{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44","short_pith_number":"pith:ZVVZ4GSZ","schema_version":"1.0","canonical_sha256":"cd6b9e1a59fc381809582d47ccdbace70e4385570aeaaee2274f4b05a609d8a2","source":{"kind":"arxiv","id":"1305.0049","version":2},"attestation_state":"computed","paper":{"title":"Lyapunov exponents for surface groups representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Bertrand Deroin, Romain Dujardin","submitted_at":"2013-04-30T22:52:15Z","abstract_excerpt":"Let (\\rho_\\la)_{\\la\\in \\La} be a holomorphic family of representations of a surface group \\pi_1(S) into PSL(2,C), where S is a topological (possibly punctured) surface with negative Euler characteristic. Given a structure of Riemann surface of finite type on S we construct a bifurcation current on the parameter space \\La, that is a (1,1) positive closed current attached to the bifurcations of the family. It is defined as the $dd^c$ of the Lyapunov exponent of the representation with respect to the Brownian motion on the Riemann surface S, endowed with its Poincare metric. We show that this bif"},"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":"1305.0049","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-30T22:52:15Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d548a2aa4a9a883c2fc52022e83536dda78bdfe117ebf16fa02ac8f2ead8b5cc","abstract_canon_sha256":"db307bc0b0038dfa51ad7c41f23ee65fe38f74f0e11bc6e41b916544dce0d399"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:51.017863Z","signature_b64":"zD7TGg4m9m4JV5zt9whoYluwkJW7EyrWOmAMZY8gLjM4gc64Al/GRM3viwXVThXgmT2kz+X2PJtBDFsNTxzzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd6b9e1a59fc381809582d47ccdbace70e4385570aeaaee2274f4b05a609d8a2","last_reissued_at":"2026-05-18T03:16:51.017245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:51.017245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lyapunov exponents for surface groups representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Bertrand Deroin, Romain Dujardin","submitted_at":"2013-04-30T22:52:15Z","abstract_excerpt":"Let (\\rho_\\la)_{\\la\\in \\La} be a holomorphic family of representations of a surface group \\pi_1(S) into PSL(2,C), where S is a topological (possibly punctured) surface with negative Euler characteristic. Given a structure of Riemann surface of finite type on S we construct a bifurcation current on the parameter space \\La, that is a (1,1) positive closed current attached to the bifurcations of the family. It is defined as the $dd^c$ of the Lyapunov exponent of the representation with respect to the Brownian motion on the Riemann surface S, endowed with its Poincare metric. We show that this bif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0049","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":"1305.0049","created_at":"2026-05-18T03:16:51.017361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0049v2","created_at":"2026-05-18T03:16:51.017361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0049","created_at":"2026-05-18T03:16:51.017361+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZVVZ4GSZ7Q4B","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZVVZ4GSZ7Q4BQCKY","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZVVZ4GSZ","created_at":"2026-05-18T12:28:09.283467+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/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44","json":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44.json","graph_json":"https://pith.science/api/pith-number/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/graph.json","events_json":"https://pith.science/api/pith-number/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/events.json","paper":"https://pith.science/paper/ZVVZ4GSZ"},"agent_actions":{"view_html":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44","download_json":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44.json","view_paper":"https://pith.science/paper/ZVVZ4GSZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0049&json=true","fetch_graph":"https://pith.science/api/pith-number/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/graph.json","fetch_events":"https://pith.science/api/pith-number/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/action/storage_attestation","attest_author":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/action/author_attestation","sign_citation":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/action/citation_signature","submit_replication":"https://pith.science/pith/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44/action/replication_record"}},"created_at":"2026-05-18T03:16:51.017361+00:00","updated_at":"2026-05-18T03:16:51.017361+00:00"}