{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TD4KBL2EGCWZW52ZQZZDIEWLPE","short_pith_number":"pith:TD4KBL2E","canonical_record":{"source":{"id":"1508.02242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-10T13:41:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c362e9ccdc89937a1c6e1b87397f73e128678696d7cacc36eee3da7996d61e6","abstract_canon_sha256":"3cbb388ed90959a7e01245c37a2f73b2a5ffc68502f032b78329782955a22879"},"schema_version":"1.0"},"canonical_sha256":"98f8a0af4430ad9b775986723412cb79152e0effd06fdac4b04996edfdacb3ea","source":{"kind":"arxiv","id":"1508.02242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02242","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02242v1","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02242","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"TD4KBL2EGCWZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TD4KBL2EGCWZW52Z","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TD4KBL2E","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TD4KBL2EGCWZW52ZQZZDIEWLPE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-10T13:41:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c362e9ccdc89937a1c6e1b87397f73e128678696d7cacc36eee3da7996d61e6","abstract_canon_sha256":"3cbb388ed90959a7e01245c37a2f73b2a5ffc68502f032b78329782955a22879"},"schema_version":"1.0"},"canonical_sha256":"98f8a0af4430ad9b775986723412cb79152e0effd06fdac4b04996edfdacb3ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:33.774963Z","signature_b64":"zi9/8M0aQGgHC20taLcGPfcThoA0i1hjoibwRvTME5pwO7lKpXwNiO1edDNiNgiopuCrhFpONTmZiT593nYeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98f8a0af4430ad9b775986723412cb79152e0effd06fdac4b04996edfdacb3ea","last_reissued_at":"2026-05-18T01:35:33.774271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:33.774271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02242","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":"2026-05-18T01:35:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jfjBRc4qrKQwgEmKTjA9UKws8O/19Wh1y0JVGZLfonf+NuYXSH5AjXLKu0BAmS/kJP2qWcP75PRcGcksiSaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:35:26.035306Z"},"content_sha256":"1e87699cde1f3fc1909ae8c67989c7fa939ff45062f8870f9c96b0604d3f5e36","schema_version":"1.0","event_id":"sha256:1e87699cde1f3fc1909ae8c67989c7fa939ff45062f8870f9c96b0604d3f5e36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TD4KBL2EGCWZW52ZQZZDIEWLPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Basic principles of hp Virtual Elements on quasiuniform meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. Chernov, A. Russo, L. Beir\\~ao da Veiga, L. Mascotto","submitted_at":"2015-08-10T13:41:24Z","abstract_excerpt":"In the present paper we initiate the study of $hp$ Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size $h$ and in the polynomial degree $p$ in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02242","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":"2026-05-18T01:35:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uShZupgXoNnuscn4+J7AfkVUpkjQOjw7UrsCYCeByEfnhbersl3lSAk62rRLPtsNtbU/Uhn8OyJqMtOeBJ5UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:35:26.035965Z"},"content_sha256":"18e984a2b80e801a0bb7ac1585df7e3d65e7f0b96a435a9efa1991199f7731d4","schema_version":"1.0","event_id":"sha256:18e984a2b80e801a0bb7ac1585df7e3d65e7f0b96a435a9efa1991199f7731d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/bundle.json","state_url":"https://pith.science/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/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":"2026-05-26T11:35:26Z","links":{"resolver":"https://pith.science/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE","bundle":"https://pith.science/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/bundle.json","state":"https://pith.science/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TD4KBL2EGCWZW52ZQZZDIEWLPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TD4KBL2EGCWZW52ZQZZDIEWLPE","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":"3cbb388ed90959a7e01245c37a2f73b2a5ffc68502f032b78329782955a22879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-10T13:41:24Z","title_canon_sha256":"1c362e9ccdc89937a1c6e1b87397f73e128678696d7cacc36eee3da7996d61e6"},"schema_version":"1.0","source":{"id":"1508.02242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02242","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02242v1","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02242","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"TD4KBL2EGCWZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TD4KBL2EGCWZW52Z","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TD4KBL2E","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:18e984a2b80e801a0bb7ac1585df7e3d65e7f0b96a435a9efa1991199f7731d4","target":"graph","created_at":"2026-05-18T01:35:33Z","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":"In the present paper we initiate the study of $hp$ Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size $h$ and in the polynomial degree $p$ in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.","authors_text":"A. Chernov, A. Russo, L. Beir\\~ao da Veiga, L. Mascotto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-10T13:41:24Z","title":"Basic principles of hp Virtual Elements on quasiuniform meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02242","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":"sha256:1e87699cde1f3fc1909ae8c67989c7fa939ff45062f8870f9c96b0604d3f5e36","target":"record","created_at":"2026-05-18T01:35:33Z","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":"3cbb388ed90959a7e01245c37a2f73b2a5ffc68502f032b78329782955a22879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-10T13:41:24Z","title_canon_sha256":"1c362e9ccdc89937a1c6e1b87397f73e128678696d7cacc36eee3da7996d61e6"},"schema_version":"1.0","source":{"id":"1508.02242","kind":"arxiv","version":1}},"canonical_sha256":"98f8a0af4430ad9b775986723412cb79152e0effd06fdac4b04996edfdacb3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98f8a0af4430ad9b775986723412cb79152e0effd06fdac4b04996edfdacb3ea","first_computed_at":"2026-05-18T01:35:33.774271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:33.774271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zi9/8M0aQGgHC20taLcGPfcThoA0i1hjoibwRvTME5pwO7lKpXwNiO1edDNiNgiopuCrhFpONTmZiT593nYeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:33.774963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e87699cde1f3fc1909ae8c67989c7fa939ff45062f8870f9c96b0604d3f5e36","sha256:18e984a2b80e801a0bb7ac1585df7e3d65e7f0b96a435a9efa1991199f7731d4"],"state_sha256":"7df64a8b13dab3e94bde17c39c2b085134a1a71b41005496af47ad0e49c090ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVVN99WPneQ89tskGAMjQ3J7nHK9SosS5DMXUlZ2mtK5RUTAWX4/keAQPFTTCyNmhZ5I9srgeyf52UVwgzlUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:35:26.039537Z","bundle_sha256":"3d3645db3c6719e763496edd4c2e0262b44c8d88dba7cece150ea020ce1cf519"}}