{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DTIWT7FZEAMOVM5WYUBQUWGD6Y","short_pith_number":"pith:DTIWT7FZ","canonical_record":{"source":{"id":"1503.01695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T17:20:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"170b51ea46a552d45fadcfe01b0b458a59b3d2f32414bae2c663ee6bb941242d","abstract_canon_sha256":"c4455078c48c2264a84b175de89f8f278136bc80e9f239f5bb75f1f3f2761e31"},"schema_version":"1.0"},"canonical_sha256":"1cd169fcb92018eab3b6c5030a58c3f60766dcbd0b231ace953459288c34b255","source":{"kind":"arxiv","id":"1503.01695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01695","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01695v1","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01695","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"DTIWT7FZEAMO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DTIWT7FZEAMOVM5W","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DTIWT7FZ","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DTIWT7FZEAMOVM5WYUBQUWGD6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T17:20:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"170b51ea46a552d45fadcfe01b0b458a59b3d2f32414bae2c663ee6bb941242d","abstract_canon_sha256":"c4455078c48c2264a84b175de89f8f278136bc80e9f239f5bb75f1f3f2761e31"},"schema_version":"1.0"},"canonical_sha256":"1cd169fcb92018eab3b6c5030a58c3f60766dcbd0b231ace953459288c34b255","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:28.767752Z","signature_b64":"JMydEtIVB1iMqfr+3U2X5KifoNSGxHKRbYAno40IWgLCbZpLeBsRQiVlcaDN5EX8f/gf9mymUNUWiTZaHPeYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cd169fcb92018eab3b6c5030a58c3f60766dcbd0b231ace953459288c34b255","last_reissued_at":"2026-05-18T00:48:28.767134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:28.767134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01695","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lyd2WjfLfk0InOGlIRj9bfxug3iwjZ/XlN2gQfVlzNt0BJyHbxYimQhE+sg2Y4HhG3Zkvl5PUOQcEBVVKL6GAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:35:30.316468Z"},"content_sha256":"84a415678306924f7771668921da73bca448827b7efe965166516ee0254a5909","schema_version":"1.0","event_id":"sha256:84a415678306924f7771668921da73bca448827b7efe965166516ee0254a5909"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DTIWT7FZEAMOVM5WYUBQUWGD6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On boundary value problems for some conformally invariant differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AP","authors_text":"Bent {\\O}rsted, Genkai Zhang, Jan M\\\"ollers","submitted_at":"2015-03-05T17:20:23Z","abstract_excerpt":"We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain $L^p$-spaces.\n  The co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01695","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cc9E+ujHhSQOaoMb1anYZELLwnhgtSyX6gA1O7yz/WGC28kSaYIHyi7el4ce8agvjgZdzAIWKIxjLVfqmi1fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:35:30.316822Z"},"content_sha256":"e2b7a4946decc5eec617d508e740eb1730a9bb39381323fec2b2beeb2dd975be","schema_version":"1.0","event_id":"sha256:e2b7a4946decc5eec617d508e740eb1730a9bb39381323fec2b2beeb2dd975be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/bundle.json","state_url":"https://pith.science/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T03:35:30Z","links":{"resolver":"https://pith.science/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y","bundle":"https://pith.science/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/bundle.json","state":"https://pith.science/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTIWT7FZEAMOVM5WYUBQUWGD6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DTIWT7FZEAMOVM5WYUBQUWGD6Y","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":"c4455078c48c2264a84b175de89f8f278136bc80e9f239f5bb75f1f3f2761e31","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T17:20:23Z","title_canon_sha256":"170b51ea46a552d45fadcfe01b0b458a59b3d2f32414bae2c663ee6bb941242d"},"schema_version":"1.0","source":{"id":"1503.01695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01695","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01695v1","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01695","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"DTIWT7FZEAMO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DTIWT7FZEAMOVM5W","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DTIWT7FZ","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:e2b7a4946decc5eec617d508e740eb1730a9bb39381323fec2b2beeb2dd975be","target":"graph","created_at":"2026-05-18T00:48:28Z","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 study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain $L^p$-spaces.\n  The co","authors_text":"Bent {\\O}rsted, Genkai Zhang, Jan M\\\"ollers","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T17:20:23Z","title":"On boundary value problems for some conformally invariant differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01695","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":"sha256:84a415678306924f7771668921da73bca448827b7efe965166516ee0254a5909","target":"record","created_at":"2026-05-18T00:48:28Z","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":"c4455078c48c2264a84b175de89f8f278136bc80e9f239f5bb75f1f3f2761e31","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T17:20:23Z","title_canon_sha256":"170b51ea46a552d45fadcfe01b0b458a59b3d2f32414bae2c663ee6bb941242d"},"schema_version":"1.0","source":{"id":"1503.01695","kind":"arxiv","version":1}},"canonical_sha256":"1cd169fcb92018eab3b6c5030a58c3f60766dcbd0b231ace953459288c34b255","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cd169fcb92018eab3b6c5030a58c3f60766dcbd0b231ace953459288c34b255","first_computed_at":"2026-05-18T00:48:28.767134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:28.767134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JMydEtIVB1iMqfr+3U2X5KifoNSGxHKRbYAno40IWgLCbZpLeBsRQiVlcaDN5EX8f/gf9mymUNUWiTZaHPeYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:28.767752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84a415678306924f7771668921da73bca448827b7efe965166516ee0254a5909","sha256:e2b7a4946decc5eec617d508e740eb1730a9bb39381323fec2b2beeb2dd975be"],"state_sha256":"8bf9ed463972958142704f88a55628b3127b8f312fc52bd8dcbc55ea2e35692c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYgdbk1vGRxEY2vOfp2lt/87hfw5sohVn/JQTNP0LxxBTO1bPTwVqNkeaayXzbMekcNjpWkHB6lxqGDxDpQ0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:35:30.319142Z","bundle_sha256":"9d1827f82c913daf2b536dfb14f5b7417ea9087918b984f1de5ac97abcdfa9ee"}}