{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N5PCO6YOYZDSZ3MA4UGG76UTN2","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":"f47bd21662981aa94848a8bf83d736751b2b568794458c665761dae1101029b6","cross_cats_sorted":["math.AP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T11:05:35Z","title_canon_sha256":"3edc6779d67c4cadfb50d7094eab2c3906e985bddb5f2fa2a732a53e6a8fcdf4"},"schema_version":"1.0","source":{"id":"1901.05304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05304","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05304v1","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05304","created_at":"2026-05-17T23:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"N5PCO6YOYZDS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N5PCO6YOYZDSZ3MA","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N5PCO6YO","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:68e4f612fa2fd16fe1f6a4629daa4ca06387c8769e814d53faba89f38b8e33ac","target":"graph","created_at":"2026-05-17T23:56:11Z","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 consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operator induced by a Morse--Smale diffeomorphism of this surface. Elements in this algebra are considered as operators in the scale of Sobolev spaces and the aim of this paper is to describe how Fredholm property of a given operator depends on the Sobolev smoothness exponent $s$.","authors_text":"A.Yu. Savin, N.R. Izvarina","cross_cats":["math.AP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T11:05:35Z","title":"On the ellipticity of operators associated with Morse-Smale diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05304","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":"sha256:9b507f233675b3aa5e683f845d7752a6533827efb826ed4880419f92a5485d5e","target":"record","created_at":"2026-05-17T23:56:11Z","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":"f47bd21662981aa94848a8bf83d736751b2b568794458c665761dae1101029b6","cross_cats_sorted":["math.AP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T11:05:35Z","title_canon_sha256":"3edc6779d67c4cadfb50d7094eab2c3906e985bddb5f2fa2a732a53e6a8fcdf4"},"schema_version":"1.0","source":{"id":"1901.05304","kind":"arxiv","version":1}},"canonical_sha256":"6f5e277b0ec6472ced80e50c6ffa936eaaa4f70a45f2b26ac53c653b6e962c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f5e277b0ec6472ced80e50c6ffa936eaaa4f70a45f2b26ac53c653b6e962c48","first_computed_at":"2026-05-17T23:56:11.205038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:11.205038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sq1KxvZ34C75/V7Z9v10YqFlc/VrUJs+HY98OUHpZqZQG1gJxJAPmYj+4Xw1/QAW35zEMqZwCPafUzTN+LOMDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:11.205696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.05304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b507f233675b3aa5e683f845d7752a6533827efb826ed4880419f92a5485d5e","sha256:68e4f612fa2fd16fe1f6a4629daa4ca06387c8769e814d53faba89f38b8e33ac"],"state_sha256":"ea65d00fdc7d27f2daa0b332c0b4b462b6acf5e0c917178ba3fcc7778a3e9208"}