{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6DSYAWRDMCVZ3DUIYLI7P7ADAH","short_pith_number":"pith:6DSYAWRD","canonical_record":{"source":{"id":"2606.04644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T09:12:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"665dfb09f611f6890c47649c7d350be645d6b09bd1e5bb6e6dcfda770ee992c6","abstract_canon_sha256":"65c7409deec6e1eb5807f63de6aaa77c8e0246fd5925fdc4cdb67834fe05f090"},"schema_version":"1.0"},"canonical_sha256":"f0e5805a2360ab9d8e88c2d1f7fc0301d513190af293586dd7ceb2c77933a962","source":{"kind":"arxiv","id":"2606.04644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04644","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04644v1","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04644","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"6DSYAWRDMCVZ","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"6DSYAWRDMCVZ3DUI","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"6DSYAWRD","created_at":"2026-06-04T01:09:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6DSYAWRDMCVZ3DUIYLI7P7ADAH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T09:12:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"665dfb09f611f6890c47649c7d350be645d6b09bd1e5bb6e6dcfda770ee992c6","abstract_canon_sha256":"65c7409deec6e1eb5807f63de6aaa77c8e0246fd5925fdc4cdb67834fe05f090"},"schema_version":"1.0"},"canonical_sha256":"f0e5805a2360ab9d8e88c2d1f7fc0301d513190af293586dd7ceb2c77933a962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:22.831641Z","signature_b64":"iOg9lDpYMN1ORgbwaEFC2NWRQG/qR7G0+B7J0nMAUL6qQcVLDkHC8qr9WRj+aMs9ET6F4wSHMP9MyYQ7e+nfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0e5805a2360ab9d8e88c2d1f7fc0301d513190af293586dd7ceb2c77933a962","last_reissued_at":"2026-06-04T01:09:22.831071Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:22.831071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04644","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":"2026-06-04T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KcKwo7tb2ugBR2TnbSPe9HRp2/hxt7dPWvgyx344fY9gKRn23KDKdbDE10M4KR2l5p0R+pAklc8EZ29TwLNKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:17:06.860994Z"},"content_sha256":"f248254643fe7b2807953f68b594b18cb07a3f099d1998718566510eee865786","schema_version":"1.0","event_id":"sha256:f248254643fe7b2807953f68b594b18cb07a3f099d1998718566510eee865786"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6DSYAWRDMCVZ3DUIYLI7P7ADAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness and finite element approximation of the electrostatic shear Alfv\\'en wave equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Annalisa Buffa, Marco Picasso, Markus Renoldner, Timon Miehling","submitted_at":"2026-06-03T09:12:56Z","abstract_excerpt":"The aim of this paper is to study the well-posedness and finite element approximation of the electrostatic shear Alfv\\'en wave equations, a coupled system of two partial differential equations arising in plasma physics as a simplified sub-model of the drift-reduced Braginskii equations. To this end, anisotropic Sobolev spaces depending on the normalized magnetic field $\\b$ are introduced, together with a Poincar\\'e-type inequality along the integral curves of $\\b$, which holds under a geometric directedness condition on the magnetic field. Using these tools, existence, uniqueness, and stabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04644","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/2606.04644/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":"2026-06-04T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/t1Kb3jwaRgSMRVoOsQXETneGvK9pezScoOMQRWeMCNDJYf/zTLdfcHuz9tAq6qawmxkRJd6dxrq0oykUfiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:17:06.861389Z"},"content_sha256":"e01a9593d8b0d8cf7b1a41523a13c93fb515dc30069767be7fd321687a4730a9","schema_version":"1.0","event_id":"sha256:e01a9593d8b0d8cf7b1a41523a13c93fb515dc30069767be7fd321687a4730a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/bundle.json","state_url":"https://pith.science/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/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":"2026-06-19T23:17:06Z","links":{"resolver":"https://pith.science/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH","bundle":"https://pith.science/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/bundle.json","state":"https://pith.science/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DSYAWRDMCVZ3DUIYLI7P7ADAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6DSYAWRDMCVZ3DUIYLI7P7ADAH","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":"65c7409deec6e1eb5807f63de6aaa77c8e0246fd5925fdc4cdb67834fe05f090","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T09:12:56Z","title_canon_sha256":"665dfb09f611f6890c47649c7d350be645d6b09bd1e5bb6e6dcfda770ee992c6"},"schema_version":"1.0","source":{"id":"2606.04644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04644","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04644v1","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04644","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"6DSYAWRDMCVZ","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"6DSYAWRDMCVZ3DUI","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"6DSYAWRD","created_at":"2026-06-04T01:09:22Z"}],"graph_snapshots":[{"event_id":"sha256:e01a9593d8b0d8cf7b1a41523a13c93fb515dc30069767be7fd321687a4730a9","target":"graph","created_at":"2026-06-04T01:09:22Z","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/2606.04644/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is to study the well-posedness and finite element approximation of the electrostatic shear Alfv\\'en wave equations, a coupled system of two partial differential equations arising in plasma physics as a simplified sub-model of the drift-reduced Braginskii equations. To this end, anisotropic Sobolev spaces depending on the normalized magnetic field $\\b$ are introduced, together with a Poincar\\'e-type inequality along the integral curves of $\\b$, which holds under a geometric directedness condition on the magnetic field. Using these tools, existence, uniqueness, and stabilit","authors_text":"Annalisa Buffa, Marco Picasso, Markus Renoldner, Timon Miehling","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T09:12:56Z","title":"Well-posedness and finite element approximation of the electrostatic shear Alfv\\'en wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04644","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:f248254643fe7b2807953f68b594b18cb07a3f099d1998718566510eee865786","target":"record","created_at":"2026-06-04T01:09:22Z","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":"65c7409deec6e1eb5807f63de6aaa77c8e0246fd5925fdc4cdb67834fe05f090","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T09:12:56Z","title_canon_sha256":"665dfb09f611f6890c47649c7d350be645d6b09bd1e5bb6e6dcfda770ee992c6"},"schema_version":"1.0","source":{"id":"2606.04644","kind":"arxiv","version":1}},"canonical_sha256":"f0e5805a2360ab9d8e88c2d1f7fc0301d513190af293586dd7ceb2c77933a962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0e5805a2360ab9d8e88c2d1f7fc0301d513190af293586dd7ceb2c77933a962","first_computed_at":"2026-06-04T01:09:22.831071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:22.831071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iOg9lDpYMN1ORgbwaEFC2NWRQG/qR7G0+B7J0nMAUL6qQcVLDkHC8qr9WRj+aMs9ET6F4wSHMP9MyYQ7e+nfAw==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:22.831641Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f248254643fe7b2807953f68b594b18cb07a3f099d1998718566510eee865786","sha256:e01a9593d8b0d8cf7b1a41523a13c93fb515dc30069767be7fd321687a4730a9"],"state_sha256":"d790f2aae7fb8b383384b4181e2e84dc3ef468c99458462b68107db44ae5f2c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ta35IXigvKPWa8yex9EFov6jySMGYy9T0wYKHu42TmEDpEsM5I/Awsdaa0m9mqJS/SddbDLb10IQkV0XYvRLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:17:06.863476Z","bundle_sha256":"48f096f4b8d39adb1b28cf162256a2e07d55ca5b292a454697e2ae47d98b65d8"}}