{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:WCCY22XY6BTVWPJ3X5HDKARG67","short_pith_number":"pith:WCCY22XY","schema_version":"1.0","canonical_sha256":"b0858d6af8f0675b3d3bbf4e350226f7d3078f8837d39c7e8e51dbbb44103ac7","source":{"kind":"arxiv","id":"1103.5915","version":1},"attestation_state":"computed","paper":{"title":"The group of invariants of an inner function with finite spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Isabelle Chalendar, Jonathan R. Partington, Pamela Gorkin","submitted_at":"2011-03-30T13:12:16Z","abstract_excerpt":"This paper determines the group of continuous invariants corresponding to an inner function $ \\Theta $ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g: T \\to T$ such that $\\Theta \\circ g = \\Theta $ on $\\T$. These mappings form a group under composition."},"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":"1103.5915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T13:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"30229a8a7d5a7a9c8fbb5eaa8f928debaa8b30fbbd709773f1907dfef7ec9a45","abstract_canon_sha256":"33d84060367d5b29fcfababa63ed1ce92f9b1b75548d7c9ee85c4b91f13f3db5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:27.207175Z","signature_b64":"oGN+f7Mi3zQM4aCtMByWzqORsfywFhk1Rh1XmgphKmgOoMtIU+9Xmc2f+wrdj13UUNCYtima2jXAwt4ZAW12Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0858d6af8f0675b3d3bbf4e350226f7d3078f8837d39c7e8e51dbbb44103ac7","last_reissued_at":"2026-05-18T04:25:27.206328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:27.206328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The group of invariants of an inner function with finite spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Isabelle Chalendar, Jonathan R. Partington, Pamela Gorkin","submitted_at":"2011-03-30T13:12:16Z","abstract_excerpt":"This paper determines the group of continuous invariants corresponding to an inner function $ \\Theta $ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g: T \\to T$ such that $\\Theta \\circ g = \\Theta $ on $\\T$. These mappings form a group under composition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5915","kind":"arxiv","version":1},"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":"1103.5915","created_at":"2026-05-18T04:25:27.206481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.5915v1","created_at":"2026-05-18T04:25:27.206481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5915","created_at":"2026-05-18T04:25:27.206481+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCCY22XY6BTV","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCCY22XY6BTVWPJ3","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCCY22XY","created_at":"2026-05-18T12:26:44.992195+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/WCCY22XY6BTVWPJ3X5HDKARG67","json":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67.json","graph_json":"https://pith.science/api/pith-number/WCCY22XY6BTVWPJ3X5HDKARG67/graph.json","events_json":"https://pith.science/api/pith-number/WCCY22XY6BTVWPJ3X5HDKARG67/events.json","paper":"https://pith.science/paper/WCCY22XY"},"agent_actions":{"view_html":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67","download_json":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67.json","view_paper":"https://pith.science/paper/WCCY22XY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.5915&json=true","fetch_graph":"https://pith.science/api/pith-number/WCCY22XY6BTVWPJ3X5HDKARG67/graph.json","fetch_events":"https://pith.science/api/pith-number/WCCY22XY6BTVWPJ3X5HDKARG67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67/action/storage_attestation","attest_author":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67/action/author_attestation","sign_citation":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67/action/citation_signature","submit_replication":"https://pith.science/pith/WCCY22XY6BTVWPJ3X5HDKARG67/action/replication_record"}},"created_at":"2026-05-18T04:25:27.206481+00:00","updated_at":"2026-05-18T04:25:27.206481+00:00"}