{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UJ6HGSTEBG35JPMRQKUHGBTXG6","short_pith_number":"pith:UJ6HGSTE","schema_version":"1.0","canonical_sha256":"a27c734a6409b7d4bd9182a87306773797c374c0a895578f9d066151ed82b46c","source":{"kind":"arxiv","id":"1203.6712","version":2},"attestation_state":"computed","paper":{"title":"Kato's residue homomorphisms and reciprocity laws on arithmetic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Dongwen Liu","submitted_at":"2012-03-30T05:02:43Z","abstract_excerpt":"We explicitly study Kato's residue homomorphisms in Milnor $K$-theory, which are closely related to Contou-Carr\\`ere symbols. As applications we establish several reciprocity laws for certain locally defined maps on $K$-groups that are associated to arithmetic surfaces."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.6712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-30T05:02:43Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"3a6733d11422930c28ccaac8cca5a6e4e74a614c2ab10f4918707a1e732ec745","abstract_canon_sha256":"8f887f5e13a8c5d96b1d2a5985166925486eb73eb0823243d87042e4560560f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:51.556800Z","signature_b64":"qU3tcVleUjGqHkdyzeGCDXfsHO1zn8cQCOKWforo2iwvzrQk0x5LCGbkf5qhBvz6oq68qK2X9OPPdiIwtZenDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a27c734a6409b7d4bd9182a87306773797c374c0a895578f9d066151ed82b46c","last_reissued_at":"2026-05-18T02:16:51.556271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:51.556271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kato's residue homomorphisms and reciprocity laws on arithmetic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Dongwen Liu","submitted_at":"2012-03-30T05:02:43Z","abstract_excerpt":"We explicitly study Kato's residue homomorphisms in Milnor $K$-theory, which are closely related to Contou-Carr\\`ere symbols. As applications we establish several reciprocity laws for certain locally defined maps on $K$-groups that are associated to arithmetic surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6712","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.6712","created_at":"2026-05-18T02:16:51.556357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.6712v2","created_at":"2026-05-18T02:16:51.556357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6712","created_at":"2026-05-18T02:16:51.556357+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJ6HGSTEBG35","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJ6HGSTEBG35JPMR","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJ6HGSTE","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6","json":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6.json","graph_json":"https://pith.science/api/pith-number/UJ6HGSTEBG35JPMRQKUHGBTXG6/graph.json","events_json":"https://pith.science/api/pith-number/UJ6HGSTEBG35JPMRQKUHGBTXG6/events.json","paper":"https://pith.science/paper/UJ6HGSTE"},"agent_actions":{"view_html":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6","download_json":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6.json","view_paper":"https://pith.science/paper/UJ6HGSTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.6712&json=true","fetch_graph":"https://pith.science/api/pith-number/UJ6HGSTEBG35JPMRQKUHGBTXG6/graph.json","fetch_events":"https://pith.science/api/pith-number/UJ6HGSTEBG35JPMRQKUHGBTXG6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6/action/storage_attestation","attest_author":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6/action/author_attestation","sign_citation":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6/action/citation_signature","submit_replication":"https://pith.science/pith/UJ6HGSTEBG35JPMRQKUHGBTXG6/action/replication_record"}},"created_at":"2026-05-18T02:16:51.556357+00:00","updated_at":"2026-05-18T02:16:51.556357+00:00"}