{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AHGBOF57DWLHCAEKQSFEYPLQ5W","short_pith_number":"pith:AHGBOF57","canonical_record":{"source":{"id":"1405.6513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:27:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5eca3d5a343e145f4286b85d5356527cdc90163f3bf014fae1967983a6d6bbe5","abstract_canon_sha256":"e0b495622b4ea086676a0228119c4c94f6e464e4d10b94fdcb3a8c8ea235d23f"},"schema_version":"1.0"},"canonical_sha256":"01cc1717bf1d9671008a848a4c3d70ed9f1f1c3fa91887dec5d6f52b6a4df3b3","source":{"kind":"arxiv","id":"1405.6513","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6513","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6513v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6513","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"AHGBOF57DWLH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AHGBOF57DWLHCAEK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AHGBOF57","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AHGBOF57DWLHCAEKQSFEYPLQ5W","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:27:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5eca3d5a343e145f4286b85d5356527cdc90163f3bf014fae1967983a6d6bbe5","abstract_canon_sha256":"e0b495622b4ea086676a0228119c4c94f6e464e4d10b94fdcb3a8c8ea235d23f"},"schema_version":"1.0"},"canonical_sha256":"01cc1717bf1d9671008a848a4c3d70ed9f1f1c3fa91887dec5d6f52b6a4df3b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.522425Z","signature_b64":"PxqeMefAWh0XVuGt198neH/UQpkp0EzpeNSD0le6ArWdJm4LabIJTZp04EcZa2RB2qusvWdXYaWBuz84KZuiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01cc1717bf1d9671008a848a4c3d70ed9f1f1c3fa91887dec5d6f52b6a4df3b3","last_reissued_at":"2026-05-18T01:37:47.522011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.522011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6513","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":"33EAePhN+tp3nidkmARUsGWhMjynPrgBlWHtYJ5TeySda2ucwaIuWaEhfGfaNgzjsdkvrmjzWspMVDXyZG76Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:35:28.325271Z"},"content_sha256":"5e2f5caef63ca01f22ea7c02010c1c0bc0659904d2fd5632b6849a758057b5fe","schema_version":"1.0","event_id":"sha256:5e2f5caef63ca01f22ea7c02010c1c0bc0659904d2fd5632b6849a758057b5fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AHGBOF57DWLHCAEKQSFEYPLQ5W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"A. Raghuram, G\\\"unter Harder","submitted_at":"2014-05-26T09:27:21Z","abstract_excerpt":"The aim of this article is to study rank-one Eisenstein cohomology for the group GL(N)/F, where F is a totally real field extension of Q. This is then used to prove rationality results for ratios of successive critical values for Rankin-Selberg L-functions for GL(n) x GL(n') over F with the parity condition that nn' is even. The key idea is to interpret Langlands's constant term theorem in terms of Eisenstein cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6513","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":"3bUWqnScSoFLlaA94I/5Y6pbW/zsxru/9aYAgWVpakntbME0OpLgwK7lmBizufVyp+QObjp28u8EeVjkkoiSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:35:28.325652Z"},"content_sha256":"fbafedd606284c170a66838dad64debfb6551a3d988b5367b684f19d89432904","schema_version":"1.0","event_id":"sha256:fbafedd606284c170a66838dad64debfb6551a3d988b5367b684f19d89432904"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/bundle.json","state_url":"https://pith.science/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/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":"2026-05-28T00:35:28Z","links":{"resolver":"https://pith.science/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W","bundle":"https://pith.science/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/bundle.json","state":"https://pith.science/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHGBOF57DWLHCAEKQSFEYPLQ5W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AHGBOF57DWLHCAEKQSFEYPLQ5W","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":"e0b495622b4ea086676a0228119c4c94f6e464e4d10b94fdcb3a8c8ea235d23f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:27:21Z","title_canon_sha256":"5eca3d5a343e145f4286b85d5356527cdc90163f3bf014fae1967983a6d6bbe5"},"schema_version":"1.0","source":{"id":"1405.6513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6513","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6513v2","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6513","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"AHGBOF57DWLH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AHGBOF57DWLHCAEK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AHGBOF57","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:fbafedd606284c170a66838dad64debfb6551a3d988b5367b684f19d89432904","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":"The aim of this article is to study rank-one Eisenstein cohomology for the group GL(N)/F, where F is a totally real field extension of Q. This is then used to prove rationality results for ratios of successive critical values for Rankin-Selberg L-functions for GL(n) x GL(n') over F with the parity condition that nn' is even. The key idea is to interpret Langlands's constant term theorem in terms of Eisenstein cohomology.","authors_text":"A. Raghuram, G\\\"unter Harder","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:27:21Z","title":"Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6513","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":"sha256:5e2f5caef63ca01f22ea7c02010c1c0bc0659904d2fd5632b6849a758057b5fe","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":"e0b495622b4ea086676a0228119c4c94f6e464e4d10b94fdcb3a8c8ea235d23f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-26T09:27:21Z","title_canon_sha256":"5eca3d5a343e145f4286b85d5356527cdc90163f3bf014fae1967983a6d6bbe5"},"schema_version":"1.0","source":{"id":"1405.6513","kind":"arxiv","version":2}},"canonical_sha256":"01cc1717bf1d9671008a848a4c3d70ed9f1f1c3fa91887dec5d6f52b6a4df3b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01cc1717bf1d9671008a848a4c3d70ed9f1f1c3fa91887dec5d6f52b6a4df3b3","first_computed_at":"2026-05-18T01:37:47.522011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:47.522011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PxqeMefAWh0XVuGt198neH/UQpkp0EzpeNSD0le6ArWdJm4LabIJTZp04EcZa2RB2qusvWdXYaWBuz84KZuiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:47.522425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e2f5caef63ca01f22ea7c02010c1c0bc0659904d2fd5632b6849a758057b5fe","sha256:fbafedd606284c170a66838dad64debfb6551a3d988b5367b684f19d89432904"],"state_sha256":"759e463162182b673b3cf888e1ed31cb0985adf03b81872abee18cd3977c6c3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nc2zusTTI3oX0T52ZpKE1ECrT3AD0PtFavirAwvaF36QDpMs0rbSYQCQ9dT+61b3CceW6QmQOP3cwCQ5xpvVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:35:28.327660Z","bundle_sha256":"056d176db10f4b0afb13165d00a2c3c0c4142fae056c343065e38ad74c58a5eb"}}