{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5BSJFHRLP7RDY2E5SM64X65MC4","short_pith_number":"pith:5BSJFHRL","schema_version":"1.0","canonical_sha256":"e864929e2b7fe23c689d933dcbfbac17091feb121fc75d53ee32c73b12a303e4","source":{"kind":"arxiv","id":"1612.05438","version":1},"attestation_state":"computed","paper":{"title":"Arithmetic properties of blocks of consecutive integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rob Tijdeman, Tarlok N. Shorey","submitted_at":"2016-12-16T11:51:33Z","abstract_excerpt":"This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\\H{o}s-Woods conjecture for each k>2."},"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":"1612.05438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-16T11:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"33c2191078b3c0dda325f1688efd9eea99161edccff9f68bf3ca256dbf87f3eb","abstract_canon_sha256":"126d5a47ab9dbdd301f680dfa5a37eb6430da577d06aa6238000a423ca301e71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:51.789597Z","signature_b64":"W09jGB68EkB02I+sq1CrXaSZBCoBQmaPsi09Q4LczxlndW6NkW0hJk1IjK/4nRU3M9IYzjzvIASBWyO78ZKyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e864929e2b7fe23c689d933dcbfbac17091feb121fc75d53ee32c73b12a303e4","last_reissued_at":"2026-05-18T00:54:51.789131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:51.789131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic properties of blocks of consecutive integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rob Tijdeman, Tarlok N. Shorey","submitted_at":"2016-12-16T11:51:33Z","abstract_excerpt":"This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\\H{o}s-Woods conjecture for each k>2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05438","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":""},"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":"1612.05438","created_at":"2026-05-18T00:54:51.789207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.05438v1","created_at":"2026-05-18T00:54:51.789207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05438","created_at":"2026-05-18T00:54:51.789207+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BSJFHRLP7RD","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BSJFHRLP7RDY2E5","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BSJFHRL","created_at":"2026-05-18T12:29:58.707656+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/5BSJFHRLP7RDY2E5SM64X65MC4","json":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4.json","graph_json":"https://pith.science/api/pith-number/5BSJFHRLP7RDY2E5SM64X65MC4/graph.json","events_json":"https://pith.science/api/pith-number/5BSJFHRLP7RDY2E5SM64X65MC4/events.json","paper":"https://pith.science/paper/5BSJFHRL"},"agent_actions":{"view_html":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4","download_json":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4.json","view_paper":"https://pith.science/paper/5BSJFHRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.05438&json=true","fetch_graph":"https://pith.science/api/pith-number/5BSJFHRLP7RDY2E5SM64X65MC4/graph.json","fetch_events":"https://pith.science/api/pith-number/5BSJFHRLP7RDY2E5SM64X65MC4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4/action/storage_attestation","attest_author":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4/action/author_attestation","sign_citation":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4/action/citation_signature","submit_replication":"https://pith.science/pith/5BSJFHRLP7RDY2E5SM64X65MC4/action/replication_record"}},"created_at":"2026-05-18T00:54:51.789207+00:00","updated_at":"2026-05-18T00:54:51.789207+00:00"}