{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HTBEWXNCU4NY35RQVZFTVDSUSI","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":"ef81f2416bdbdecb3fc87a09417c7df67731cf93d28adf209ef66dde64c24108","cross_cats_sorted":["math.DG","math.FA","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-04-05T14:01:49Z","title_canon_sha256":"4e256d6d455172cf4b9a01c9f866c68af107bfecddb7f2d40a3aab089dcebebb"},"schema_version":"1.0","source":{"id":"2104.01919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.01919","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"2104.01919v2","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.01919","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"HTBEWXNCU4NY","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_16","alias_value":"HTBEWXNCU4NY35RQ","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_8","alias_value":"HTBEWXNC","created_at":"2026-07-05T06:02:44Z"}],"graph_snapshots":[{"event_id":"sha256:4e80d04c576f10b0acffb842b819f8a240700ead4539be04556a39c4826b8c33","target":"graph","created_at":"2026-07-05T06:02:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.01919/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\\\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of elements in the maximal domain is described as a Hilbert space densely sandwiched between two mixed order Sobolev spaces. The description uses Calder\\'on projectors which, in the first order case, is equivalent to results of B\\\"ar-Bandara using spectral projectors of an adapted boundary operator. Boundary conditions that induce Fredholm as well as regular realisati","authors_text":"Hemanth Saratchandran, Lashi Bandara, Magnus Goffeng","cross_cats":["math.DG","math.FA","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-04-05T14:01:49Z","title":"Realisations of elliptic operators on compact manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.01919","kind":"arxiv","version":2},"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":"sha256:5f6ca4e7c13eab40a70e503dc6884d69655505fcc9c62277149bbf04d4d6cba4","target":"record","created_at":"2026-07-05T06:02:44Z","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":"ef81f2416bdbdecb3fc87a09417c7df67731cf93d28adf209ef66dde64c24108","cross_cats_sorted":["math.DG","math.FA","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-04-05T14:01:49Z","title_canon_sha256":"4e256d6d455172cf4b9a01c9f866c68af107bfecddb7f2d40a3aab089dcebebb"},"schema_version":"1.0","source":{"id":"2104.01919","kind":"arxiv","version":2}},"canonical_sha256":"3cc24b5da2a71b8df630ae4b3a8e54920ab33f51621d93932cdf2ce5c79c93ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cc24b5da2a71b8df630ae4b3a8e54920ab33f51621d93932cdf2ce5c79c93ef","first_computed_at":"2026-07-05T06:02:44.009085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:02:44.009085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m+okcNwZPtkgEHO4U366YLqKSonOL8e18ul1KkYuau0+ek6czlBeAmgKx0UUoMORpG/jprjPpe+U0IVnZaPaBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:02:44.009528Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.01919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6ca4e7c13eab40a70e503dc6884d69655505fcc9c62277149bbf04d4d6cba4","sha256:4e80d04c576f10b0acffb842b819f8a240700ead4539be04556a39c4826b8c33"],"state_sha256":"2547a8d537764562f4420cc0cd3a0d81e9b3fa2a569fc3d95433a061d36b13d1"}