{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E4AIQYX43Y3IRYBCBLDDTP2S2S","short_pith_number":"pith:E4AIQYX4","canonical_record":{"source":{"id":"2602.22861","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-02-26T10:55:43Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"bfb38288f86eb171c100dfe6853d538bb91b27e337264d98f861511f522dbe33","abstract_canon_sha256":"8efbd63861cef19038b7c6037b921d9cc05ae8615f7ac9788576e36d79ba756c"},"schema_version":"1.0"},"canonical_sha256":"27008862fcde3688e0220ac639bf52d4a0916d384959776854b01dd77ed94daf","source":{"kind":"arxiv","id":"2602.22861","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.22861","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"2602.22861v3","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.22861","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"E4AIQYX43Y3I","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_16","alias_value":"E4AIQYX43Y3IRYBC","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_8","alias_value":"E4AIQYX4","created_at":"2026-07-14T02:21:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E4AIQYX43Y3IRYBCBLDDTP2S2S","target":"record","payload":{"canonical_record":{"source":{"id":"2602.22861","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-02-26T10:55:43Z","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"title_canon_sha256":"bfb38288f86eb171c100dfe6853d538bb91b27e337264d98f861511f522dbe33","abstract_canon_sha256":"8efbd63861cef19038b7c6037b921d9cc05ae8615f7ac9788576e36d79ba756c"},"schema_version":"1.0"},"canonical_sha256":"27008862fcde3688e0220ac639bf52d4a0916d384959776854b01dd77ed94daf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T02:21:30.159873Z","signature_b64":"/AG7ZDsbq6Z+px6DbcbEqMnHXS8TOGT6Ek9RabpCWdpLYtPZtrj2sDG9hWv9VAf2YQWO8IGKwoeJpVy4T48zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27008862fcde3688e0220ac639bf52d4a0916d384959776854b01dd77ed94daf","last_reissued_at":"2026-07-14T02:21:30.158936Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T02:21:30.158936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.22861","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T02:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0igFWZOm1dEecCQr3u/eEy1QiUJqJNY9b09f/Tsxnmuvb034vQWbvwJc1VRXqj9naMFB6tsAvQNWDcsMNS+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:25:05.222225Z"},"content_sha256":"660beec2fa7a69204495264b40cc3d4a0a0cba01b5fc4c43bc9cf2be4d08e087","schema_version":"1.0","event_id":"sha256:660beec2fa7a69204495264b40cc3d4a0a0cba01b5fc4c43bc9cf2be4d08e087"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E4AIQYX43Y3IRYBCBLDDTP2S2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $hp$-adaptive Structure-Preservion for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Jimmy Kornelije Gunnarsson, Robert Kl\\\"ofkorn","submitted_at":"2026-02-26T10:55:43Z","abstract_excerpt":"We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.22861","kind":"arxiv","version":3},"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/2602.22861/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":"2026-07-14T02:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGHxUgcHDfI4zRVSqTpu7BlZrV9TxxmJStG1d15Kcbs13OlGKgHLq+5tn/MCwLC38V9CdNcASZQT8v5Cg3vBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:25:05.223181Z"},"content_sha256":"182dffef32b260ebbf54c9fa2281e15b577d8581af90ffd8a5f2f5ac796f9227","schema_version":"1.0","event_id":"sha256:182dffef32b260ebbf54c9fa2281e15b577d8581af90ffd8a5f2f5ac796f9227"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/bundle.json","state_url":"https://pith.science/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/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":"2026-08-06T16:25:05Z","links":{"resolver":"https://pith.science/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S","bundle":"https://pith.science/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/bundle.json","state":"https://pith.science/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4AIQYX43Y3IRYBCBLDDTP2S2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E4AIQYX43Y3IRYBCBLDDTP2S2S","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":"8efbd63861cef19038b7c6037b921d9cc05ae8615f7ac9788576e36d79ba756c","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-02-26T10:55:43Z","title_canon_sha256":"bfb38288f86eb171c100dfe6853d538bb91b27e337264d98f861511f522dbe33"},"schema_version":"1.0","source":{"id":"2602.22861","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.22861","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"2602.22861v3","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.22861","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"E4AIQYX43Y3I","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_16","alias_value":"E4AIQYX43Y3IRYBC","created_at":"2026-07-14T02:21:30Z"},{"alias_kind":"pith_short_8","alias_value":"E4AIQYX4","created_at":"2026-07-14T02:21:30Z"}],"graph_snapshots":[{"event_id":"sha256:182dffef32b260ebbf54c9fa2281e15b577d8581af90ffd8a5f2f5ac796f9227","target":"graph","created_at":"2026-07-14T02:21:30Z","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/2602.22861/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes fo","authors_text":"Jimmy Kornelije Gunnarsson, Robert Kl\\\"ofkorn","cross_cats":["cs.NA","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-02-26T10:55:43Z","title":"On $hp$-adaptive Structure-Preservion for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.22861","kind":"arxiv","version":3},"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":"sha256:660beec2fa7a69204495264b40cc3d4a0a0cba01b5fc4c43bc9cf2be4d08e087","target":"record","created_at":"2026-07-14T02:21:30Z","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":"8efbd63861cef19038b7c6037b921d9cc05ae8615f7ac9788576e36d79ba756c","cross_cats_sorted":["cs.NA","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-02-26T10:55:43Z","title_canon_sha256":"bfb38288f86eb171c100dfe6853d538bb91b27e337264d98f861511f522dbe33"},"schema_version":"1.0","source":{"id":"2602.22861","kind":"arxiv","version":3}},"canonical_sha256":"27008862fcde3688e0220ac639bf52d4a0916d384959776854b01dd77ed94daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27008862fcde3688e0220ac639bf52d4a0916d384959776854b01dd77ed94daf","first_computed_at":"2026-07-14T02:21:30.158936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T02:21:30.158936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/AG7ZDsbq6Z+px6DbcbEqMnHXS8TOGT6Ek9RabpCWdpLYtPZtrj2sDG9hWv9VAf2YQWO8IGKwoeJpVy4T48zDw==","signature_status":"signed_v1","signed_at":"2026-07-14T02:21:30.159873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.22861","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:660beec2fa7a69204495264b40cc3d4a0a0cba01b5fc4c43bc9cf2be4d08e087","sha256:182dffef32b260ebbf54c9fa2281e15b577d8581af90ffd8a5f2f5ac796f9227"],"state_sha256":"ce1405947aa116095a2e1c79dee9ed1e0b3e746758ad46d38782a0b13044fbc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pE4NaYj7R21uH+xBoCy2lzRR/J20jgeIw5NYb+U8drYK6UBGg7uAEKAS3/FoCF/t4a/xYJPErDYJfc+VOLySCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T16:25:05.230577Z","bundle_sha256":"3f80a8fce17d6e321af8ced693e85bf4af18c1dcb30d6a8eb75b13b19b5a5953"}}