{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QHGKOAWNDFA6TGYUJ53YROUJP5","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":"11e3ac0d28b4ba32eeb973acc4314d0d4a28749410677ea0b7d0760cb5ac6ac4","cross_cats_sorted":["math-ph","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-30T22:04:26Z","title_canon_sha256":"fb834b00b8c86b332bec69a1bb6711ee6694b909a8f2ff9d7269e79b996608ac"},"schema_version":"1.0","source":{"id":"1705.00379","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00379","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00379v6","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00379","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"QHGKOAWNDFA6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHGKOAWNDFA6TGYU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHGKOAWN","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:b33d194c236a6b4a212dfb9f30a11cca86284b895fd1a7bab6c9a9e3ebcdf540","target":"graph","created_at":"2026-05-18T00:06:41Z","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":"Let $\\mathcal{A}$ be a $C^*$-algebra of bounded uniformly continuous functions on $X=\\mathbb{R}^d$ such that $\\mathcal{A}$ is stable under translations and contains the continuous functions that have a limit at infinity. Denote $\\mathcal{A}^\\dagger$ the boundary of $X$ in the character space of $\\mathcal{A}$. Then the crossed product $\\mathscr{A}=\\mathcal{A}\\rtimes X$ of $\\mathcal{A}$ by the natural action of $X$ on $\\mathcal{A}$ is a well defined $C^*$-algebra and to each operator $A\\in\\mathscr{A}$ one may naturally associate a family of bounded operators $A_\\varkappa$ on $L^2(X)$ indexed by ","authors_text":"Vladimir Georgescu","cross_cats":["math-ph","math.MP","math.SP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-30T22:04:26Z","title":"On the essential spectrum of elliptic differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00379","kind":"arxiv","version":6},"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":"sha256:55055f9971b18b234ced3a473ced12826a078d060db18de1669b8c8816529e6c","target":"record","created_at":"2026-05-18T00:06:41Z","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":"11e3ac0d28b4ba32eeb973acc4314d0d4a28749410677ea0b7d0760cb5ac6ac4","cross_cats_sorted":["math-ph","math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-30T22:04:26Z","title_canon_sha256":"fb834b00b8c86b332bec69a1bb6711ee6694b909a8f2ff9d7269e79b996608ac"},"schema_version":"1.0","source":{"id":"1705.00379","kind":"arxiv","version":6}},"canonical_sha256":"81cca702cd1941e99b144f7788ba897f63b781b49354848a613dacd1a1c1edd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81cca702cd1941e99b144f7788ba897f63b781b49354848a613dacd1a1c1edd7","first_computed_at":"2026-05-18T00:06:41.957085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:41.957085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FVNwnXWFLLUA105kNpSGBfuiEJqG52fncj+py3HEJpKM1wOeuy4zs31MeEzslnEF1M2v9hGM6KBHZnI3MY5sDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:41.957567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00379","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55055f9971b18b234ced3a473ced12826a078d060db18de1669b8c8816529e6c","sha256:b33d194c236a6b4a212dfb9f30a11cca86284b895fd1a7bab6c9a9e3ebcdf540"],"state_sha256":"1dd29f1282167d3effb704666d508f704b7ddfc08a5145cdb30574176c8a85b7"}