{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NLVJ5RMKEB5JALFPYOYKGVOE5E","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":"4e1e58a66fd723d9a3a8c4dac9fad34dabd3c0cc6b578edd13f5d5334bd0e9a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-20T12:58:58Z","title_canon_sha256":"1aa486b799f2f47b3738beb6e1afed333e091e0fe8f1687fe711abb6f6a805a0"},"schema_version":"1.0","source":{"id":"1212.5015","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5015","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5015v2","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5015","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"NLVJ5RMKEB5J","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NLVJ5RMKEB5JALFP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NLVJ5RMK","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:cd6c89f174a21d6980b80781562d8223309233c73c6eb9d29a1bfd755424b88d","target":"graph","created_at":"2026-05-18T00:20:07Z","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":"We define a Poisson Algebra called the {\\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functions on the Hitchin component as well as on the space of $\\mathsf{SL}_n(\\mathbb R)$-opers with trivial holonomy. We relate this Poisson algebra to the Atiyah--Bott--Goldman symplectic structure and to the Drinfel'd--Sokolov reduction. We also prove an extension of Wolpert formula.","authors_text":"Fran\\c{c}ois Labourie","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-20T12:58:58Z","title":"Goldman Algebra, Opers and the Swapping Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5015","kind":"arxiv","version":2},"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":"sha256:87bd52594f74cc2a9e6a2cbdbacf576504f48f288d64653a906fd3b399d45734","target":"record","created_at":"2026-05-18T00:20:07Z","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":"4e1e58a66fd723d9a3a8c4dac9fad34dabd3c0cc6b578edd13f5d5334bd0e9a9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-20T12:58:58Z","title_canon_sha256":"1aa486b799f2f47b3738beb6e1afed333e091e0fe8f1687fe711abb6f6a805a0"},"schema_version":"1.0","source":{"id":"1212.5015","kind":"arxiv","version":2}},"canonical_sha256":"6aea9ec58a207a902cafc3b0a355c4e939fae5c268d1861967a3ac8bc5c5871d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6aea9ec58a207a902cafc3b0a355c4e939fae5c268d1861967a3ac8bc5c5871d","first_computed_at":"2026-05-18T00:20:07.891533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.891533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pcIvYsh/dxg78ac9crJfvzvkwrMcvm6bA3O3h0Wy/qwKHmKWNGZRFTPUsSgaNNWjTrpkcuachpadUMxWYkOLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.892060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5015","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87bd52594f74cc2a9e6a2cbdbacf576504f48f288d64653a906fd3b399d45734","sha256:cd6c89f174a21d6980b80781562d8223309233c73c6eb9d29a1bfd755424b88d"],"state_sha256":"5e87bc7a5a38330d2781fb9b4ba32399f182c805b32306e9689815c5d371f4bd"}