{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OO6I22MGB5FP6UCM2WKOFZA4FT","short_pith_number":"pith:OO6I22MG","canonical_record":{"source":{"id":"1708.01923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-06T19:11:18Z","cross_cats_sorted":[],"title_canon_sha256":"e549e7d17bc190183e05288a4e2698f077072c421fb2285dd7a0886edb6c2922","abstract_canon_sha256":"977a92117b53979a535c93ff0dcbb8c2998deea8794bc7cf724a1712a4f01e4d"},"schema_version":"1.0"},"canonical_sha256":"73bc8d69860f4aff504cd594e2e41c2ccc82c51ce0734af1fb78b5596c3745cc","source":{"kind":"arxiv","id":"1708.01923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01923","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01923v1","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01923","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"OO6I22MGB5FP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OO6I22MGB5FP6UCM","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OO6I22MG","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OO6I22MGB5FP6UCM2WKOFZA4FT","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-06T19:11:18Z","cross_cats_sorted":[],"title_canon_sha256":"e549e7d17bc190183e05288a4e2698f077072c421fb2285dd7a0886edb6c2922","abstract_canon_sha256":"977a92117b53979a535c93ff0dcbb8c2998deea8794bc7cf724a1712a4f01e4d"},"schema_version":"1.0"},"canonical_sha256":"73bc8d69860f4aff504cd594e2e41c2ccc82c51ce0734af1fb78b5596c3745cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:15.705609Z","signature_b64":"+hOsxH5qByV87H2z7VLgsiUoajOi7lfXDH/Pdk/wXe5F04qSC3kLLIsfSVkjmfWjRDKWF5/dGcqFjQpk/b0NDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73bc8d69860f4aff504cd594e2e41c2ccc82c51ce0734af1fb78b5596c3745cc","last_reissued_at":"2026-05-17T23:45:15.705047Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:15.705047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01923","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":"2026-05-17T23:45:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ijv+mLwDubpBlXUSJS+jszjuE6llFVzn1JbHYkGtFM6fdRIGSg6FPkeHL03EUiXCDZwZQWEtwRW2m4E/cY7bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:05:15.092744Z"},"content_sha256":"f72b43f785c2793c14727bccce240cffcc0466a7fe2a05273db4f0fda0a6abf9","schema_version":"1.0","event_id":"sha256:f72b43f785c2793c14727bccce240cffcc0466a7fe2a05273db4f0fda0a6abf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OO6I22MGB5FP6UCM2WKOFZA4FT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Glusa, Mark Ainsworth","submitted_at":"2017-08-06T19:11:18Z","abstract_excerpt":"We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01923","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":""},"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":"2026-05-17T23:45:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JknbXpz7kXWWU9aLjsuOQbbhazIvMEhhRlfnsPJCkMyZw2OZ5KOZA890blSN3Nb/U5yN3RGmFmnTzx8j39+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:05:15.093085Z"},"content_sha256":"e1b4ae86375f64baddfaa0e5b7279ee9eb83d9175e0c692397c99ce243fef584","schema_version":"1.0","event_id":"sha256:e1b4ae86375f64baddfaa0e5b7279ee9eb83d9175e0c692397c99ce243fef584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/bundle.json","state_url":"https://pith.science/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/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":"2026-06-25T07:05:15Z","links":{"resolver":"https://pith.science/pith/OO6I22MGB5FP6UCM2WKOFZA4FT","bundle":"https://pith.science/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/bundle.json","state":"https://pith.science/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OO6I22MGB5FP6UCM2WKOFZA4FT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OO6I22MGB5FP6UCM2WKOFZA4FT","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":"977a92117b53979a535c93ff0dcbb8c2998deea8794bc7cf724a1712a4f01e4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-06T19:11:18Z","title_canon_sha256":"e549e7d17bc190183e05288a4e2698f077072c421fb2285dd7a0886edb6c2922"},"schema_version":"1.0","source":{"id":"1708.01923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01923","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01923v1","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01923","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"OO6I22MGB5FP","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OO6I22MGB5FP6UCM","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OO6I22MG","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:e1b4ae86375f64baddfaa0e5b7279ee9eb83d9175e0c692397c99ce243fef584","target":"graph","created_at":"2026-05-17T23:45:15Z","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"},"paper":{"abstract_excerpt":"We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to gene","authors_text":"Christian Glusa, Mark Ainsworth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-06T19:11:18Z","title":"Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01923","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:f72b43f785c2793c14727bccce240cffcc0466a7fe2a05273db4f0fda0a6abf9","target":"record","created_at":"2026-05-17T23:45:15Z","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":"977a92117b53979a535c93ff0dcbb8c2998deea8794bc7cf724a1712a4f01e4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-08-06T19:11:18Z","title_canon_sha256":"e549e7d17bc190183e05288a4e2698f077072c421fb2285dd7a0886edb6c2922"},"schema_version":"1.0","source":{"id":"1708.01923","kind":"arxiv","version":1}},"canonical_sha256":"73bc8d69860f4aff504cd594e2e41c2ccc82c51ce0734af1fb78b5596c3745cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73bc8d69860f4aff504cd594e2e41c2ccc82c51ce0734af1fb78b5596c3745cc","first_computed_at":"2026-05-17T23:45:15.705047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:15.705047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hOsxH5qByV87H2z7VLgsiUoajOi7lfXDH/Pdk/wXe5F04qSC3kLLIsfSVkjmfWjRDKWF5/dGcqFjQpk/b0NDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:15.705609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f72b43f785c2793c14727bccce240cffcc0466a7fe2a05273db4f0fda0a6abf9","sha256:e1b4ae86375f64baddfaa0e5b7279ee9eb83d9175e0c692397c99ce243fef584"],"state_sha256":"9bffc251c68974a64f74734fb68ec81a34e8810a9e9a55f86fe7b4153fd4334c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZ2peBGIQE51xGs1x0TPdxRr8EfrrUhkLmZ8VXoCI8Yp3jMoFx/jrZyf/Dacy3nTLF3gauliXLKlUTY3VtLxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T07:05:15.095294Z","bundle_sha256":"9b3418033d12d97b3093aa54650c2bdd1dceff3e28aed544d375b3377c5114b3"}}