{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:G3Z7JYRDFCFWKV2V4GJSTGCT5O","short_pith_number":"pith:G3Z7JYRD","schema_version":"1.0","canonical_sha256":"36f3f4e223288b655755e193299853eb821754902a94f00f73aa86ceae72da40","source":{"kind":"arxiv","id":"math/0506212","version":2},"attestation_state":"computed","paper":{"title":"Energy of Twisted Harmonic Maps of Riemann Surfaces","license":"","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DG","authors_text":"Richard A. Wentworth, William M. Goldman","submitted_at":"2005-06-10T21:00:28Z","abstract_excerpt":"The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\\rho$ on Teichm\\\"uller space $\\Teich$ which is a qualitative invariant of the holonomy representation $\\rho$ of $\\pi_1(S)$. Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function $E_\\rho$ is proper for any convex cocompact representation of the fundamental group. More generally, if $\\rho$ is a discrete embedding onto a normal subgroup of a convex cocompact group $\\Gamma$, then $E_\\rho$ defines a proper function on the quotie"},"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":"math/0506212","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-06-10T21:00:28Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"1a5bea253826f637f0dd11c4c03aeea32728f36be2d89c0c2176c100f8ba887c","abstract_canon_sha256":"e81c65b5861c11280db169c0d6ab5758bd3e282c2bdd37488f9e16c2b977747f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.425754Z","signature_b64":"i+VzkbpTsBX8zHqmpGPpbNMikIhWKk/4nyac8ZHoEsCTE91kdPsWkdrA6mbhPaHqQNIZYrvv6pDfo+tjrxoICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36f3f4e223288b655755e193299853eb821754902a94f00f73aa86ceae72da40","last_reissued_at":"2026-05-18T04:18:33.425151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.425151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy of Twisted Harmonic Maps of Riemann Surfaces","license":"","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DG","authors_text":"Richard A. Wentworth, William M. Goldman","submitted_at":"2005-06-10T21:00:28Z","abstract_excerpt":"The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\\rho$ on Teichm\\\"uller space $\\Teich$ which is a qualitative invariant of the holonomy representation $\\rho$ of $\\pi_1(S)$. Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function $E_\\rho$ is proper for any convex cocompact representation of the fundamental group. More generally, if $\\rho$ is a discrete embedding onto a normal subgroup of a convex cocompact group $\\Gamma$, then $E_\\rho$ defines a proper function on the quotie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506212","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":"math/0506212","created_at":"2026-05-18T04:18:33.425232+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506212v2","created_at":"2026-05-18T04:18:33.425232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506212","created_at":"2026-05-18T04:18:33.425232+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3Z7JYRDFCFW","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3Z7JYRDFCFWKV2V","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3Z7JYRD","created_at":"2026-05-18T12:25:53.335082+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/G3Z7JYRDFCFWKV2V4GJSTGCT5O","json":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O.json","graph_json":"https://pith.science/api/pith-number/G3Z7JYRDFCFWKV2V4GJSTGCT5O/graph.json","events_json":"https://pith.science/api/pith-number/G3Z7JYRDFCFWKV2V4GJSTGCT5O/events.json","paper":"https://pith.science/paper/G3Z7JYRD"},"agent_actions":{"view_html":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O","download_json":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O.json","view_paper":"https://pith.science/paper/G3Z7JYRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506212&json=true","fetch_graph":"https://pith.science/api/pith-number/G3Z7JYRDFCFWKV2V4GJSTGCT5O/graph.json","fetch_events":"https://pith.science/api/pith-number/G3Z7JYRDFCFWKV2V4GJSTGCT5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O/action/storage_attestation","attest_author":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O/action/author_attestation","sign_citation":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O/action/citation_signature","submit_replication":"https://pith.science/pith/G3Z7JYRDFCFWKV2V4GJSTGCT5O/action/replication_record"}},"created_at":"2026-05-18T04:18:33.425232+00:00","updated_at":"2026-05-18T04:18:33.425232+00:00"}