{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HZUBYOF7G3K3334FZVQHAO3XE7","short_pith_number":"pith:HZUBYOF7","canonical_record":{"source":{"id":"1111.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-03T20:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"b3ca90316f377a2d4b7de701ddb2f549652025a6985fbe0f547369edf60f0810","abstract_canon_sha256":"a5220954f55f0c09152116bba44f2cf4a2a0ea581f237558f4534369b49f33d0"},"schema_version":"1.0"},"canonical_sha256":"3e681c38bf36d5bdef85cd60703b7727d22a418dddf4e2cfa6ca0fdf3af6342d","source":{"kind":"arxiv","id":"1111.0974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0974","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0974v1","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0974","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"HZUBYOF7G3K3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HZUBYOF7G3K3334F","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HZUBYOF7","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HZUBYOF7G3K3334FZVQHAO3XE7","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-03T20:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"b3ca90316f377a2d4b7de701ddb2f549652025a6985fbe0f547369edf60f0810","abstract_canon_sha256":"a5220954f55f0c09152116bba44f2cf4a2a0ea581f237558f4534369b49f33d0"},"schema_version":"1.0"},"canonical_sha256":"3e681c38bf36d5bdef85cd60703b7727d22a418dddf4e2cfa6ca0fdf3af6342d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:36.067031Z","signature_b64":"aQecRlYotjx71QXhdtbefr8jYvzL25wq1yi4Pxuya9b9/etLULZXXrUbQY9dCHtY8ug55oGMuFj0/sPb5+QBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e681c38bf36d5bdef85cd60703b7727d22a418dddf4e2cfa6ca0fdf3af6342d","last_reissued_at":"2026-05-18T04:09:36.066626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:36.066626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0974","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":"2026-05-18T04:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TeV0SGEwcABQPyG9qS7U5FC7mIEUc5i82ZrIiHfnPB34KKxeiSOvN1Nvuvq+7XDxpSTXqlAuqXoq7p8t5JbHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:51:33.821966Z"},"content_sha256":"e32ff71f28e8cca6db9560d6dc79b77dbd0796e1af1e6f60948cf135aa93c4a2","schema_version":"1.0","event_id":"sha256:e32ff71f28e8cca6db9560d6dc79b77dbd0796e1af1e6f60948cf135aa93c4a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HZUBYOF7G3K3334FZVQHAO3XE7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Roman Lavicka","submitted_at":"2011-11-03T20:05:40Z","abstract_excerpt":"Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this paper, we give another construction of these bases and, mainly, we show that the bases even form complete orthogonal Appell systems. Moreover, we study the corresponding Taylor series expansions. As an application, we construct quite explicitly orthogonal bases for homogeneous solutions of an arbitrary generalized Moisil-Theodoresco system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0974","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":"2026-05-18T04:09:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EL1dJFBsL59Y+3tlwzd/vItpyB0fD4J3q7pGtCGCyPBGTEWWPaPKqjVBctmU/CiY2yZh6xOiLl5NydtVwf+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:51:33.822530Z"},"content_sha256":"a9bc7fc0f30ed662d537b66219b55707fb50706e80670fba76c03109111afd9d","schema_version":"1.0","event_id":"sha256:a9bc7fc0f30ed662d537b66219b55707fb50706e80670fba76c03109111afd9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZUBYOF7G3K3334FZVQHAO3XE7/bundle.json","state_url":"https://pith.science/pith/HZUBYOF7G3K3334FZVQHAO3XE7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZUBYOF7G3K3334FZVQHAO3XE7/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":"2026-06-12T06:51:33Z","links":{"resolver":"https://pith.science/pith/HZUBYOF7G3K3334FZVQHAO3XE7","bundle":"https://pith.science/pith/HZUBYOF7G3K3334FZVQHAO3XE7/bundle.json","state":"https://pith.science/pith/HZUBYOF7G3K3334FZVQHAO3XE7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZUBYOF7G3K3334FZVQHAO3XE7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HZUBYOF7G3K3334FZVQHAO3XE7","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":"a5220954f55f0c09152116bba44f2cf4a2a0ea581f237558f4534369b49f33d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-03T20:05:40Z","title_canon_sha256":"b3ca90316f377a2d4b7de701ddb2f549652025a6985fbe0f547369edf60f0810"},"schema_version":"1.0","source":{"id":"1111.0974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0974","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0974v1","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0974","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"HZUBYOF7G3K3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HZUBYOF7G3K3334F","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HZUBYOF7","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:a9bc7fc0f30ed662d537b66219b55707fb50706e80670fba76c03109111afd9d","target":"graph","created_at":"2026-05-18T04:09:36Z","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":"Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this paper, we give another construction of these bases and, mainly, we show that the bases even form complete orthogonal Appell systems. Moreover, we study the corresponding Taylor series expansions. As an application, we construct quite explicitly orthogonal bases for homogeneous solutions of an arbitrary generalized Moisil-Theodoresco system.","authors_text":"Roman Lavicka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-03T20:05:40Z","title":"Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0974","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:e32ff71f28e8cca6db9560d6dc79b77dbd0796e1af1e6f60948cf135aa93c4a2","target":"record","created_at":"2026-05-18T04:09:36Z","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":"a5220954f55f0c09152116bba44f2cf4a2a0ea581f237558f4534369b49f33d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-03T20:05:40Z","title_canon_sha256":"b3ca90316f377a2d4b7de701ddb2f549652025a6985fbe0f547369edf60f0810"},"schema_version":"1.0","source":{"id":"1111.0974","kind":"arxiv","version":1}},"canonical_sha256":"3e681c38bf36d5bdef85cd60703b7727d22a418dddf4e2cfa6ca0fdf3af6342d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e681c38bf36d5bdef85cd60703b7727d22a418dddf4e2cfa6ca0fdf3af6342d","first_computed_at":"2026-05-18T04:09:36.066626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:36.066626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aQecRlYotjx71QXhdtbefr8jYvzL25wq1yi4Pxuya9b9/etLULZXXrUbQY9dCHtY8ug55oGMuFj0/sPb5+QBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:36.067031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e32ff71f28e8cca6db9560d6dc79b77dbd0796e1af1e6f60948cf135aa93c4a2","sha256:a9bc7fc0f30ed662d537b66219b55707fb50706e80670fba76c03109111afd9d"],"state_sha256":"9fdd575c0cadfbf875e737c272e5b7684aaf0595ef92723bfee0cc2d8abaee7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lrmJbBi6E/VvSAvaCZSzYBxYJfaLU7O57673nHcWg6g9DQbViAtbM4f3C8lPFvneJUiWlllMOKbKMYAKR+DVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:51:33.825337Z","bundle_sha256":"156f8dbde6638ce6e937a2dfdf81dc4c1e6ebaf29b1816055ccae8f9735c60b0"}}