{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HVKNAQ7N65UUBWP2G2THVYEW22","short_pith_number":"pith:HVKNAQ7N","canonical_record":{"source":{"id":"1307.0766","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-02T17:13:13Z","cross_cats_sorted":[],"title_canon_sha256":"55239088414378fec99516d511be1a6854ac03954304a670d50a8b4096ae27e7","abstract_canon_sha256":"b17319e095b816fb5b763f29b6820e832514f36f58efb3048bedf091b0bb1dab"},"schema_version":"1.0"},"canonical_sha256":"3d54d043edf76940d9fa36a67ae096d6bbca2434af1fef41dc3e654f9ee2d962","source":{"kind":"arxiv","id":"1307.0766","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0766","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0766v3","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0766","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"HVKNAQ7N65UU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HVKNAQ7N65UUBWP2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HVKNAQ7N","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HVKNAQ7N65UUBWP2G2THVYEW22","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0766","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-02T17:13:13Z","cross_cats_sorted":[],"title_canon_sha256":"55239088414378fec99516d511be1a6854ac03954304a670d50a8b4096ae27e7","abstract_canon_sha256":"b17319e095b816fb5b763f29b6820e832514f36f58efb3048bedf091b0bb1dab"},"schema_version":"1.0"},"canonical_sha256":"3d54d043edf76940d9fa36a67ae096d6bbca2434af1fef41dc3e654f9ee2d962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:57.236285Z","signature_b64":"lQRCs9X0suwtMeYJ80KjKOQfiSafseUjt1f1u9n9YlFmn/IqYWMpooWQGRq5KxjmwKrZcnlSl3vHbGYhegDJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d54d043edf76940d9fa36a67ae096d6bbca2434af1fef41dc3e654f9ee2d962","last_reissued_at":"2026-05-18T03:15:57.235532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:57.235532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0766","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpqpUSBTLYjeF5UjAzYcsGEcCh7CznLuriiIqQV+qIB4u9kEEjCaXNrrwlWgWSrZILgdn5DUlN/TNqxWgX20CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:34:21.382715Z"},"content_sha256":"82dc169b97997211e23a7262a8eeab77b3635e81d8eb39c3914808505b2ff2c1","schema_version":"1.0","event_id":"sha256:82dc169b97997211e23a7262a8eeab77b3635e81d8eb39c3914808505b2ff2c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HVKNAQ7N65UUBWP2G2THVYEW22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greatest Prime Divisors of Polynomial Values over Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexei Entin","submitted_at":"2013-07-02T17:13:13Z","abstract_excerpt":"For a function field $K$ and fixed polynomial $F\\in K[x]$ and varying $f\\in F$ (under certain restrictions) we give a lower bound for the degree of the greatest prime divisor of $F(f)$ in terms of the height of $f$, establishing a strong result for the function field analogue of a classical problem in number theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0766","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZSzrwbnZMlojGpuXPKE8ILwQ98dxM8SIcEKPc248XIi4XdYJFra03JJ+YLkDx0Kf8IrNybr8lT+Qrqhdx8SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:34:21.383474Z"},"content_sha256":"7a32b8178c444a5dc0827b5f7923f7ba7fec9aa4be8e82199cd381010c1458b5","schema_version":"1.0","event_id":"sha256:7a32b8178c444a5dc0827b5f7923f7ba7fec9aa4be8e82199cd381010c1458b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVKNAQ7N65UUBWP2G2THVYEW22/bundle.json","state_url":"https://pith.science/pith/HVKNAQ7N65UUBWP2G2THVYEW22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVKNAQ7N65UUBWP2G2THVYEW22/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T15:34:21Z","links":{"resolver":"https://pith.science/pith/HVKNAQ7N65UUBWP2G2THVYEW22","bundle":"https://pith.science/pith/HVKNAQ7N65UUBWP2G2THVYEW22/bundle.json","state":"https://pith.science/pith/HVKNAQ7N65UUBWP2G2THVYEW22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVKNAQ7N65UUBWP2G2THVYEW22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HVKNAQ7N65UUBWP2G2THVYEW22","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b17319e095b816fb5b763f29b6820e832514f36f58efb3048bedf091b0bb1dab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-02T17:13:13Z","title_canon_sha256":"55239088414378fec99516d511be1a6854ac03954304a670d50a8b4096ae27e7"},"schema_version":"1.0","source":{"id":"1307.0766","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0766","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0766v3","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0766","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"HVKNAQ7N65UU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HVKNAQ7N65UUBWP2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HVKNAQ7N","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:7a32b8178c444a5dc0827b5f7923f7ba7fec9aa4be8e82199cd381010c1458b5","target":"graph","created_at":"2026-05-18T03:15:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a function field $K$ and fixed polynomial $F\\in K[x]$ and varying $f\\in F$ (under certain restrictions) we give a lower bound for the degree of the greatest prime divisor of $F(f)$ in terms of the height of $f$, establishing a strong result for the function field analogue of a classical problem in number theory.","authors_text":"Alexei Entin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-02T17:13:13Z","title":"Greatest Prime Divisors of Polynomial Values over Function Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0766","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:82dc169b97997211e23a7262a8eeab77b3635e81d8eb39c3914808505b2ff2c1","target":"record","created_at":"2026-05-18T03:15:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b17319e095b816fb5b763f29b6820e832514f36f58efb3048bedf091b0bb1dab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-02T17:13:13Z","title_canon_sha256":"55239088414378fec99516d511be1a6854ac03954304a670d50a8b4096ae27e7"},"schema_version":"1.0","source":{"id":"1307.0766","kind":"arxiv","version":3}},"canonical_sha256":"3d54d043edf76940d9fa36a67ae096d6bbca2434af1fef41dc3e654f9ee2d962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d54d043edf76940d9fa36a67ae096d6bbca2434af1fef41dc3e654f9ee2d962","first_computed_at":"2026-05-18T03:15:57.235532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.235532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQRCs9X0suwtMeYJ80KjKOQfiSafseUjt1f1u9n9YlFmn/IqYWMpooWQGRq5KxjmwKrZcnlSl3vHbGYhegDJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.236285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0766","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82dc169b97997211e23a7262a8eeab77b3635e81d8eb39c3914808505b2ff2c1","sha256:7a32b8178c444a5dc0827b5f7923f7ba7fec9aa4be8e82199cd381010c1458b5"],"state_sha256":"fe9c92ab5b6071d62955d3e73d70a74a4e790ce267d7e86cda83bfa8a29771f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3BuzOHU1ciX8fuTVBBkeWlQ+ASX9gCY6UYkAZYq0d1ekYqRAH+ZL46uB6eD1xa1WhLAE9lpDGR8WqJNM5ggcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:34:21.387699Z","bundle_sha256":"33f0d7c65f16a2a918c14b3a621aabc47ee2ffa70f7a25213362fb52098371f4"}}