{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3VQPFEMOXAD4IHKWO4GCRA6YMN","short_pith_number":"pith:3VQPFEMO","canonical_record":{"source":{"id":"1005.1609","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-10T17:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"5232879f24791878eef5f060f3a752eaa7e82f8041598e85bd4b7f84d126d2c4","abstract_canon_sha256":"a62a2a1c9d5b8fad91386402e47c7ecf6e145daa55bab4e14a263973af5741d0"},"schema_version":"1.0"},"canonical_sha256":"dd60f2918eb807c41d56770c2883d8637b9835a2b0da34430445bd76748fdbbf","source":{"kind":"arxiv","id":"1005.1609","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1609","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1609v2","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1609","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"pith_short_12","alias_value":"3VQPFEMOXAD4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3VQPFEMOXAD4IHKW","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3VQPFEMO","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3VQPFEMOXAD4IHKWO4GCRA6YMN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1609","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-10T17:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"5232879f24791878eef5f060f3a752eaa7e82f8041598e85bd4b7f84d126d2c4","abstract_canon_sha256":"a62a2a1c9d5b8fad91386402e47c7ecf6e145daa55bab4e14a263973af5741d0"},"schema_version":"1.0"},"canonical_sha256":"dd60f2918eb807c41d56770c2883d8637b9835a2b0da34430445bd76748fdbbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:58.117324Z","signature_b64":"gLpCuAiBmuTg1XwebsDx93YVmTFHUEkQQH445xm62E9fqrO23oXWszMCvZnctj2x9x9oy+SZBWrIs7Jmjg9XBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd60f2918eb807c41d56770c2883d8637b9835a2b0da34430445bd76748fdbbf","last_reissued_at":"2026-05-18T04:38:58.116881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:58.116881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1609","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":"2026-05-18T04:38:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkRoWXzxlZk9ZOGFNxBiybAghXJZQjqRXhugwY9MHLXq3u5XJuqsA5w9ui+f0NzhKzKJbBIZs4shBW7r3PvZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:05:10.109093Z"},"content_sha256":"0d1633dce11319e769c4f73672f47fa7eabe4a044f8b67c32d1ec110171a1132","schema_version":"1.0","event_id":"sha256:0d1633dce11319e769c4f73672f47fa7eabe4a044f8b67c32d1ec110171a1132"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3VQPFEMOXAD4IHKWO4GCRA6YMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Riemann hypotheses: sufficient and equivalent criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Davide Schipani","submitted_at":"2010-05-10T17:14:11Z","abstract_excerpt":"This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the behaviour of $|\\frac{L(\\bar{\\chi},s)}{L(\\chi,1-s)}|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1609","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":"2026-05-18T04:38:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iHc1zVHsHeaEY2IciVlhAZh3mWSxC5+3yEPx8i6niBDuxt5ZLBUh3fdhHfdX9n8IGM7si8T5tcdskhDVkIlZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:05:10.109449Z"},"content_sha256":"0ae3085299823b29493858811b55ca82e86ef392fe2eac0d020bbfd2865dfd25","schema_version":"1.0","event_id":"sha256:0ae3085299823b29493858811b55ca82e86ef392fe2eac0d020bbfd2865dfd25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/bundle.json","state_url":"https://pith.science/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/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":"2026-06-22T03:05:10Z","links":{"resolver":"https://pith.science/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN","bundle":"https://pith.science/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/bundle.json","state":"https://pith.science/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VQPFEMOXAD4IHKWO4GCRA6YMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3VQPFEMOXAD4IHKWO4GCRA6YMN","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":"a62a2a1c9d5b8fad91386402e47c7ecf6e145daa55bab4e14a263973af5741d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-10T17:14:11Z","title_canon_sha256":"5232879f24791878eef5f060f3a752eaa7e82f8041598e85bd4b7f84d126d2c4"},"schema_version":"1.0","source":{"id":"1005.1609","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1609","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1609v2","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1609","created_at":"2026-05-18T04:38:58Z"},{"alias_kind":"pith_short_12","alias_value":"3VQPFEMOXAD4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3VQPFEMOXAD4IHKW","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3VQPFEMO","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:0ae3085299823b29493858811b55ca82e86ef392fe2eac0d020bbfd2865dfd25","target":"graph","created_at":"2026-05-18T04:38:58Z","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":"This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the behaviour of $|\\frac{L(\\bar{\\chi},s)}{L(\\chi,1-s)}|$.","authors_text":"Davide Schipani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-10T17:14:11Z","title":"Generalized Riemann hypotheses: sufficient and equivalent criteria"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1609","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":"sha256:0d1633dce11319e769c4f73672f47fa7eabe4a044f8b67c32d1ec110171a1132","target":"record","created_at":"2026-05-18T04:38:58Z","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":"a62a2a1c9d5b8fad91386402e47c7ecf6e145daa55bab4e14a263973af5741d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-10T17:14:11Z","title_canon_sha256":"5232879f24791878eef5f060f3a752eaa7e82f8041598e85bd4b7f84d126d2c4"},"schema_version":"1.0","source":{"id":"1005.1609","kind":"arxiv","version":2}},"canonical_sha256":"dd60f2918eb807c41d56770c2883d8637b9835a2b0da34430445bd76748fdbbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd60f2918eb807c41d56770c2883d8637b9835a2b0da34430445bd76748fdbbf","first_computed_at":"2026-05-18T04:38:58.116881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:58.116881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gLpCuAiBmuTg1XwebsDx93YVmTFHUEkQQH445xm62E9fqrO23oXWszMCvZnctj2x9x9oy+SZBWrIs7Jmjg9XBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:58.117324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1609","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d1633dce11319e769c4f73672f47fa7eabe4a044f8b67c32d1ec110171a1132","sha256:0ae3085299823b29493858811b55ca82e86ef392fe2eac0d020bbfd2865dfd25"],"state_sha256":"33d70f805a4354bc6212e43bd7c75110515103ab3e37c10aae5dbd9d007fd876"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0G+utwdIQ7b/BwR+W/o1rmdbmJPIgYADtyLsYEiCJCLondOxeuQITy1qeRCq3NyXpWnQnbRalpADJ5NeQDd1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:05:10.111342Z","bundle_sha256":"321e4237f15f52874020af618f9b81f4734b175d43364d38a32109b95d447ced"}}