{"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"}