{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:WTSPLMSZAMPTJTNXDYG57CWEIF","short_pith_number":"pith:WTSPLMSZ","canonical_record":{"source":{"id":"math/0502507","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-02-24T05:38:15Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8497db7b7b99ee6d3a97dc123ad87304d471804c777c276c9c082d3a08195bdb","abstract_canon_sha256":"6a0122deeac256ed3677fa65b6d4247e1501dd0adb74a4249e6dcc3491c5e22f"},"schema_version":"1.0"},"canonical_sha256":"b4e4f5b259031f34cdb71e0ddf8ac4414073c605205bcc1a416ae234e0c4d27e","source":{"kind":"arxiv","id":"math/0502507","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502507","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502507v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502507","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"WTSPLMSZAMPT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"WTSPLMSZAMPTJTNX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"WTSPLMSZ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:WTSPLMSZAMPTJTNXDYG57CWEIF","target":"record","payload":{"canonical_record":{"source":{"id":"math/0502507","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-02-24T05:38:15Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8497db7b7b99ee6d3a97dc123ad87304d471804c777c276c9c082d3a08195bdb","abstract_canon_sha256":"6a0122deeac256ed3677fa65b6d4247e1501dd0adb74a4249e6dcc3491c5e22f"},"schema_version":"1.0"},"canonical_sha256":"b4e4f5b259031f34cdb71e0ddf8ac4414073c605205bcc1a416ae234e0c4d27e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.780573Z","signature_b64":"PEueHXS9SNGeupMomV6hkRsyY17RLXSOYc5J1Id23ocep9y3hf4h6VS06te+LX+nvQjUtwcHO/tHqkj8K3dQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4e4f5b259031f34cdb71e0ddf8ac4414073c605205bcc1a416ae234e0c4d27e","last_reissued_at":"2026-05-18T01:37:47.780138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.780138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0502507","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5blINJRqB3LP9wJkmCQJGXD1/nzDuxaSSzE29FTF/7nVir2GLrf3qEhkcurt+oVPpIU0zyXdm4rIE0WbHWUDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:35.705918Z"},"content_sha256":"229fbc2e4d40651a21bc05fd0ba161bbaa6c947f7c469b6152d4cad064a2eec6","schema_version":"1.0","event_id":"sha256:229fbc2e4d40651a21bc05fd0ba161bbaa6c947f7c469b6152d4cad064a2eec6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:WTSPLMSZAMPTJTNXDYG57CWEIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Values of zeta functions at s=1/2","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Niranjan Ramachandran","submitted_at":"2005-02-24T05:38:15Z","abstract_excerpt":"We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is constructed from the Weil-etale cohomology of a certain supersingular elliptic curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502507","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9uXsHxcZt7Rs514/A5LBRxD1MYCPLRwhUB9bzOnWCOoStBWZo600WqQsiL2DJ5VAofjNe1+jR9P4hRst6LMTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:35.706258Z"},"content_sha256":"6d224c38e0f4489e2f46eb37a14a12035860ebe5e96682e8deb03a5a53a90423","schema_version":"1.0","event_id":"sha256:6d224c38e0f4489e2f46eb37a14a12035860ebe5e96682e8deb03a5a53a90423"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/bundle.json","state_url":"https://pith.science/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/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":"2026-06-03T00:18:35Z","links":{"resolver":"https://pith.science/pith/WTSPLMSZAMPTJTNXDYG57CWEIF","bundle":"https://pith.science/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/bundle.json","state":"https://pith.science/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTSPLMSZAMPTJTNXDYG57CWEIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:WTSPLMSZAMPTJTNXDYG57CWEIF","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":"6a0122deeac256ed3677fa65b6d4247e1501dd0adb74a4249e6dcc3491c5e22f","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-24T05:38:15Z","title_canon_sha256":"8497db7b7b99ee6d3a97dc123ad87304d471804c777c276c9c082d3a08195bdb"},"schema_version":"1.0","source":{"id":"math/0502507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502507","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502507v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502507","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"WTSPLMSZAMPT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"WTSPLMSZAMPTJTNX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"WTSPLMSZ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:6d224c38e0f4489e2f46eb37a14a12035860ebe5e96682e8deb03a5a53a90423","target":"graph","created_at":"2026-05-18T01:37:47Z","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":"We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is constructed from the Weil-etale cohomology of a certain supersingular elliptic curve.","authors_text":"Niranjan Ramachandran","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-02-24T05:38:15Z","title":"Values of zeta functions at s=1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502507","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":"sha256:229fbc2e4d40651a21bc05fd0ba161bbaa6c947f7c469b6152d4cad064a2eec6","target":"record","created_at":"2026-05-18T01:37:47Z","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":"6a0122deeac256ed3677fa65b6d4247e1501dd0adb74a4249e6dcc3491c5e22f","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2005-02-24T05:38:15Z","title_canon_sha256":"8497db7b7b99ee6d3a97dc123ad87304d471804c777c276c9c082d3a08195bdb"},"schema_version":"1.0","source":{"id":"math/0502507","kind":"arxiv","version":2}},"canonical_sha256":"b4e4f5b259031f34cdb71e0ddf8ac4414073c605205bcc1a416ae234e0c4d27e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4e4f5b259031f34cdb71e0ddf8ac4414073c605205bcc1a416ae234e0c4d27e","first_computed_at":"2026-05-18T01:37:47.780138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:47.780138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PEueHXS9SNGeupMomV6hkRsyY17RLXSOYc5J1Id23ocep9y3hf4h6VS06te+LX+nvQjUtwcHO/tHqkj8K3dQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:47.780573Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:229fbc2e4d40651a21bc05fd0ba161bbaa6c947f7c469b6152d4cad064a2eec6","sha256:6d224c38e0f4489e2f46eb37a14a12035860ebe5e96682e8deb03a5a53a90423"],"state_sha256":"9fbe3519f46c927c572897925c7dc3b3a7a4b8077fb2cf672c1e75531efd0913"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dnuraAJZsuUX3Lh/mr/6JPLYOJMg1huN6oEMS4gVHQ2u8/p97yr3EG/vlEY7EaFsJgmBq+tuNLkVC3ue5eeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:18:35.708444Z","bundle_sha256":"2fb3e9e3dec1de6bef0c53925e0ef6e17ed27b0ffe55b60d3eb3b52231d57940"}}