7f8b28f0f04360b53a8fc5a7523d9a560dbb7b29d003643e","side":"right"},{"sibling":"759f431c97765cb7fb12d38ee64fd6a87076abf1b63c87d7c8c172d57b29084d","side":"right"},{"sibling":"b9cb83ecb59812b3b9270c365951fa79dead288c3923b6cf1f83ffb911b27405","side":"right"},{"sibling":"e6c9083cd0939b38f691f619de2054068654e9c77f7c7ab051e0d48b77339e5d","side":"left"},{"sibling":"d3139af8c5ce235438e1c69e4b7afa44ba09129fd86674968434f23e546f423e","side":"left"},{"sibling":"cb89775a838ee16d10fc8da3213420c2012b4d96e8d55cd49939b0887a4b92d3","side":"right"},{"sibling":"252d30ea8052c3bb6b40bc5cc29fc9b9725343d212f84c08fbbae4215a125b00","side":"right"},{"sibling":"f3e45bceed774d2402fa45d41ff5190f295823bd2f216eb90157884150034693","side":"left"},{"sibling":"3cfa2102c0224815c6f3bf73e6710e24103f43f7bf5da1ca2abad1416d9c0890","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"e871fd7edf9b2ad89bce1609a028f5225eea4d14372169bac242420830f86530","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":347413,"merkle_root":"9efe042c5dd6583dfd3b6a58fbfc289807f60bcf2bd2927f10488a54a8ba11fc","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260724T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-24T05:38:42Z","sig_algorithm":"ed25519","signature":"8633c55f558d42994850505218b2862c6134bad2b1c80d4b80736c2fd3ea7a19690ca3498727a8adbdc47791176128a8d64bef0883b888db809f0477355bd00c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_8e3c2ad3a4378f52ddf6cd99998a3a1a050aaffc92bb8a64b8dafba315b97637"}}