{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VTFQO4P4STDKIEPY476JMVAROX","short_pith_number":"pith:VTFQO4P4","canonical_record":{"source":{"id":"1106.4211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-21T14:20:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"832dfccc0a1dc0ba897589edc6cfd041fa74687f157402168378d1083d58ac7a","abstract_canon_sha256":"1330f6c818acac6c8f541ab4c05f26a3cfb6f245396a489f2d006f401370e177"},"schema_version":"1.0"},"canonical_sha256":"accb0771fc94c6a411f8e7fc96541175c845df291d9115a5fd250d462af66f2e","source":{"kind":"arxiv","id":"1106.4211","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4211","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4211v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4211","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"VTFQO4P4STDK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VTFQO4P4STDKIEPY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VTFQO4P4","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VTFQO4P4STDKIEPY476JMVAROX","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-21T14:20:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"832dfccc0a1dc0ba897589edc6cfd041fa74687f157402168378d1083d58ac7a","abstract_canon_sha256":"1330f6c818acac6c8f541ab4c05f26a3cfb6f245396a489f2d006f401370e177"},"schema_version":"1.0"},"canonical_sha256":"accb0771fc94c6a411f8e7fc96541175c845df291d9115a5fd250d462af66f2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:12.343371Z","signature_b64":"rmzjbqkTMVTpZSulKmqvdeVOKJMFtkyOxVbVG8iZ3REcCAY6bmRBzd4TGFqtwUlaZhnx/GqOqh40ck0BFwuKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"accb0771fc94c6a411f8e7fc96541175c845df291d9115a5fd250d462af66f2e","last_reissued_at":"2026-05-18T03:55:12.342751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:12.342751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4211","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6rHEcFph3ZwnoHcOThv5uYyq3PO4qeKLI2/sVT0ZkaH8k+q0PBeXEh3mEk62Vrt5EsP1YBPoDrs5m8Kgnr3ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:20.623723Z"},"content_sha256":"6079fa1e46287348f6c5200b72c923d89ea5484e4d49907df4145a03ff1883b6","schema_version":"1.0","event_id":"sha256:6079fa1e46287348f6c5200b72c923d89ea5484e4d49907df4145a03ff1883b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VTFQO4P4STDKIEPY476JMVAROX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A locking free hp DPG method for linear elasticity with symmetric stresses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Jamie Bramwell, Jay Gopalakrishnan, Leszek Demkowicz, Weifeng Qiu","submitted_at":"2011-06-21T14:20:05Z","abstract_excerpt":"We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4211","kind":"arxiv","version":2},"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":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlLrEdoEDukbeqgYbwUwGkcH1lD9aTuD9fOFORJcu5HBnsie3O/C2YakhQEJWS2YQ8jZCdwBcmgz1H14laV7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:20.624356Z"},"content_sha256":"30e875841220e7aede2f3688700da6464d53521033eb915a4abf6d99ad083a8c","schema_version":"1.0","event_id":"sha256:30e875841220e7aede2f3688700da6464d53521033eb915a4abf6d99ad083a8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTFQO4P4STDKIEPY476JMVAROX/bundle.json","state_url":"https://pith.science/pith/VTFQO4P4STDKIEPY476JMVAROX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTFQO4P4STDKIEPY476JMVAROX/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":"2026-06-06T17:13:20Z","links":{"resolver":"https://pith.science/pith/VTFQO4P4STDKIEPY476JMVAROX","bundle":"https://pith.science/pith/VTFQO4P4STDKIEPY476JMVAROX/bundle.json","state":"https://pith.science/pith/VTFQO4P4STDKIEPY476JMVAROX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTFQO4P4STDKIEPY476JMVAROX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VTFQO4P4STDKIEPY476JMVAROX","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":"1330f6c818acac6c8f541ab4c05f26a3cfb6f245396a489f2d006f401370e177","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-21T14:20:05Z","title_canon_sha256":"832dfccc0a1dc0ba897589edc6cfd041fa74687f157402168378d1083d58ac7a"},"schema_version":"1.0","source":{"id":"1106.4211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4211","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4211v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4211","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"VTFQO4P4STDK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VTFQO4P4STDKIEPY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VTFQO4P4","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:30e875841220e7aede2f3688700da6464d53521033eb915a4abf6d99ad083a8c","target":"graph","created_at":"2026-05-18T03:55:12Z","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 two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.","authors_text":"Jamie Bramwell, Jay Gopalakrishnan, Leszek Demkowicz, Weifeng Qiu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-21T14:20:05Z","title":"A locking free hp DPG method for linear elasticity with symmetric stresses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4211","kind":"arxiv","version":2},"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":"sha256:6079fa1e46287348f6c5200b72c923d89ea5484e4d49907df4145a03ff1883b6","target":"record","created_at":"2026-05-18T03:55:12Z","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":"1330f6c818acac6c8f541ab4c05f26a3cfb6f245396a489f2d006f401370e177","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-21T14:20:05Z","title_canon_sha256":"832dfccc0a1dc0ba897589edc6cfd041fa74687f157402168378d1083d58ac7a"},"schema_version":"1.0","source":{"id":"1106.4211","kind":"arxiv","version":2}},"canonical_sha256":"accb0771fc94c6a411f8e7fc96541175c845df291d9115a5fd250d462af66f2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"accb0771fc94c6a411f8e7fc96541175c845df291d9115a5fd250d462af66f2e","first_computed_at":"2026-05-18T03:55:12.342751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:12.342751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rmzjbqkTMVTpZSulKmqvdeVOKJMFtkyOxVbVG8iZ3REcCAY6bmRBzd4TGFqtwUlaZhnx/GqOqh40ck0BFwuKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:12.343371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6079fa1e46287348f6c5200b72c923d89ea5484e4d49907df4145a03ff1883b6","sha256:30e875841220e7aede2f3688700da6464d53521033eb915a4abf6d99ad083a8c"],"state_sha256":"91adef2eb49a5c5bba604e713a808415338ea93a86e3bad4a48319f204d0cc9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMYwFuKuB3anm4vCtHeFhjFnpf9hsUkKbXenrtTbBAqW6rwDkj9UnPrCM27vX/pr1XhJy8FBtHD91LGnhU3dAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:13:20.627403Z","bundle_sha256":"d7c4d220deb5d01dd0bd4e7f59e1d0efa7fc8d5e89ee07e82d04da7f9ad31bfd"}}