{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JOQBX2ZTUDHHMV2GVACRQSHIYU","short_pith_number":"pith:JOQBX2ZT","schema_version":"1.0","canonical_sha256":"4ba01beb33a0ce765746a8051848e8c511205e67ad27765525b36efd85121d44","source":{"kind":"arxiv","id":"1206.5817","version":4},"attestation_state":"computed","paper":{"title":"Reciprocity Laws on Algebraic Surfaces via Iterated Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Horozov, Matt Kerr","submitted_at":"2012-06-25T20:06:35Z","abstract_excerpt":"This paper presents a proof of reciprocity laws for the Parshin symbol and for two new local symbols, defined here, which we call 4-function local symbols. The reciprocity laws for the Parshin symbol are proven using a new method - via iterated integrals. The usefulness of this method is shown by two facts - first, by establishing new local symbols - the 4-function local symbols and their reciprocity laws and, second, by providing refinements of the Parshin symbol in terms of bi-local symbols, each of which satisfies a reciprocity law. The K-theoretic variant of the first 4-function local symb"},"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":"1206.5817","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T20:06:35Z","cross_cats_sorted":[],"title_canon_sha256":"9ceec28d3c9e80418f1f479be1a85047833e7b0bdff731ea0a018e58029d9bea","abstract_canon_sha256":"c7a378a8ee450157e49719c5176b7f332e3489883c3379f1d7372a79cbdc990f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:23.166154Z","signature_b64":"9mxrvwLaq6ihJE9LV++xbE7NjGs0KMD/YdRbVi3oR9pyj/M0VusQ/XkThef8ejP0C2wQ2SssvVOt/710vClsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ba01beb33a0ce765746a8051848e8c511205e67ad27765525b36efd85121d44","last_reissued_at":"2026-05-18T00:00:23.165643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:23.165643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reciprocity Laws on Algebraic Surfaces via Iterated Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Horozov, Matt Kerr","submitted_at":"2012-06-25T20:06:35Z","abstract_excerpt":"This paper presents a proof of reciprocity laws for the Parshin symbol and for two new local symbols, defined here, which we call 4-function local symbols. The reciprocity laws for the Parshin symbol are proven using a new method - via iterated integrals. The usefulness of this method is shown by two facts - first, by establishing new local symbols - the 4-function local symbols and their reciprocity laws and, second, by providing refinements of the Parshin symbol in terms of bi-local symbols, each of which satisfies a reciprocity law. The K-theoretic variant of the first 4-function local symb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5817","kind":"arxiv","version":4},"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":"1206.5817","created_at":"2026-05-18T00:00:23.165716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5817v4","created_at":"2026-05-18T00:00:23.165716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5817","created_at":"2026-05-18T00:00:23.165716+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOQBX2ZTUDHH","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOQBX2ZTUDHHMV2G","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOQBX2ZT","created_at":"2026-05-18T12:27:11.947152+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/JOQBX2ZTUDHHMV2GVACRQSHIYU","json":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU.json","graph_json":"https://pith.science/api/pith-number/JOQBX2ZTUDHHMV2GVACRQSHIYU/graph.json","events_json":"https://pith.science/api/pith-number/JOQBX2ZTUDHHMV2GVACRQSHIYU/events.json","paper":"https://pith.science/paper/JOQBX2ZT"},"agent_actions":{"view_html":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU","download_json":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU.json","view_paper":"https://pith.science/paper/JOQBX2ZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5817&json=true","fetch_graph":"https://pith.science/api/pith-number/JOQBX2ZTUDHHMV2GVACRQSHIYU/graph.json","fetch_events":"https://pith.science/api/pith-number/JOQBX2ZTUDHHMV2GVACRQSHIYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU/action/storage_attestation","attest_author":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU/action/author_attestation","sign_citation":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU/action/citation_signature","submit_replication":"https://pith.science/pith/JOQBX2ZTUDHHMV2GVACRQSHIYU/action/replication_record"}},"created_at":"2026-05-18T00:00:23.165716+00:00","updated_at":"2026-05-18T00:00:23.165716+00:00"}