{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CXVGO4ZCWEKX4AVY7DZNSE6VS4","short_pith_number":"pith:CXVGO4ZC","canonical_record":{"source":{"id":"1605.00132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-30T16:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"5fa7306a6823b6dc9a018a3fd6dbbc78cbbf191e2c131c58a4c19b6abc2b9d14","abstract_canon_sha256":"f8dd8b30b04aea74b217c3e241325d64132f7d3077014d6b8ee63a7515e1b061"},"schema_version":"1.0"},"canonical_sha256":"15ea677322b1157e02b8f8f2d913d5970118549fe13c6e325cb8a14f275757fb","source":{"kind":"arxiv","id":"1605.00132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00132","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00132v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00132","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"CXVGO4ZCWEKX","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CXVGO4ZCWEKX4AVY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CXVGO4ZC","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CXVGO4ZCWEKX4AVY7DZNSE6VS4","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-30T16:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"5fa7306a6823b6dc9a018a3fd6dbbc78cbbf191e2c131c58a4c19b6abc2b9d14","abstract_canon_sha256":"f8dd8b30b04aea74b217c3e241325d64132f7d3077014d6b8ee63a7515e1b061"},"schema_version":"1.0"},"canonical_sha256":"15ea677322b1157e02b8f8f2d913d5970118549fe13c6e325cb8a14f275757fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:56.682161Z","signature_b64":"C2MKvxACRSzLL2xgf87uhC6tZhi4iojB4kNhNRBxJU1zGHbH6QuMLMydlub4yY+Y1pdjMc9eAYsVPyG9CSDpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15ea677322b1157e02b8f8f2d913d5970118549fe13c6e325cb8a14f275757fb","last_reissued_at":"2026-05-18T01:15:56.681553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:56.681553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00132","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":"2026-05-18T01:15:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W3HY9uxI4ZF/D9Vw25ezY400o66AB993eloonmj8cubxrsA1pKCaDKTS8gTyeiyAoVfwzTYYJ9+qJxK2v/E4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:43:00.509559Z"},"content_sha256":"7cad3facf6793b9391e4ee3c7455772722aa244db8bd7148538d6d98d62aeec6","schema_version":"1.0","event_id":"sha256:7cad3facf6793b9391e4ee3c7455772722aa244db8bd7148538d6d98d62aeec6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CXVGO4ZCWEKX4AVY7DZNSE6VS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A systematic construction of finite element commuting exact sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bernardo Cockburn, Guosheng Fu","submitted_at":"2016-04-30T16:14:33Z","abstract_excerpt":"We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in three-space dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms; and to uncover four ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00132","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":"2026-05-18T01:15:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bodZSU+/cTAZ5xkgdiwCXwwTfXxIalP0TrqBNfIGNPahq5Kw4GNVACXIcLRgBZjMi5uxD4zm2CrqPCie+ctnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:43:00.509908Z"},"content_sha256":"9249c15e0216ba4e4b73a23ea7f3bf689f60b5b33e12c79d5b2c433918aa549b","schema_version":"1.0","event_id":"sha256:9249c15e0216ba4e4b73a23ea7f3bf689f60b5b33e12c79d5b2c433918aa549b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/bundle.json","state_url":"https://pith.science/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/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":"2026-06-23T17:43:00Z","links":{"resolver":"https://pith.science/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4","bundle":"https://pith.science/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/bundle.json","state":"https://pith.science/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXVGO4ZCWEKX4AVY7DZNSE6VS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CXVGO4ZCWEKX4AVY7DZNSE6VS4","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":"f8dd8b30b04aea74b217c3e241325d64132f7d3077014d6b8ee63a7515e1b061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-30T16:14:33Z","title_canon_sha256":"5fa7306a6823b6dc9a018a3fd6dbbc78cbbf191e2c131c58a4c19b6abc2b9d14"},"schema_version":"1.0","source":{"id":"1605.00132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00132","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00132v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00132","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"CXVGO4ZCWEKX","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CXVGO4ZCWEKX4AVY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CXVGO4ZC","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:9249c15e0216ba4e4b73a23ea7f3bf689f60b5b33e12c79d5b2c433918aa549b","target":"graph","created_at":"2026-05-18T01:15:56Z","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 present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in three-space dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms; and to uncover four ne","authors_text":"Bernardo Cockburn, Guosheng Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-30T16:14:33Z","title":"A systematic construction of finite element commuting exact sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00132","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":"sha256:7cad3facf6793b9391e4ee3c7455772722aa244db8bd7148538d6d98d62aeec6","target":"record","created_at":"2026-05-18T01:15:56Z","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":"f8dd8b30b04aea74b217c3e241325d64132f7d3077014d6b8ee63a7515e1b061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-30T16:14:33Z","title_canon_sha256":"5fa7306a6823b6dc9a018a3fd6dbbc78cbbf191e2c131c58a4c19b6abc2b9d14"},"schema_version":"1.0","source":{"id":"1605.00132","kind":"arxiv","version":1}},"canonical_sha256":"15ea677322b1157e02b8f8f2d913d5970118549fe13c6e325cb8a14f275757fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15ea677322b1157e02b8f8f2d913d5970118549fe13c6e325cb8a14f275757fb","first_computed_at":"2026-05-18T01:15:56.681553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:56.681553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C2MKvxACRSzLL2xgf87uhC6tZhi4iojB4kNhNRBxJU1zGHbH6QuMLMydlub4yY+Y1pdjMc9eAYsVPyG9CSDpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:56.682161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cad3facf6793b9391e4ee3c7455772722aa244db8bd7148538d6d98d62aeec6","sha256:9249c15e0216ba4e4b73a23ea7f3bf689f60b5b33e12c79d5b2c433918aa549b"],"state_sha256":"c812b4da3bb6544e17d089f6d85f26dc02b26a6ae0d9c61566d89e448c1dcf60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNBWjEY5gY3g81XkyAp21JrS34KrUdQiTCG4ZaZfxCGORqDhzXVxthx4k4luhv6k9cUx3gic4BI7FFjUO9lDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:43:00.511992Z","bundle_sha256":"43cd332b11a0830ee669723589cbc3616b7e7eeda081bd7a261e492d809b82ed"}}