{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AAYSSDOAYEXLFVUFQ5XKJLB7LG","short_pith_number":"pith:AAYSSDOA","canonical_record":{"source":{"id":"2412.10045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-13T11:14:24Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9482f2e6eea8076384d5dd5f52feb3688cedd36d08b984eb3a70d749f2fdf610","abstract_canon_sha256":"92f6e4f274f7707b315d21ab9843c2d7cba7544625687ba08e5c0cda727d7315"},"schema_version":"1.0"},"canonical_sha256":"0031290dc0c12eb2d685876ea4ac3f599b783df4e06a3a5b66e0074bcdecda2c","source":{"kind":"arxiv","id":"2412.10045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.10045","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.10045v1","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.10045","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"AAYSSDOAYEXL","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_16","alias_value":"AAYSSDOAYEXLFVUF","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_8","alias_value":"AAYSSDOA","created_at":"2026-07-05T09:48:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AAYSSDOAYEXLFVUFQ5XKJLB7LG","target":"record","payload":{"canonical_record":{"source":{"id":"2412.10045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-13T11:14:24Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9482f2e6eea8076384d5dd5f52feb3688cedd36d08b984eb3a70d749f2fdf610","abstract_canon_sha256":"92f6e4f274f7707b315d21ab9843c2d7cba7544625687ba08e5c0cda727d7315"},"schema_version":"1.0"},"canonical_sha256":"0031290dc0c12eb2d685876ea4ac3f599b783df4e06a3a5b66e0074bcdecda2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:46.171156Z","signature_b64":"nNQtyZSfyfJRfmct8S9EkQyDk1D+RnEN3UtWpumeAL7Dybg2fI7y3/R6EfJAhtxB7CdD6ROBdNxFVUdvidtmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0031290dc0c12eb2d685876ea4ac3f599b783df4e06a3a5b66e0074bcdecda2c","last_reissued_at":"2026-07-05T09:48:46.170748Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:46.170748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.10045","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":"2026-07-05T09:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NDJQMVpU7HKh7IABQ9vhHeb7z0899M9VFUXknTuOf+QwnyToqolzkxDFB2mHxrPdjwsjgVMglqcupdMqUxHyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:59:59.455447Z"},"content_sha256":"2bfb88dffc7b91924192c3965680eb8ddb27bb29790da64239352de1ed86c4f3","schema_version":"1.0","event_id":"sha256:2bfb88dffc7b91924192c3965680eb8ddb27bb29790da64239352de1ed86c4f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AAYSSDOAYEXLFVUFQ5XKJLB7LG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Xiaoxu Li, Xucheng Meng","submitted_at":"2024-12-13T11:14:24Z","abstract_excerpt":"In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10045","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/2412.10045/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":"2026-07-05T09:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i+1iDFFsFODN/B6igVZ8G/2aeWMW3TcCqaxFDTuAcCzCYjQgsWgcMRui5qJmozFpcxy/vT+e2SXEUCozI6AhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:59:59.455820Z"},"content_sha256":"ff907e8cec8b7f83034f0578781edf5455b4ff140d88698b3a13a4b389e66ecd","schema_version":"1.0","event_id":"sha256:ff907e8cec8b7f83034f0578781edf5455b4ff140d88698b3a13a4b389e66ecd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/bundle.json","state_url":"https://pith.science/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/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":"2026-07-07T11:59:59Z","links":{"resolver":"https://pith.science/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG","bundle":"https://pith.science/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/bundle.json","state":"https://pith.science/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAYSSDOAYEXLFVUFQ5XKJLB7LG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AAYSSDOAYEXLFVUFQ5XKJLB7LG","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":"92f6e4f274f7707b315d21ab9843c2d7cba7544625687ba08e5c0cda727d7315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-13T11:14:24Z","title_canon_sha256":"9482f2e6eea8076384d5dd5f52feb3688cedd36d08b984eb3a70d749f2fdf610"},"schema_version":"1.0","source":{"id":"2412.10045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.10045","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"2412.10045v1","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.10045","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"AAYSSDOAYEXL","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_16","alias_value":"AAYSSDOAYEXLFVUF","created_at":"2026-07-05T09:48:46Z"},{"alias_kind":"pith_short_8","alias_value":"AAYSSDOA","created_at":"2026-07-05T09:48:46Z"}],"graph_snapshots":[{"event_id":"sha256:ff907e8cec8b7f83034f0578781edf5455b4ff140d88698b3a13a4b389e66ecd","target":"graph","created_at":"2026-07-05T09:48:46Z","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/2412.10045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the wavefunction separately using B-spline basis functions, possibly with different degrees, on varying mesh sizes, and then combine them by DG methods. We also provide a rigorous {\\em a priori} error analysis of the DG-IGA approximations for linear eigenvalue problems. Furthermore, this work offers a unified analysis framework for the DG-IGA method applied to a ","authors_text":"Xiaoxu Li, Xucheng Meng","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-13T11:14:24Z","title":"Numerical Analysis of Multi-patch Discontinuous Galerkin Isogeometric Method for Full-potential Electronic Structure Calculations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10045","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":"sha256:2bfb88dffc7b91924192c3965680eb8ddb27bb29790da64239352de1ed86c4f3","target":"record","created_at":"2026-07-05T09:48:46Z","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":"92f6e4f274f7707b315d21ab9843c2d7cba7544625687ba08e5c0cda727d7315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-13T11:14:24Z","title_canon_sha256":"9482f2e6eea8076384d5dd5f52feb3688cedd36d08b984eb3a70d749f2fdf610"},"schema_version":"1.0","source":{"id":"2412.10045","kind":"arxiv","version":1}},"canonical_sha256":"0031290dc0c12eb2d685876ea4ac3f599b783df4e06a3a5b66e0074bcdecda2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0031290dc0c12eb2d685876ea4ac3f599b783df4e06a3a5b66e0074bcdecda2c","first_computed_at":"2026-07-05T09:48:46.170748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:48:46.170748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nNQtyZSfyfJRfmct8S9EkQyDk1D+RnEN3UtWpumeAL7Dybg2fI7y3/R6EfJAhtxB7CdD6ROBdNxFVUdvidtmAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:48:46.171156Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.10045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bfb88dffc7b91924192c3965680eb8ddb27bb29790da64239352de1ed86c4f3","sha256:ff907e8cec8b7f83034f0578781edf5455b4ff140d88698b3a13a4b389e66ecd"],"state_sha256":"5256fe8f8b7eb44c6cde774189d0af5ca81d76e5a046e5f9eeea69a0904cacbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmwUJ5/D0QGlyEnlzNwkXxtV6Avu4+ywWIbYdSwAG+FqTDeqwQgimx2qBTU4vFU2F7z/aGPMpuYrAbHaZZcbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:59:59.457728Z","bundle_sha256":"381cd4f28eb3797501071c371b2812f828f7c1c45b3333c0ccc452755759b35b"}}