{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:BP3FWXAMNW6PZONIOXXXSAJKSJ","short_pith_number":"pith:BP3FWXAM","schema_version":"1.0","canonical_sha256":"0bf65b5c0c6dbcfcb9a875ef79012a92420528c41132fca2ad8bfee64f582c6b","source":{"kind":"arxiv","id":"2104.05581","version":4},"attestation_state":"computed","paper":{"title":"The principal transmission condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2021-04-12T15:54:37Z","abstract_excerpt":"The paper treats pseudodifferential operators $P=Op(p(\\xi ))$ with homogeneous complex symbol $p(\\xi )$ of order $2a>0$, generalizing the fractional Laplacian $(-\\Delta )^a$ but lacking its symmetries, and taken to act on the halfspace $R^n_+$. The operators are seen to satisfy a principal $\\mu $-transmission condition relative to $R^n_+$, but generally not the full $\\mu $-transmission condition satisfied by $(-\\Delta )^a$ and related operators (with $\\mu =a$). However, $P$ acts well on the so-called $\\mu $-transmission spaces over $R^n_+$ (defined in earlier works), and when $P$ moreover is s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2104.05581","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-12T15:54:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c5512731364ec827c9f0825e989960d153c8bd1c45c3736dfd686f5d8209de98","abstract_canon_sha256":"7ad99700e88f39b4b00bd88fc138f3b3ee7ace0d647fbbba435938359737e6d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:07:48.369752Z","signature_b64":"E7+Dv8ZM0kv3iAOHfh5YOXRBpEQpb7euwxid5X7uv5ycjQjsXFxrBaj8s0+p40O94Ts4W7JuwP1nRhkm2f7/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bf65b5c0c6dbcfcb9a875ef79012a92420528c41132fca2ad8bfee64f582c6b","last_reissued_at":"2026-07-05T03:07:48.369279Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:07:48.369279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The principal transmission condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2021-04-12T15:54:37Z","abstract_excerpt":"The paper treats pseudodifferential operators $P=Op(p(\\xi ))$ with homogeneous complex symbol $p(\\xi )$ of order $2a>0$, generalizing the fractional Laplacian $(-\\Delta )^a$ but lacking its symmetries, and taken to act on the halfspace $R^n_+$. The operators are seen to satisfy a principal $\\mu $-transmission condition relative to $R^n_+$, but generally not the full $\\mu $-transmission condition satisfied by $(-\\Delta )^a$ and related operators (with $\\mu =a$). However, $P$ acts well on the so-called $\\mu $-transmission spaces over $R^n_+$ (defined in earlier works), and when $P$ moreover is s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.05581","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.05581/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2104.05581","created_at":"2026-07-05T03:07:48.369343+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.05581v4","created_at":"2026-07-05T03:07:48.369343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.05581","created_at":"2026-07-05T03:07:48.369343+00:00"},{"alias_kind":"pith_short_12","alias_value":"BP3FWXAMNW6P","created_at":"2026-07-05T03:07:48.369343+00:00"},{"alias_kind":"pith_short_16","alias_value":"BP3FWXAMNW6PZONI","created_at":"2026-07-05T03:07:48.369343+00:00"},{"alias_kind":"pith_short_8","alias_value":"BP3FWXAM","created_at":"2026-07-05T03:07:48.369343+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ","json":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ.json","graph_json":"https://pith.science/api/pith-number/BP3FWXAMNW6PZONIOXXXSAJKSJ/graph.json","events_json":"https://pith.science/api/pith-number/BP3FWXAMNW6PZONIOXXXSAJKSJ/events.json","paper":"https://pith.science/paper/BP3FWXAM"},"agent_actions":{"view_html":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ","download_json":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ.json","view_paper":"https://pith.science/paper/BP3FWXAM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.05581&json=true","fetch_graph":"https://pith.science/api/pith-number/BP3FWXAMNW6PZONIOXXXSAJKSJ/graph.json","fetch_events":"https://pith.science/api/pith-number/BP3FWXAMNW6PZONIOXXXSAJKSJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ/action/storage_attestation","attest_author":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ/action/author_attestation","sign_citation":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ/action/citation_signature","submit_replication":"https://pith.science/pith/BP3FWXAMNW6PZONIOXXXSAJKSJ/action/replication_record"}},"created_at":"2026-07-05T03:07:48.369343+00:00","updated_at":"2026-07-05T03:07:48.369343+00:00"}