{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2IFRRY5ITDYD2EBRNBDNLNOWLC","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":"93a5d76f039f935d65d2b80fb24e4c96232bbcb6f0ed654ae0eae704c78c0707","cross_cats_sorted":["math.AP","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-30T10:31:22Z","title_canon_sha256":"fed18634fc570c94d4bd5a3cf47c5386fce9f7bf2e6a50ad2bbf9d3f2effd6fa"},"schema_version":"1.0","source":{"id":"1101.0067","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0067","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0067v4","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0067","created_at":"2026-05-18T04:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"2IFRRY5ITDYD","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2IFRRY5ITDYD2EBR","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2IFRRY5I","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b9ea712e322be816e404cac8856aef7ffc1b04fc15686697270d2917d9b52cf2","target":"graph","created_at":"2026-05-18T04:00:49Z","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":"Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We show that it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology which we explicitly describe. Our main application deals with a continuous curve of arbitrary first order linear elliptic differential operators over a compact manifold with boundary. Under the additional assumption of the weak inner unique continuation property, we derive the continuity of a related curve of Calde","authors_text":"Bernhelm Booss-Bavnbek, Chaofeng Zhu, Guoyuan Chen, Matthias Lesch","cross_cats":["math.AP","math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-30T10:31:22Z","title":"Perturbation of Sectorial Projections of Elliptic Pseudo-differential Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0067","kind":"arxiv","version":4},"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:b830ae36245ea4153d53d79078d3ad0ae94c530a8b7384097df8e5f0baee7573","target":"record","created_at":"2026-05-18T04:00:49Z","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":"93a5d76f039f935d65d2b80fb24e4c96232bbcb6f0ed654ae0eae704c78c0707","cross_cats_sorted":["math.AP","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-30T10:31:22Z","title_canon_sha256":"fed18634fc570c94d4bd5a3cf47c5386fce9f7bf2e6a50ad2bbf9d3f2effd6fa"},"schema_version":"1.0","source":{"id":"1101.0067","kind":"arxiv","version":4}},"canonical_sha256":"d20b18e3a898f03d10316846d5b5d6589312464974f628b98ef58488fa1cc62a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d20b18e3a898f03d10316846d5b5d6589312464974f628b98ef58488fa1cc62a","first_computed_at":"2026-05-18T04:00:49.574587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:49.574587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8OhLyQrgf+7uToRASQXyHdO3JYhWc/3+4esnT3ZrgjmBenEqQnfyYFKZxCOLnl75NTRd24oJb4waozipjeQfBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:49.575234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0067","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b830ae36245ea4153d53d79078d3ad0ae94c530a8b7384097df8e5f0baee7573","sha256:b9ea712e322be816e404cac8856aef7ffc1b04fc15686697270d2917d9b52cf2"],"state_sha256":"5e9c37d8c43b6c38a3c3abf1fdea2dc2b2647338aff0256c1f5a2e06d162e3a8"}