{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2VJBVIBRTMIJXJ5IYLSEQLDWIP","short_pith_number":"pith:2VJBVIBR","canonical_record":{"source":{"id":"2502.06286","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-10T09:27:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e5252a6cc76ea8ec018747617ad0e69fb1613251ae46d534f6b5b33853a5eec3","abstract_canon_sha256":"991adb7ae986daa6618e7e23ff19d8bc633463a8ea19f1c73e1a476ca5b157d1"},"schema_version":"1.0"},"canonical_sha256":"d5521aa0319b109ba7a8c2e4482c7643cdaf6ba9ce7273113b04b62f27a0dbf7","source":{"kind":"arxiv","id":"2502.06286","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06286","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06286v1","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06286","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"2VJBVIBRTMIJ","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_16","alias_value":"2VJBVIBRTMIJXJ5I","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_8","alias_value":"2VJBVIBR","created_at":"2026-07-05T10:11:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2VJBVIBRTMIJXJ5IYLSEQLDWIP","target":"record","payload":{"canonical_record":{"source":{"id":"2502.06286","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-10T09:27:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e5252a6cc76ea8ec018747617ad0e69fb1613251ae46d534f6b5b33853a5eec3","abstract_canon_sha256":"991adb7ae986daa6618e7e23ff19d8bc633463a8ea19f1c73e1a476ca5b157d1"},"schema_version":"1.0"},"canonical_sha256":"d5521aa0319b109ba7a8c2e4482c7643cdaf6ba9ce7273113b04b62f27a0dbf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:50.069170Z","signature_b64":"nqpdsQ/yOPKoeO6oMuZ1z2wUq7XlHIG3naq0PVdBkgWufUmB1+O026irP2RcQDCwxj6OXmcAVGQl6Vi0smUkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5521aa0319b109ba7a8c2e4482c7643cdaf6ba9ce7273113b04b62f27a0dbf7","last_reissued_at":"2026-07-05T10:11:50.068672Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:50.068672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.06286","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":"2026-07-05T10:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zw3RMz5oh9cynqxxF7WL0xNZFsE+7PfvSs2KFc80s/sCedR2BHyAHvnknN4tITTTiP2b8P4DEUkcdGo3KfjDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:32:59.300676Z"},"content_sha256":"8b8f3c7b6bacb6a36e0152ba2ad07ad48c130e293665ffe9ced9280ddedd7bad","schema_version":"1.0","event_id":"sha256:8b8f3c7b6bacb6a36e0152ba2ad07ad48c130e293665ffe9ced9280ddedd7bad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2VJBVIBRTMIJXJ5IYLSEQLDWIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and interpolation estimates of Hellinger-Reissner virtual element spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Giuseppe Vacca, Lorenzo Mascotto, Michele Botti, Michele Visinoni","submitted_at":"2025-02-10T09:27:47Z","abstract_excerpt":"We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme. We further investigate numerically the behaviour of the constants appearing in the stability estimates on sequences of badly-shaped polytopes and for increasing degree of accuracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06286","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/2502.06286/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":"2026-07-05T10:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrEIPJtddqydCbKDDrty/C/TKsGLlbyPEvRfznUiZC8ktusm+KLi/a/hRAD4AcbSO5/eFN8RLd9loG5iXCQoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:32:59.301189Z"},"content_sha256":"b27f6422e8fd13018980f464a8a9b63ba06015ba5480caccbbd3be400d4c66f9","schema_version":"1.0","event_id":"sha256:b27f6422e8fd13018980f464a8a9b63ba06015ba5480caccbbd3be400d4c66f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/bundle.json","state_url":"https://pith.science/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/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":"2026-08-09T01:32:59Z","links":{"resolver":"https://pith.science/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP","bundle":"https://pith.science/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/bundle.json","state":"https://pith.science/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VJBVIBRTMIJXJ5IYLSEQLDWIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2VJBVIBRTMIJXJ5IYLSEQLDWIP","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":"991adb7ae986daa6618e7e23ff19d8bc633463a8ea19f1c73e1a476ca5b157d1","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-10T09:27:47Z","title_canon_sha256":"e5252a6cc76ea8ec018747617ad0e69fb1613251ae46d534f6b5b33853a5eec3"},"schema_version":"1.0","source":{"id":"2502.06286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06286","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06286v1","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06286","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"2VJBVIBRTMIJ","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_16","alias_value":"2VJBVIBRTMIJXJ5I","created_at":"2026-07-05T10:11:50Z"},{"alias_kind":"pith_short_8","alias_value":"2VJBVIBR","created_at":"2026-07-05T10:11:50Z"}],"graph_snapshots":[{"event_id":"sha256:b27f6422e8fd13018980f464a8a9b63ba06015ba5480caccbbd3be400d4c66f9","target":"graph","created_at":"2026-07-05T10:11:50Z","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/2502.06286/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme. We further investigate numerically the behaviour of the constants appearing in the stability estimates on sequences of badly-shaped polytopes and for increasing degree of accuracy.","authors_text":"Giuseppe Vacca, Lorenzo Mascotto, Michele Botti, Michele Visinoni","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-10T09:27:47Z","title":"Stability and interpolation estimates of Hellinger-Reissner virtual element spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06286","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":"sha256:8b8f3c7b6bacb6a36e0152ba2ad07ad48c130e293665ffe9ced9280ddedd7bad","target":"record","created_at":"2026-07-05T10:11:50Z","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":"991adb7ae986daa6618e7e23ff19d8bc633463a8ea19f1c73e1a476ca5b157d1","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-10T09:27:47Z","title_canon_sha256":"e5252a6cc76ea8ec018747617ad0e69fb1613251ae46d534f6b5b33853a5eec3"},"schema_version":"1.0","source":{"id":"2502.06286","kind":"arxiv","version":1}},"canonical_sha256":"d5521aa0319b109ba7a8c2e4482c7643cdaf6ba9ce7273113b04b62f27a0dbf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5521aa0319b109ba7a8c2e4482c7643cdaf6ba9ce7273113b04b62f27a0dbf7","first_computed_at":"2026-07-05T10:11:50.068672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:50.068672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqpdsQ/yOPKoeO6oMuZ1z2wUq7XlHIG3naq0PVdBkgWufUmB1+O026irP2RcQDCwxj6OXmcAVGQl6Vi0smUkBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:50.069170Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b8f3c7b6bacb6a36e0152ba2ad07ad48c130e293665ffe9ced9280ddedd7bad","sha256:b27f6422e8fd13018980f464a8a9b63ba06015ba5480caccbbd3be400d4c66f9"],"state_sha256":"db4c6af11f8955ae415f060223586e002993c849120fba1473a28023f7f37c34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/W4v9Lb/ybWqpDx8GJbDJtUwN+k1q0NIjlmCyN0/HoXFr5E5EFh3oY1Ung2gOnovVuiOXtu8B8ZTsZY1SHdvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:32:59.306555Z","bundle_sha256":"b7aca412be03887abc372001c4af21d0ef8d0ebe32ad71578890c1049bc8cc67"}}