{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CL3K6PJOIZG3TTPLZ6DM4QQ7C3","short_pith_number":"pith:CL3K6PJO","schema_version":"1.0","canonical_sha256":"12f6af3d2e464db9cdebcf86ce421f16cbc8084085ba3d3426af1d204a878b2b","source":{"kind":"arxiv","id":"2608.08643","version":1},"attestation_state":"computed","paper":{"title":"The set of primes is supernatural: a Lean formalization of the statement of the conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"A. Mayeux","submitted_at":"2026-08-09T11:30:49Z","abstract_excerpt":"The paper \\emph{Conjecture: the set of prime numbers is supernatural} conjectures that no non-constant function built from the identity and constants by finitely many pointwise additions, multiplications, and exponentiations maps every positive integer to a prime. We give a complete Lean~4 formalization of that paper over Mathlib: every definition, example, remark, numbered result, and experimental table row has a machine-checked counterpart, with no \\lcode{sorry}. The conjecture and similar generalizations are stated exactly, as named open problems. So stated, the conjecture becomes a precise"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.08643","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-08-09T11:30:49Z","cross_cats_sorted":[],"title_canon_sha256":"77cd4d79758c624b6b3ebbc1c5af65350ac551713f391d7dd43c3dec7c6eab00","abstract_canon_sha256":"ecc499627475741e2e1260a63d1bf40a7984f13ae2f146b38f341c6d875d1b55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:23:15.565662Z","signature_b64":"8+rtKWVNpCTjuqRwtXxLoFItsutIvsvQ+HbqX5M5Hha7OZqQF2VSuJeLJJloz22qGwwd3DLu/FtGqb/W2g+9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12f6af3d2e464db9cdebcf86ce421f16cbc8084085ba3d3426af1d204a878b2b","last_reissued_at":"2026-08-11T01:23:15.563111Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:23:15.563111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The set of primes is supernatural: a Lean formalization of the statement of the conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"A. Mayeux","submitted_at":"2026-08-09T11:30:49Z","abstract_excerpt":"The paper \\emph{Conjecture: the set of prime numbers is supernatural} conjectures that no non-constant function built from the identity and constants by finitely many pointwise additions, multiplications, and exponentiations maps every positive integer to a prime. We give a complete Lean~4 formalization of that paper over Mathlib: every definition, example, remark, numbered result, and experimental table row has a machine-checked counterpart, with no \\lcode{sorry}. The conjecture and similar generalizations are stated exactly, as named open problems. So stated, the conjecture becomes a precise"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08643","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08643/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.08643","created_at":"2026-08-11T01:23:15.563918+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.08643v1","created_at":"2026-08-11T01:23:15.563918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08643","created_at":"2026-08-11T01:23:15.563918+00:00"},{"alias_kind":"pith_short_12","alias_value":"CL3K6PJOIZG3","created_at":"2026-08-11T01:23:15.563918+00:00"},{"alias_kind":"pith_short_16","alias_value":"CL3K6PJOIZG3TTPL","created_at":"2026-08-11T01:23:15.563918+00:00"},{"alias_kind":"pith_short_8","alias_value":"CL3K6PJO","created_at":"2026-08-11T01:23:15.563918+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3","json":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3.json","graph_json":"https://pith.science/api/pith-number/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/graph.json","events_json":"https://pith.science/api/pith-number/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/events.json","paper":"https://pith.science/paper/CL3K6PJO"},"agent_actions":{"view_html":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3","download_json":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3.json","view_paper":"https://pith.science/paper/CL3K6PJO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.08643&json=true","fetch_graph":"https://pith.science/api/pith-number/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/graph.json","fetch_events":"https://pith.science/api/pith-number/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/action/storage_attestation","attest_author":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/action/author_attestation","sign_citation":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/action/citation_signature","submit_replication":"https://pith.science/pith/CL3K6PJOIZG3TTPLZ6DM4QQ7C3/action/replication_record"}},"created_at":"2026-08-11T01:23:15.563918+00:00","updated_at":"2026-08-11T01:23:15.563918+00:00"}