{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I7FPLKSDUX3QFX4VLROJURFUUA","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":"8d37ca2d55f65cd40c848fd16eb123592bc0efc145f761b0b32df2e5aefd53af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T10:24:05Z","title_canon_sha256":"ef92f6354a29b243b5c220f15447e11507bfb3ee170ffabde04870713291a307"},"schema_version":"1.0","source":{"id":"1507.05773","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05773","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05773v6","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05773","created_at":"2026-05-18T00:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"I7FPLKSDUX3Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I7FPLKSDUX3QFX4V","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I7FPLKSD","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:97d61611a9c543e5618417f9dc8d2d22d761c170038a96356d7e763a09a74e65","target":"graph","created_at":"2026-05-18T00:40:24Z","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":"In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\\mathbb{D})$ and weighted Bergman spaces $A_\\alpha^2(\\mathbb{D})$.","authors_text":"Yong-Xin Gao, Ze-Hua Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T10:24:05Z","title":"Spectra of weighted composition operators induced by automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05773","kind":"arxiv","version":6},"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:e350e9e7302d555ecab27732a80a9b109a6753cc262649876ba61c17e5c8fcf7","target":"record","created_at":"2026-05-18T00:40:24Z","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":"8d37ca2d55f65cd40c848fd16eb123592bc0efc145f761b0b32df2e5aefd53af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T10:24:05Z","title_canon_sha256":"ef92f6354a29b243b5c220f15447e11507bfb3ee170ffabde04870713291a307"},"schema_version":"1.0","source":{"id":"1507.05773","kind":"arxiv","version":6}},"canonical_sha256":"47caf5aa43a5f702df955c5c9a44b4a02a5a8642a9e264efa2310ec5a223af2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47caf5aa43a5f702df955c5c9a44b4a02a5a8642a9e264efa2310ec5a223af2f","first_computed_at":"2026-05-18T00:40:24.503018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:24.503018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V64Omy5eWB16HgenRyCwqDqJjoVUyOltbGkz85GoESgwsy/3KIErPp6YjGZXqsN4h0q8fTi4CYNFNtzDQHroBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:24.503500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05773","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e350e9e7302d555ecab27732a80a9b109a6753cc262649876ba61c17e5c8fcf7","sha256:97d61611a9c543e5618417f9dc8d2d22d761c170038a96356d7e763a09a74e65"],"state_sha256":"93a1f9513b2801f579337218d81e21f265ddce6361bf072f9d1c476e6f54fe95"}