{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UCCM4Y6KGKZ663T6WKW7L3RHFY","short_pith_number":"pith:UCCM4Y6K","schema_version":"1.0","canonical_sha256":"a084ce63ca32b3ef6e7eb2adf5ee272e2a685d58e7a73d86a717288d9a686fb9","source":{"kind":"arxiv","id":"1410.3526","version":2},"attestation_state":"computed","paper":{"title":"Symplectic double for moduli spaces of G-local systems on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"math.AG","authors_text":"Alexander Goncharov, Vladimir Fock","submitted_at":"2014-10-13T22:17:44Z","abstract_excerpt":"Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and define a collection of special rational coordinate systems on it.\n  The moduli space D(G,S) is the symplectic double of the Poisson moduli space of framed G-local systems on S. Its symplectic form is upgraded to a K2-symplectic structure for which the special coordinates are K2-Darboux coordinates."},"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":"1410.3526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-13T22:17:44Z","cross_cats_sorted":["math.GT","math.QA"],"title_canon_sha256":"9411fee5acfaaefaa55d867e77901f5c87a16da468841239c657910f40890bad","abstract_canon_sha256":"4eea79f1761b268bfce26575ee41a1398e25a809a0cd1e776dc96845a7533980"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:00.152413Z","signature_b64":"gxgLrzxDI4DKtUTE5R8MLMb1HpLWkCLmavVvIpQlfPMhf+wYVu6iF4zoN3D5X+O7KFrq3cojfPxbLv1JJM43Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a084ce63ca32b3ef6e7eb2adf5ee272e2a685d58e7a73d86a717288d9a686fb9","last_reissued_at":"2026-05-18T02:04:00.151568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:00.151568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic double for moduli spaces of G-local systems on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"math.AG","authors_text":"Alexander Goncharov, Vladimir Fock","submitted_at":"2014-10-13T22:17:44Z","abstract_excerpt":"Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and define a collection of special rational coordinate systems on it.\n  The moduli space D(G,S) is the symplectic double of the Poisson moduli space of framed G-local systems on S. Its symplectic form is upgraded to a K2-symplectic structure for which the special coordinates are K2-Darboux coordinates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3526","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":"1410.3526","created_at":"2026-05-18T02:04:00.151704+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3526v2","created_at":"2026-05-18T02:04:00.151704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3526","created_at":"2026-05-18T02:04:00.151704+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCCM4Y6KGKZ6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCCM4Y6KGKZ663T6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCCM4Y6K","created_at":"2026-05-18T12:28:52.271510+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/UCCM4Y6KGKZ663T6WKW7L3RHFY","json":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY.json","graph_json":"https://pith.science/api/pith-number/UCCM4Y6KGKZ663T6WKW7L3RHFY/graph.json","events_json":"https://pith.science/api/pith-number/UCCM4Y6KGKZ663T6WKW7L3RHFY/events.json","paper":"https://pith.science/paper/UCCM4Y6K"},"agent_actions":{"view_html":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY","download_json":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY.json","view_paper":"https://pith.science/paper/UCCM4Y6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3526&json=true","fetch_graph":"https://pith.science/api/pith-number/UCCM4Y6KGKZ663T6WKW7L3RHFY/graph.json","fetch_events":"https://pith.science/api/pith-number/UCCM4Y6KGKZ663T6WKW7L3RHFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY/action/storage_attestation","attest_author":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY/action/author_attestation","sign_citation":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY/action/citation_signature","submit_replication":"https://pith.science/pith/UCCM4Y6KGKZ663T6WKW7L3RHFY/action/replication_record"}},"created_at":"2026-05-18T02:04:00.151704+00:00","updated_at":"2026-05-18T02:04:00.151704+00:00"}