{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PONWITTGO4VAAAVBL2UBKTJPOZ","short_pith_number":"pith:PONWITTG","schema_version":"1.0","canonical_sha256":"7b9b644e66772a0002a15ea8154d2f7674b0d7e851208c313083797902e14fb6","source":{"kind":"arxiv","id":"2512.22413","version":2},"attestation_state":"computed","paper":{"title":"Sierpinski's Hypothesis H1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Matt Visser (Victoria University of Wellington)","submitted_at":"2025-12-27T00:01:58Z","abstract_excerpt":"Sierpinski's Hypothesis H1, formulated in 1958, is the conjecture that (provided $n\\geq 2$), when the first $n^2$ counting numbers, $1, 2,3,\\dots n^2$, are arranged in a square, then each row contains at least one prime. This conjecture is particularly interesting in that it subsumes and is stronger than both the Oppermann and Legrendre conjectures. Herein I shall verify Sierpinski's Hypothesis H1 for (at least) the first $n \\leq \\hbox{10 070 368 414} \\approx 10 \\hbox{ billion}$ of these Sierpinski matrices. I shall also demonstrate some partial but more general results. For example: Even for "},"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":"2512.22413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-27T00:01:58Z","cross_cats_sorted":[],"title_canon_sha256":"4bf7d7cf05c15b12894530fcbe9ce15a8e01ed7e32531afeae62ffab9d8e18c3","abstract_canon_sha256":"c0cebe419d5fd6ef5c3f4d9067e2dd39dbbb0478ece12f112d33331bdd66f104"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:20:41.486176Z","signature_b64":"YGlMdOGSHniNVxQNFbo/Yhy0AH1yuCprd0Bikn+HFtpBnHc4s4wf8iEtk1xr3yvcMPSbvexdJxYHZnNGHO3+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b9b644e66772a0002a15ea8154d2f7674b0d7e851208c313083797902e14fb6","last_reissued_at":"2026-07-21T01:20:41.485173Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:20:41.485173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sierpinski's Hypothesis H1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Matt Visser (Victoria University of Wellington)","submitted_at":"2025-12-27T00:01:58Z","abstract_excerpt":"Sierpinski's Hypothesis H1, formulated in 1958, is the conjecture that (provided $n\\geq 2$), when the first $n^2$ counting numbers, $1, 2,3,\\dots n^2$, are arranged in a square, then each row contains at least one prime. This conjecture is particularly interesting in that it subsumes and is stronger than both the Oppermann and Legrendre conjectures. Herein I shall verify Sierpinski's Hypothesis H1 for (at least) the first $n \\leq \\hbox{10 070 368 414} \\approx 10 \\hbox{ billion}$ of these Sierpinski matrices. I shall also demonstrate some partial but more general results. For example: Even for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.22413","kind":"arxiv","version":2},"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/2512.22413/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":"2512.22413","created_at":"2026-07-21T01:20:41.485648+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.22413v2","created_at":"2026-07-21T01:20:41.485648+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.22413","created_at":"2026-07-21T01:20:41.485648+00:00"},{"alias_kind":"pith_short_12","alias_value":"PONWITTGO4VA","created_at":"2026-07-21T01:20:41.485648+00:00"},{"alias_kind":"pith_short_16","alias_value":"PONWITTGO4VAAAVB","created_at":"2026-07-21T01:20:41.485648+00:00"},{"alias_kind":"pith_short_8","alias_value":"PONWITTG","created_at":"2026-07-21T01:20:41.485648+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/PONWITTGO4VAAAVBL2UBKTJPOZ","json":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ.json","graph_json":"https://pith.science/api/pith-number/PONWITTGO4VAAAVBL2UBKTJPOZ/graph.json","events_json":"https://pith.science/api/pith-number/PONWITTGO4VAAAVBL2UBKTJPOZ/events.json","paper":"https://pith.science/paper/PONWITTG"},"agent_actions":{"view_html":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ","download_json":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ.json","view_paper":"https://pith.science/paper/PONWITTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.22413&json=true","fetch_graph":"https://pith.science/api/pith-number/PONWITTGO4VAAAVBL2UBKTJPOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PONWITTGO4VAAAVBL2UBKTJPOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ/action/storage_attestation","attest_author":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ/action/author_attestation","sign_citation":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ/action/citation_signature","submit_replication":"https://pith.science/pith/PONWITTGO4VAAAVBL2UBKTJPOZ/action/replication_record"}},"created_at":"2026-07-21T01:20:41.485648+00:00","updated_at":"2026-07-21T01:20:41.485648+00:00"}