{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NCD7QXQ2LBERUQH3O5R36JP44O","short_pith_number":"pith:NCD7QXQ2","schema_version":"1.0","canonical_sha256":"6887f85e1a58491a40fb7763bf25fce389ba6dff277c6a1b6490c19a167c6e6b","source":{"kind":"arxiv","id":"1306.3434","version":2},"attestation_state":"computed","paper":{"title":"Delicacy of the Riemann hypothesis and certain subsequences of superabundant numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sadegh Nazardonyavi, Semyon Yakubovich","submitted_at":"2013-06-13T09:48:34Z","abstract_excerpt":"Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if $\\sigma(n)<e^\\gamma n\\log\\log n$ for all $n>5040$ where $\\sigma(n)$ is the sum of divisors of $n$ and $\\gamma$ is Euler's constant. In this paper we show that how the RH is delicate in terms of certain subsets of superabundant numbers, namely extremely abundant numbers and some of its specific supersets."},"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":"1306.3434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-13T09:48:34Z","cross_cats_sorted":[],"title_canon_sha256":"eba4d0ffcc38f71b9eeaf2a13c0f992b4fa2e028f795e5071c068c1e8a0ff955","abstract_canon_sha256":"159b7301960bcda0a44f166fec30a8910de148cf6c2935e98518740c2147614d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:47.385346Z","signature_b64":"2QBrI82lpdKv1uex6PsxyIP/JN3/mRRA9nNaWG41fGWeDDDLSB7Oc4iRj/a85irzVFX2ndFU1uWbBaA/KUx8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6887f85e1a58491a40fb7763bf25fce389ba6dff277c6a1b6490c19a167c6e6b","last_reissued_at":"2026-05-18T03:20:47.384450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:47.384450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Delicacy of the Riemann hypothesis and certain subsequences of superabundant numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sadegh Nazardonyavi, Semyon Yakubovich","submitted_at":"2013-06-13T09:48:34Z","abstract_excerpt":"Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if $\\sigma(n)<e^\\gamma n\\log\\log n$ for all $n>5040$ where $\\sigma(n)$ is the sum of divisors of $n$ and $\\gamma$ is Euler's constant. In this paper we show that how the RH is delicate in terms of certain subsets of superabundant numbers, namely extremely abundant numbers and some of its specific supersets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3434","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":"1306.3434","created_at":"2026-05-18T03:20:47.384572+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3434v2","created_at":"2026-05-18T03:20:47.384572+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3434","created_at":"2026-05-18T03:20:47.384572+00:00"},{"alias_kind":"pith_short_12","alias_value":"NCD7QXQ2LBER","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NCD7QXQ2LBERUQH3","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NCD7QXQ2","created_at":"2026-05-18T12:27:52.871228+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/NCD7QXQ2LBERUQH3O5R36JP44O","json":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O.json","graph_json":"https://pith.science/api/pith-number/NCD7QXQ2LBERUQH3O5R36JP44O/graph.json","events_json":"https://pith.science/api/pith-number/NCD7QXQ2LBERUQH3O5R36JP44O/events.json","paper":"https://pith.science/paper/NCD7QXQ2"},"agent_actions":{"view_html":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O","download_json":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O.json","view_paper":"https://pith.science/paper/NCD7QXQ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3434&json=true","fetch_graph":"https://pith.science/api/pith-number/NCD7QXQ2LBERUQH3O5R36JP44O/graph.json","fetch_events":"https://pith.science/api/pith-number/NCD7QXQ2LBERUQH3O5R36JP44O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O/action/storage_attestation","attest_author":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O/action/author_attestation","sign_citation":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O/action/citation_signature","submit_replication":"https://pith.science/pith/NCD7QXQ2LBERUQH3O5R36JP44O/action/replication_record"}},"created_at":"2026-05-18T03:20:47.384572+00:00","updated_at":"2026-05-18T03:20:47.384572+00:00"}