{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XFL3EKGVFNTCD5R4EGI6NMNIDK","short_pith_number":"pith:XFL3EKGV","canonical_record":{"source":{"id":"2607.01933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-02T09:27:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"27b6712927a6615d2bca232a35ac84ec79bc4bc2c3aff9dd1a7d1fbc2531e757","abstract_canon_sha256":"9c51ecb4ab1ff1ba4881da86ab0394374d0d3c1047b028463c02614da64af675"},"schema_version":"1.0"},"canonical_sha256":"b957b228d52b6621f63c2191e6b1a81ab00c7684a47638150c3dcc0b0a7779ba","source":{"kind":"arxiv","id":"2607.01933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01933","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01933v1","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01933","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"XFL3EKGVFNTC","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"XFL3EKGVFNTCD5R4","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"XFL3EKGV","created_at":"2026-07-03T01:17:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XFL3EKGVFNTCD5R4EGI6NMNIDK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-02T09:27:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"27b6712927a6615d2bca232a35ac84ec79bc4bc2c3aff9dd1a7d1fbc2531e757","abstract_canon_sha256":"9c51ecb4ab1ff1ba4881da86ab0394374d0d3c1047b028463c02614da64af675"},"schema_version":"1.0"},"canonical_sha256":"b957b228d52b6621f63c2191e6b1a81ab00c7684a47638150c3dcc0b0a7779ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:33.777434Z","signature_b64":"MC6scneTVYXox+7J474kibnX5v4/2inzHRGRlHqu7kJfNrKmgUmYJLFbsW8bn+f7ReliJtpMh3lmbowrA0R6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b957b228d52b6621f63c2191e6b1a81ab00c7684a47638150c3dcc0b0a7779ba","last_reissued_at":"2026-07-03T01:17:33.777066Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:33.777066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01933","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":"2026-07-03T01:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVEMhiLoOqADFfcGrQ67PVGpaqWCWKVldjkpvWIKvcjv3F3wmXRyEpROUZ3P7/6tDL4/WimLW6S8Xe82PQVnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:24:52.750504Z"},"content_sha256":"28ac0ec5fd3170198e0767542a78b24e2bc904c9ee9fac2e26d6e0c035c52462","schema_version":"1.0","event_id":"sha256:28ac0ec5fd3170198e0767542a78b24e2bc904c9ee9fac2e26d6e0c035c52462"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XFL3EKGVFNTCD5R4EGI6NMNIDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-regularity finite element elasticity complexes with hybridizable stresses on tetrahedral Alfeld splits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Johnny Guzm\\'an, Xuehai Huang","submitted_at":"2026-07-02T09:27:56Z","abstract_excerpt":"Finite element elasticity complexes of low regularity are constructed on tetrahedral Alfeld splits. In comparison with existing three-dimensional elasticity complexes on such splits, the complexes constructed here lower both the Sobolev regularity and the polynomial degrees, while ending in a hybridizable $H({\\rm div};\\mathbb S)$-conforming symmetric stress space with no vertex degrees of freedom. The construction is obtained from local Bernstein-Gelfand-Gelfand arguments applied to polynomial de Rham complexes on the Alfeld split. Two local polynomial elasticity complexes are proved: an $H^2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01933","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01933/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-03T01:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScRkhD1w1TzBuktFCIUHEwOyi0CRFfnLnh5zzRZJuHHG1hduj5vfUhHNBl4/FUPm8ltd+hGhduwbEUdpd29TBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:24:52.750881Z"},"content_sha256":"63b1af698a0535fcd0f627b4c7bd4b103c0f757520d3c1868df436c600724139","schema_version":"1.0","event_id":"sha256:63b1af698a0535fcd0f627b4c7bd4b103c0f757520d3c1868df436c600724139"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/bundle.json","state_url":"https://pith.science/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/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":"2026-07-07T12:24:52Z","links":{"resolver":"https://pith.science/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK","bundle":"https://pith.science/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/bundle.json","state":"https://pith.science/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFL3EKGVFNTCD5R4EGI6NMNIDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XFL3EKGVFNTCD5R4EGI6NMNIDK","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":"9c51ecb4ab1ff1ba4881da86ab0394374d0d3c1047b028463c02614da64af675","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-02T09:27:56Z","title_canon_sha256":"27b6712927a6615d2bca232a35ac84ec79bc4bc2c3aff9dd1a7d1fbc2531e757"},"schema_version":"1.0","source":{"id":"2607.01933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01933","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01933v1","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01933","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"XFL3EKGVFNTC","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"XFL3EKGVFNTCD5R4","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"XFL3EKGV","created_at":"2026-07-03T01:17:33Z"}],"graph_snapshots":[{"event_id":"sha256:63b1af698a0535fcd0f627b4c7bd4b103c0f757520d3c1868df436c600724139","target":"graph","created_at":"2026-07-03T01:17:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.01933/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finite element elasticity complexes of low regularity are constructed on tetrahedral Alfeld splits. In comparison with existing three-dimensional elasticity complexes on such splits, the complexes constructed here lower both the Sobolev regularity and the polynomial degrees, while ending in a hybridizable $H({\\rm div};\\mathbb S)$-conforming symmetric stress space with no vertex degrees of freedom. The construction is obtained from local Bernstein-Gelfand-Gelfand arguments applied to polynomial de Rham complexes on the Alfeld split. Two local polynomial elasticity complexes are proved: an $H^2$","authors_text":"Johnny Guzm\\'an, Xuehai Huang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-02T09:27:56Z","title":"Low-regularity finite element elasticity complexes with hybridizable stresses on tetrahedral Alfeld splits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01933","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":"sha256:28ac0ec5fd3170198e0767542a78b24e2bc904c9ee9fac2e26d6e0c035c52462","target":"record","created_at":"2026-07-03T01:17:33Z","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":"9c51ecb4ab1ff1ba4881da86ab0394374d0d3c1047b028463c02614da64af675","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-02T09:27:56Z","title_canon_sha256":"27b6712927a6615d2bca232a35ac84ec79bc4bc2c3aff9dd1a7d1fbc2531e757"},"schema_version":"1.0","source":{"id":"2607.01933","kind":"arxiv","version":1}},"canonical_sha256":"b957b228d52b6621f63c2191e6b1a81ab00c7684a47638150c3dcc0b0a7779ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b957b228d52b6621f63c2191e6b1a81ab00c7684a47638150c3dcc0b0a7779ba","first_computed_at":"2026-07-03T01:17:33.777066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:33.777066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MC6scneTVYXox+7J474kibnX5v4/2inzHRGRlHqu7kJfNrKmgUmYJLFbsW8bn+f7ReliJtpMh3lmbowrA0R6DA==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:33.777434Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28ac0ec5fd3170198e0767542a78b24e2bc904c9ee9fac2e26d6e0c035c52462","sha256:63b1af698a0535fcd0f627b4c7bd4b103c0f757520d3c1868df436c600724139"],"state_sha256":"c4c9878b57553f0d852b25f1588b218837140490b55b31ea35fc16fae15a4f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lMHM7kFJkWWub8mWjQ3fbNP57vLePjzN/FC7OEUjuvEofW1pzdJQAAOVZ9X7pMuiAiUXJeA+bq6Vnz1yhicAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:24:52.752791Z","bundle_sha256":"7981194efb5843d3703ef54a7c53dc3ac85306d535b49a4ea3aa9c06b69f6c77"}}