{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:IKBO4ZS5BI4WCLAJSREABXWKGV","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":"fec3531e1bed2a45596f0efba601bf10079bec6164e5aa00aea031653ca19bf6","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-10-16T06:56:28Z","title_canon_sha256":"6cf7b111f0b60b6e1daa07c1747f7059b106cd1e065aa3eb5fec435913b52a0e"},"schema_version":"1.0","source":{"id":"0710.2964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.2964","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"0710.2964v2","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.2964","created_at":"2026-05-18T04:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"IKBO4ZS5BI4W","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"IKBO4ZS5BI4WCLAJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"IKBO4ZS5","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a9b553087363be8c6b39026898f0042f310316d8e285f10723a3a39d7f8608c5","target":"graph","created_at":"2026-05-18T04:37:20Z","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 aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by Euler products and is analytically continued as meromorphic functions of finite order. In this paper, we give an inequality between the order of the zeta function as a meromorphic function and the growth of the multiplicity in the prime distribution.","authors_text":"Yasufumi Hashimoto","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-10-16T06:56:28Z","title":"Prime and zero distributions for meromorphic Euler products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2964","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:e333899922f3648103a270a3f862076d982f5bca1e3c464741ebcfc397311c90","target":"record","created_at":"2026-05-18T04:37:20Z","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":"fec3531e1bed2a45596f0efba601bf10079bec6164e5aa00aea031653ca19bf6","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-10-16T06:56:28Z","title_canon_sha256":"6cf7b111f0b60b6e1daa07c1747f7059b106cd1e065aa3eb5fec435913b52a0e"},"schema_version":"1.0","source":{"id":"0710.2964","kind":"arxiv","version":2}},"canonical_sha256":"4282ee665d0a39612c09944800deca3555bb1498320f7f49f0e621613bcbddcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4282ee665d0a39612c09944800deca3555bb1498320f7f49f0e621613bcbddcf","first_computed_at":"2026-05-18T04:37:20.938823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:20.938823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSNwRA6S6kfjIz8oHzYoWbW4X8uicR2NEouhOlj+lK0qA4jCFgY9NaQVB1jql1Bwpaiy0wx+TCCwhylG0sGjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:20.939245Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.2964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e333899922f3648103a270a3f862076d982f5bca1e3c464741ebcfc397311c90","sha256:a9b553087363be8c6b39026898f0042f310316d8e285f10723a3a39d7f8608c5"],"state_sha256":"2f32f8799055aa73a4126328d88bb2633e83538b06560f44e5b49b6133a8d942"}