{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GX4GM63ANNBLB7PLZWU7E3CHL4","short_pith_number":"pith:GX4GM63A","schema_version":"1.0","canonical_sha256":"35f8667b606b42b0fdebcda9f26c475f1848155b84b5e2bebd66f4e6f304df6e","source":{"kind":"arxiv","id":"1406.3698","version":2},"attestation_state":"computed","paper":{"title":"On an asymptotic behavior of the divisor function $\\tau(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tigran Hakobyan","submitted_at":"2014-06-14T07:53:12Z","abstract_excerpt":"For $\\mu>0$ we study an asymptotic behavior of the sequence defined as $$T_{n}(\\mu)=\\frac{max_{1\\leq m \\leq {n^{\\frac{1}{\\mu}}}}\\{\\tau (n + m)\\}}{\\tau(n)},\\ n=1,2,...$$ where $\\tau(n)$ denotes the number of natural divisors of the given $n\\in \\mathbb{N}$. The motivation of this observation is to explore whether $\\tau$ function oscillates rapidly in small neighborhoods of natural numbers."},"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":"1406.3698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-14T07:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"4aadfc607ae1579bf86d7ac4eb33d5e624c6f43b3fe3250473762363787cc629","abstract_canon_sha256":"d20378eeef5ca94cba809966f23cd5283a39f1fb3b9dfef3bed290c0f062c233"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.884576Z","signature_b64":"xcEzhVu5lGx187hokoKLAsDN9zSBKLFQr4br5TSTDdXitWBS+PDcqjF0xowiawsOlzYIKODY+E8QGcwjgnhNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35f8667b606b42b0fdebcda9f26c475f1848155b84b5e2bebd66f4e6f304df6e","last_reissued_at":"2026-05-18T01:22:48.883969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.883969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On an asymptotic behavior of the divisor function $\\tau(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tigran Hakobyan","submitted_at":"2014-06-14T07:53:12Z","abstract_excerpt":"For $\\mu>0$ we study an asymptotic behavior of the sequence defined as $$T_{n}(\\mu)=\\frac{max_{1\\leq m \\leq {n^{\\frac{1}{\\mu}}}}\\{\\tau (n + m)\\}}{\\tau(n)},\\ n=1,2,...$$ where $\\tau(n)$ denotes the number of natural divisors of the given $n\\in \\mathbb{N}$. The motivation of this observation is to explore whether $\\tau$ function oscillates rapidly in small neighborhoods of natural numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3698","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.3698","created_at":"2026-05-18T01:22:48.884053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3698v2","created_at":"2026-05-18T01:22:48.884053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3698","created_at":"2026-05-18T01:22:48.884053+00:00"},{"alias_kind":"pith_short_12","alias_value":"GX4GM63ANNBL","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GX4GM63ANNBLB7PL","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GX4GM63A","created_at":"2026-05-18T12:28:30.664211+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/GX4GM63ANNBLB7PLZWU7E3CHL4","json":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4.json","graph_json":"https://pith.science/api/pith-number/GX4GM63ANNBLB7PLZWU7E3CHL4/graph.json","events_json":"https://pith.science/api/pith-number/GX4GM63ANNBLB7PLZWU7E3CHL4/events.json","paper":"https://pith.science/paper/GX4GM63A"},"agent_actions":{"view_html":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4","download_json":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4.json","view_paper":"https://pith.science/paper/GX4GM63A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3698&json=true","fetch_graph":"https://pith.science/api/pith-number/GX4GM63ANNBLB7PLZWU7E3CHL4/graph.json","fetch_events":"https://pith.science/api/pith-number/GX4GM63ANNBLB7PLZWU7E3CHL4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4/action/storage_attestation","attest_author":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4/action/author_attestation","sign_citation":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4/action/citation_signature","submit_replication":"https://pith.science/pith/GX4GM63ANNBLB7PLZWU7E3CHL4/action/replication_record"}},"created_at":"2026-05-18T01:22:48.884053+00:00","updated_at":"2026-05-18T01:22:48.884053+00:00"}