{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SUU6PISW3ILSKFH5FLFPSKSJ7C","short_pith_number":"pith:SUU6PISW","canonical_record":{"source":{"id":"1708.09205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-30T10:21:33Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"08986f1c82a47f0e5679906f8b8692ed53258946b328eb0de0dcfb8983f24feb","abstract_canon_sha256":"a76138cfe55b15127ea9c88bc0a9b71d2b6b00d65bb72ba086e35033c4012dd2"},"schema_version":"1.0"},"canonical_sha256":"9529e7a256da172514fd2acaf92a49f8848296103c0d4861a6929b6ebf28d0e4","source":{"kind":"arxiv","id":"1708.09205","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09205","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09205v1","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09205","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"SUU6PISW3ILS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUU6PISW3ILSKFH5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUU6PISW","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SUU6PISW3ILSKFH5FLFPSKSJ7C","target":"record","payload":{"canonical_record":{"source":{"id":"1708.09205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-30T10:21:33Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"08986f1c82a47f0e5679906f8b8692ed53258946b328eb0de0dcfb8983f24feb","abstract_canon_sha256":"a76138cfe55b15127ea9c88bc0a9b71d2b6b00d65bb72ba086e35033c4012dd2"},"schema_version":"1.0"},"canonical_sha256":"9529e7a256da172514fd2acaf92a49f8848296103c0d4861a6929b6ebf28d0e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:20.629149Z","signature_b64":"2H3RPvQkSVPcASNjlqeUfdaOlBc/sIcdgCD/zl7Onl9dj4NuFNvADw49k6E1RBPjYdKVWki9gYjdjF8tgxRhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9529e7a256da172514fd2acaf92a49f8848296103c0d4861a6929b6ebf28d0e4","last_reissued_at":"2026-05-18T00:36:20.628447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:20.628447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.09205","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":"2026-05-18T00:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elyqt4iyHHy/MVHJdgTy74Qdm/F3XP/8zdIeWXgZlvWerEpp11WE7HRhI0CYyMhovzvoqR2bjOZqF06kNFvCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:39.691811Z"},"content_sha256":"6d30b1e02162cd1610304c875ffe2b38fc936193f15b9fb5080aeff186cbcaff","schema_version":"1.0","event_id":"sha256:6d30b1e02162cd1610304c875ffe2b38fc936193f15b9fb5080aeff186cbcaff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SUU6PISW3ILSKFH5FLFPSKSJ7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LCA(2), Weil index, and product formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dongwen Liu, Yongchang Zhu","submitted_at":"2017-08-30T10:21:33Z","abstract_excerpt":"In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09205","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":"2026-05-18T00:36:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4N4TaxlvSPm+xZ8KdDfPpFWQVMrbDWHJud+UYUfSjEVcQuhDPfe0CxHOPnRu0lR11DU6MwajkJv7hbmIe86DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:32:39.692490Z"},"content_sha256":"a029bace53a20f0703e6d1a949076bee8164d37a9559462708b59d9821ecd69f","schema_version":"1.0","event_id":"sha256:a029bace53a20f0703e6d1a949076bee8164d37a9559462708b59d9821ecd69f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/bundle.json","state_url":"https://pith.science/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/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":"2026-06-05T18:32:39Z","links":{"resolver":"https://pith.science/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C","bundle":"https://pith.science/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/bundle.json","state":"https://pith.science/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUU6PISW3ILSKFH5FLFPSKSJ7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SUU6PISW3ILSKFH5FLFPSKSJ7C","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":"a76138cfe55b15127ea9c88bc0a9b71d2b6b00d65bb72ba086e35033c4012dd2","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-30T10:21:33Z","title_canon_sha256":"08986f1c82a47f0e5679906f8b8692ed53258946b328eb0de0dcfb8983f24feb"},"schema_version":"1.0","source":{"id":"1708.09205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09205","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09205v1","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09205","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"SUU6PISW3ILS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SUU6PISW3ILSKFH5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SUU6PISW","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:a029bace53a20f0703e6d1a949076bee8164d37a9559462708b59d9821ecd69f","target":"graph","created_at":"2026-05-18T00:36:20Z","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":"In this paper we study the category LCA(2) of certain non-locally compact abelian topological groups, and extend the notion of Weil index. As applications we deduce some product formulas for curves over local fields and arithmetic surfaces.","authors_text":"Dongwen Liu, Yongchang Zhu","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-30T10:21:33Z","title":"LCA(2), Weil index, and product formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09205","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":"sha256:6d30b1e02162cd1610304c875ffe2b38fc936193f15b9fb5080aeff186cbcaff","target":"record","created_at":"2026-05-18T00:36:20Z","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":"a76138cfe55b15127ea9c88bc0a9b71d2b6b00d65bb72ba086e35033c4012dd2","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-30T10:21:33Z","title_canon_sha256":"08986f1c82a47f0e5679906f8b8692ed53258946b328eb0de0dcfb8983f24feb"},"schema_version":"1.0","source":{"id":"1708.09205","kind":"arxiv","version":1}},"canonical_sha256":"9529e7a256da172514fd2acaf92a49f8848296103c0d4861a6929b6ebf28d0e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9529e7a256da172514fd2acaf92a49f8848296103c0d4861a6929b6ebf28d0e4","first_computed_at":"2026-05-18T00:36:20.628447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:20.628447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2H3RPvQkSVPcASNjlqeUfdaOlBc/sIcdgCD/zl7Onl9dj4NuFNvADw49k6E1RBPjYdKVWki9gYjdjF8tgxRhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:20.629149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d30b1e02162cd1610304c875ffe2b38fc936193f15b9fb5080aeff186cbcaff","sha256:a029bace53a20f0703e6d1a949076bee8164d37a9559462708b59d9821ecd69f"],"state_sha256":"5898898b14b8502594f35600744fe12f6e201cc054d848bec325bcae4bf2fb27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGeliVXZWYEBbiHwaGnVYebt1j+vaaRJsMpVSBCvBZ+n3SlJVVuM5OdLKcNJWfR46qZtTmkp4DVEBDxGzrBqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:32:39.695695Z","bundle_sha256":"b0265fcb300ccd913f5e2d323b274138a261c6a00e890a695d52083ab6b03e7c"}}