{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FBPOT6UWHPLIELYYKNMS2GSK5W","short_pith_number":"pith:FBPOT6UW","canonical_record":{"source":{"id":"1703.07471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T23:54:23Z","cross_cats_sorted":[],"title_canon_sha256":"ad72403078ccc187973f04a296b87ba666a5b234404d886122c4b98c9ffe63eb","abstract_canon_sha256":"dae0bec1d29230661de562c32a8e22d01e5e3ccdfceed855ab4e91479dcda6cb"},"schema_version":"1.0"},"canonical_sha256":"285ee9fa963bd6822f1853592d1a4aed907905f41df648b6a667ade04065ce01","source":{"kind":"arxiv","id":"1703.07471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07471","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07471v1","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07471","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"FBPOT6UWHPLI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBPOT6UWHPLIELYY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBPOT6UW","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FBPOT6UWHPLIELYYKNMS2GSK5W","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T23:54:23Z","cross_cats_sorted":[],"title_canon_sha256":"ad72403078ccc187973f04a296b87ba666a5b234404d886122c4b98c9ffe63eb","abstract_canon_sha256":"dae0bec1d29230661de562c32a8e22d01e5e3ccdfceed855ab4e91479dcda6cb"},"schema_version":"1.0"},"canonical_sha256":"285ee9fa963bd6822f1853592d1a4aed907905f41df648b6a667ade04065ce01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:08.729986Z","signature_b64":"YnYnsA3vr3nq12EXU+vf3a6wX5W81hDA5kW+UuT4jpXE+ZbWhr3gRIJHIVv07FRbSe4gq23Ev8toIhAqlc6TBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"285ee9fa963bd6822f1853592d1a4aed907905f41df648b6a667ade04065ce01","last_reissued_at":"2026-05-18T00:48:08.729578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:08.729578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07471","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOW1NjnvERAPYgBaYwo/x937kXk1BRv4JRATjtYtd5njfiyqL7tv/KXGn5TRUQ0pmxT9twaR3VeR2bwjDXyiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:29.380724Z"},"content_sha256":"791aa587d879648b1ccadbf867d9cb0599377d6bce9daa8383aeb3da9d103f74","schema_version":"1.0","event_id":"sha256:791aa587d879648b1ccadbf867d9cb0599377d6bce9daa8383aeb3da9d103f74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FBPOT6UWHPLIELYYKNMS2GSK5W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of Tornheim's type of double series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Koji Tasaka, Shin-ya Kadota, Takuya Okamoto","submitted_at":"2017-03-21T23:54:23Z","abstract_excerpt":"We examine values of certain Tornheim's type of double series with odd weight. As a result, an affirmative answer to a conjecture about the parity theorem for the zeta function of the root system of the exceptional Lie algebra $G_2$, proposed by Komori, Matsumoto and Tsumura, is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07471","kind":"arxiv","version":1},"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":"2026-05-18T00:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGQ0f8wKFRjTzq0Sfam2h1yR8aKTH2GoBnejeVWAXfX8BZ3fzanCsibf3UP8lLpm3N5UJuexFVIzUq25FRwGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:29.381383Z"},"content_sha256":"00ae3c3d92d4b975b6fdd4486e20c4ec6223a7a27b49350035e116bfe773a68f","schema_version":"1.0","event_id":"sha256:00ae3c3d92d4b975b6fdd4486e20c4ec6223a7a27b49350035e116bfe773a68f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/bundle.json","state_url":"https://pith.science/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/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":"2026-06-10T23:33:29Z","links":{"resolver":"https://pith.science/pith/FBPOT6UWHPLIELYYKNMS2GSK5W","bundle":"https://pith.science/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/bundle.json","state":"https://pith.science/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FBPOT6UWHPLIELYYKNMS2GSK5W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FBPOT6UWHPLIELYYKNMS2GSK5W","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":"dae0bec1d29230661de562c32a8e22d01e5e3ccdfceed855ab4e91479dcda6cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T23:54:23Z","title_canon_sha256":"ad72403078ccc187973f04a296b87ba666a5b234404d886122c4b98c9ffe63eb"},"schema_version":"1.0","source":{"id":"1703.07471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07471","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07471v1","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07471","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"FBPOT6UWHPLI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBPOT6UWHPLIELYY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBPOT6UW","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:00ae3c3d92d4b975b6fdd4486e20c4ec6223a7a27b49350035e116bfe773a68f","target":"graph","created_at":"2026-05-18T00:48:08Z","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 examine values of certain Tornheim's type of double series with odd weight. As a result, an affirmative answer to a conjecture about the parity theorem for the zeta function of the root system of the exceptional Lie algebra $G_2$, proposed by Komori, Matsumoto and Tsumura, is given.","authors_text":"Koji Tasaka, Shin-ya Kadota, Takuya Okamoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T23:54:23Z","title":"Evaluation of Tornheim's type of double series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07471","kind":"arxiv","version":1},"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":"sha256:791aa587d879648b1ccadbf867d9cb0599377d6bce9daa8383aeb3da9d103f74","target":"record","created_at":"2026-05-18T00:48:08Z","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":"dae0bec1d29230661de562c32a8e22d01e5e3ccdfceed855ab4e91479dcda6cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T23:54:23Z","title_canon_sha256":"ad72403078ccc187973f04a296b87ba666a5b234404d886122c4b98c9ffe63eb"},"schema_version":"1.0","source":{"id":"1703.07471","kind":"arxiv","version":1}},"canonical_sha256":"285ee9fa963bd6822f1853592d1a4aed907905f41df648b6a667ade04065ce01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"285ee9fa963bd6822f1853592d1a4aed907905f41df648b6a667ade04065ce01","first_computed_at":"2026-05-18T00:48:08.729578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:08.729578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YnYnsA3vr3nq12EXU+vf3a6wX5W81hDA5kW+UuT4jpXE+ZbWhr3gRIJHIVv07FRbSe4gq23Ev8toIhAqlc6TBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:08.729986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:791aa587d879648b1ccadbf867d9cb0599377d6bce9daa8383aeb3da9d103f74","sha256:00ae3c3d92d4b975b6fdd4486e20c4ec6223a7a27b49350035e116bfe773a68f"],"state_sha256":"2d64cec4bf53282350b4350ae2846d36b6557af3cc9b1bbb22756b39200915d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBLV50wicuntyGf2wN68O7Dd+iODoBUp/9LeXXKnGaxBpymzQ3sI6CTx7KhEifyxBrSHzhUBAqsKdAyXBCn+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:33:29.384913Z","bundle_sha256":"3b39960c8786453aefefbd6ee89d38bebad1b946d2e6769f0bae366daef7c245"}}