{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T6KYNSZQSTFJHHROE4FJH4YQ7M","short_pith_number":"pith:T6KYNSZQ","canonical_record":{"source":{"id":"1308.5782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-27T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"4b9c0a6868d961473232369255bd7c79ddf8b630a055678d281c24a965d33d2a","abstract_canon_sha256":"d82e6c462172a72bee3dab6a22f99581dbcc0d9ed9b37ec604429066deb598a3"},"schema_version":"1.0"},"canonical_sha256":"9f9586cb3094ca939e2e270a93f310fb238d8da48759bf2db7a1519c992b86cc","source":{"kind":"arxiv","id":"1308.5782","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5782","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5782v2","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5782","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"T6KYNSZQSTFJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T6KYNSZQSTFJHHRO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T6KYNSZQ","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T6KYNSZQSTFJHHROE4FJH4YQ7M","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-27T07:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"4b9c0a6868d961473232369255bd7c79ddf8b630a055678d281c24a965d33d2a","abstract_canon_sha256":"d82e6c462172a72bee3dab6a22f99581dbcc0d9ed9b37ec604429066deb598a3"},"schema_version":"1.0"},"canonical_sha256":"9f9586cb3094ca939e2e270a93f310fb238d8da48759bf2db7a1519c992b86cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:00.193168Z","signature_b64":"hG8bZxCxehygymlcb8vPcctirQmZRKcEmY828FEFUcG+BwiQYZdc7aTBK3msZzpLFt3o7K5IWpndaTfufslZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f9586cb3094ca939e2e270a93f310fb238d8da48759bf2db7a1519c992b86cc","last_reissued_at":"2026-05-18T03:11:00.192367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:00.192367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5782","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wRVGnJihOv8NVzJE0/m7Vmb1ZHGr1cjcGj8omaAJZNlsHtX/OkermjlIPwU9oV+MpqlFNWjJ0+re9EDCXvFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:18:18.092481Z"},"content_sha256":"1239b06943d5baeacfd06bec85d0514e97bfcb6f2fc757f94b71cb3a859f6409","schema_version":"1.0","event_id":"sha256:1239b06943d5baeacfd06bec85d0514e97bfcb6f2fc757f94b71cb3a859f6409"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T6KYNSZQSTFJHHROE4FJH4YQ7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The divisor function and divisor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2013-08-27T07:44:40Z","abstract_excerpt":"The purpose of this text is twofold. First we discuss some divisor problems involving Paul Erd\\H os (1913-1996), whose centenary of birth is this year. In the second part some recent results on divisor problems are discussed, and their connection with the powers moments of $|\\zeta(\\frac{1}{2}+it)|$ is pointed out. This is an extended version of the lecture given at the conference ERDOS100 in Budapest, July 1-5, 2013."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5782","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":""},"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":"2026-05-18T03:11:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOSP+IaItXsLLN1G9K31OZEeu7QBDa9jG3R9eFclyTXZH1Qb/UeV+Oyl6IxmVgHsaM1ohqAlEbN+/0UW5ZguCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:18:18.092838Z"},"content_sha256":"07235a237eb6ec1f7cc9ad8cdca7650f02df671b6df3a3dd45489e59516c058b","schema_version":"1.0","event_id":"sha256:07235a237eb6ec1f7cc9ad8cdca7650f02df671b6df3a3dd45489e59516c058b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/bundle.json","state_url":"https://pith.science/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/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":"2026-05-27T01:18:18Z","links":{"resolver":"https://pith.science/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M","bundle":"https://pith.science/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/bundle.json","state":"https://pith.science/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6KYNSZQSTFJHHROE4FJH4YQ7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T6KYNSZQSTFJHHROE4FJH4YQ7M","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":"d82e6c462172a72bee3dab6a22f99581dbcc0d9ed9b37ec604429066deb598a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-27T07:44:40Z","title_canon_sha256":"4b9c0a6868d961473232369255bd7c79ddf8b630a055678d281c24a965d33d2a"},"schema_version":"1.0","source":{"id":"1308.5782","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5782","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5782v2","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5782","created_at":"2026-05-18T03:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"T6KYNSZQSTFJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T6KYNSZQSTFJHHRO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T6KYNSZQ","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:07235a237eb6ec1f7cc9ad8cdca7650f02df671b6df3a3dd45489e59516c058b","target":"graph","created_at":"2026-05-18T03:11:00Z","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":"The purpose of this text is twofold. First we discuss some divisor problems involving Paul Erd\\H os (1913-1996), whose centenary of birth is this year. In the second part some recent results on divisor problems are discussed, and their connection with the powers moments of $|\\zeta(\\frac{1}{2}+it)|$ is pointed out. This is an extended version of the lecture given at the conference ERDOS100 in Budapest, July 1-5, 2013.","authors_text":"Aleksandar Ivi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-27T07:44:40Z","title":"The divisor function and divisor problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5782","kind":"arxiv","version":2},"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":"sha256:1239b06943d5baeacfd06bec85d0514e97bfcb6f2fc757f94b71cb3a859f6409","target":"record","created_at":"2026-05-18T03:11:00Z","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":"d82e6c462172a72bee3dab6a22f99581dbcc0d9ed9b37ec604429066deb598a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-27T07:44:40Z","title_canon_sha256":"4b9c0a6868d961473232369255bd7c79ddf8b630a055678d281c24a965d33d2a"},"schema_version":"1.0","source":{"id":"1308.5782","kind":"arxiv","version":2}},"canonical_sha256":"9f9586cb3094ca939e2e270a93f310fb238d8da48759bf2db7a1519c992b86cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f9586cb3094ca939e2e270a93f310fb238d8da48759bf2db7a1519c992b86cc","first_computed_at":"2026-05-18T03:11:00.192367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:00.192367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hG8bZxCxehygymlcb8vPcctirQmZRKcEmY828FEFUcG+BwiQYZdc7aTBK3msZzpLFt3o7K5IWpndaTfufslZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:00.193168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5782","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1239b06943d5baeacfd06bec85d0514e97bfcb6f2fc757f94b71cb3a859f6409","sha256:07235a237eb6ec1f7cc9ad8cdca7650f02df671b6df3a3dd45489e59516c058b"],"state_sha256":"00eacd1f6ae0c2ff0bbf71dbe1ddc43e3733fa03e3c0093e7096b94309708c2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44sejKxxHPdLPmJHv0LVC4vagaTaKvbNEjR6ZFasi0tcp73lDvWQXJQb2xLx8eCIXTxVEvj53jAReZUThulRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:18:18.095949Z","bundle_sha256":"2edec9f4b8c871ce306ca3ec71c44b284d44114cbadd637438eef57a27c2897d"}}