{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:KUBR4HCNJPT2745ZED7W6JPSRL","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":"2e7b5418bccd0d45b74b62e45c95d9e91df222acfb94daa88ec82a6338c715c5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2004-05-04T14:11:27Z","title_canon_sha256":"dbdfdeba8b61cf5a0b813890a63811dfe30d2a42ac531ea4c2a3e8d7ab4aec93"},"schema_version":"1.0","source":{"id":"math/0405055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405055","created_at":"2026-05-18T04:28:10Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405055v1","created_at":"2026-05-18T04:28:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405055","created_at":"2026-05-18T04:28:10Z"},{"alias_kind":"pith_short_12","alias_value":"KUBR4HCNJPT2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KUBR4HCNJPT2745Z","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KUBR4HCN","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:010c2cd2199038aabf8b63e15306448a8d843c86016df7352db1383e83473014","target":"graph","created_at":"2026-05-18T04:28:10Z","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 construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.","authors_text":"Gerhard Keller, Hans Henrik Rugh","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2004-05-04T14:11:27Z","title":"Eigenfunctions for smooth expanding circle maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405055","kind":"arxiv","version":1},"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":"sha256:1187cde82f4d989127081d99102d945ce6aff6109831a9a1a8e2666dbd20c1d6","target":"record","created_at":"2026-05-18T04:28:10Z","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":"2e7b5418bccd0d45b74b62e45c95d9e91df222acfb94daa88ec82a6338c715c5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2004-05-04T14:11:27Z","title_canon_sha256":"dbdfdeba8b61cf5a0b813890a63811dfe30d2a42ac531ea4c2a3e8d7ab4aec93"},"schema_version":"1.0","source":{"id":"math/0405055","kind":"arxiv","version":1}},"canonical_sha256":"55031e1c4d4be7aff3b920ff6f25f28ac290c915ffdc27f37f78018f6552a596","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55031e1c4d4be7aff3b920ff6f25f28ac290c915ffdc27f37f78018f6552a596","first_computed_at":"2026-05-18T04:28:10.315048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:10.315048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S5ueR00CA/FYnH7erV4v8lUlTb8F7SFj5VUm0JLLUegsbCulhKqYNX/KJBBwgbxh7zs6gDSMX25+Ww1v2/65AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:10.315815Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1187cde82f4d989127081d99102d945ce6aff6109831a9a1a8e2666dbd20c1d6","sha256:010c2cd2199038aabf8b63e15306448a8d843c86016df7352db1383e83473014"],"state_sha256":"9c02c6165d1c1b8ba8afb2fc57e1cfd7cec85eda95e9accf4db82c7bb1c84ecc"}