{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X4ZLIUUCRVFN465TTVLAKP7BJI","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":"acff3ec9917f5e49c8c3e44f8e377a61ba28814b92db427ad806f98b243a17c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T18:05:18Z","title_canon_sha256":"0dedc30cfebd645ef3397be8c3f334958136d7a3f2450fb73888601249ab0cdd"},"schema_version":"1.0","source":{"id":"1307.0780","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0780","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0780v3","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0780","created_at":"2026-05-18T01:49:00Z"},{"alias_kind":"pith_short_12","alias_value":"X4ZLIUUCRVFN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X4ZLIUUCRVFN465T","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X4ZLIUUC","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:632f94f2bb64796419e858af258225b0ed6cbd8194db10731a488bd94a8e1a54","target":"graph","created_at":"2026-05-18T01:49:00Z","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 this article, we study analyticity properties of (directed) areas of epsilon-neighborhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using epsilon-neighborhoods of orbits in the simplest formal class. We show that the coefficient in front of epsilon^2 term in the asymptotic expansion in epsilon, which we call the principal part of the area, is a sectorially analytic function of initial point of the orbit. It satisfies a cohomological equation similar to the standard trivialization equation for parabolic diffeomorphisms. We give necessa","authors_text":"Maja Resman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T18:05:18Z","title":"Epsilon-neighborhoods of orbits of parabolic diffeomorphisms and cohomological equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0780","kind":"arxiv","version":3},"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":"sha256:04324709f53cab0044884e86e7c992b00b550b1a5cf447b8f69e4040b49b8e2c","target":"record","created_at":"2026-05-18T01:49:00Z","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":"acff3ec9917f5e49c8c3e44f8e377a61ba28814b92db427ad806f98b243a17c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-02T18:05:18Z","title_canon_sha256":"0dedc30cfebd645ef3397be8c3f334958136d7a3f2450fb73888601249ab0cdd"},"schema_version":"1.0","source":{"id":"1307.0780","kind":"arxiv","version":3}},"canonical_sha256":"bf32b452828d4ade7bb39d56053fe14a3b9d282eac26be570a5dfc733346bb43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf32b452828d4ade7bb39d56053fe14a3b9d282eac26be570a5dfc733346bb43","first_computed_at":"2026-05-18T01:49:00.572873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:00.572873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwPjMI2oAnu0dpw/TKpntvqIlQG061b72QlNsagbqcNO4eouoxqedtDYFDP2xGqXCHEK5dTmwyPKZAayWc3+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:00.573403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0780","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04324709f53cab0044884e86e7c992b00b550b1a5cf447b8f69e4040b49b8e2c","sha256:632f94f2bb64796419e858af258225b0ed6cbd8194db10731a488bd94a8e1a54"],"state_sha256":"9e491e9f9e3d6c954307dc28817e0cbc3efc1db56997cc7f5a8a64f3838696b9"}