{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P34XGTDJP35CDEMQS6VU243FJ2","short_pith_number":"pith:P34XGTDJ","canonical_record":{"source":{"id":"1811.09667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T20:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"6f02770703b77ae568a576ee4863d376bf85dd04a262c218baa247a82f0b39be","abstract_canon_sha256":"41ae3ce6f2640657769e0758a58e078fa719aed31fbd91d7dba2eeebac3b456a"},"schema_version":"1.0"},"canonical_sha256":"7ef9734c697efa21919097ab4d73654e9ad25221d29a3dfbc68b232bc57514df","source":{"kind":"arxiv","id":"1811.09667","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09667","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09667v1","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09667","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"P34XGTDJP35C","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P34XGTDJP35CDEMQ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P34XGTDJ","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P34XGTDJP35CDEMQS6VU243FJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T20:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"6f02770703b77ae568a576ee4863d376bf85dd04a262c218baa247a82f0b39be","abstract_canon_sha256":"41ae3ce6f2640657769e0758a58e078fa719aed31fbd91d7dba2eeebac3b456a"},"schema_version":"1.0"},"canonical_sha256":"7ef9734c697efa21919097ab4d73654e9ad25221d29a3dfbc68b232bc57514df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:52.502898Z","signature_b64":"d0izIiH0mJhDI5bPDlzDEpeeiu+LRRv/0nTnpoLwPTrc17BIr6kZX32cbcKosKPJc1q69zUIUFeISyODyM7eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ef9734c697efa21919097ab4d73654e9ad25221d29a3dfbc68b232bc57514df","last_reissued_at":"2026-05-17T23:45:52.502364Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:52.502364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09667","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":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1s+kkNfIPBftFrePUb0tknRQGMW9irCqazp8o1RozkVIYmXrl5+NdiStc7zuAv5ZjLnC7GDtIWSewY/krNtsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:36:25.195308Z"},"content_sha256":"235bba9f64788607deae21835686f13bf0d24ea5c299e479e7b1908d143e11de","schema_version":"1.0","event_id":"sha256:235bba9f64788607deae21835686f13bf0d24ea5c299e479e7b1908d143e11de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P34XGTDJP35CDEMQS6VU243FJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolatory HDG Method for Parabolic Semilinear PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bernardo Cockburn, John Richard Singler, Yangwen Zhang","submitted_at":"2018-11-23T20:30:05Z","abstract_excerpt":"We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately approximate the nonlinear term. This procedure avoids the numerical quadrature typically required for the assembly of the global matrix at each iteration in each time step, which is a computationally costly component of the standard HDG method for nonlinear PDEs. Furthermore, the Interpolatory HDG interpolation procedure yields simple explicit expressions for the no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09667","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":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAKErhgG/U5wiYwIoXFXV29JXetUxccb9HiCI9q3XmoXkxmYefYFoqMcvKBKvUJ2cW1rZ1K7QaMjPr3Vf0j8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:36:25.195926Z"},"content_sha256":"0b4613d683429dbf8b3c35508724bea676b58c7de82c976480e5a6dae5dc0f8f","schema_version":"1.0","event_id":"sha256:0b4613d683429dbf8b3c35508724bea676b58c7de82c976480e5a6dae5dc0f8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P34XGTDJP35CDEMQS6VU243FJ2/bundle.json","state_url":"https://pith.science/pith/P34XGTDJP35CDEMQS6VU243FJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P34XGTDJP35CDEMQS6VU243FJ2/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":"2026-06-04T15:36:25Z","links":{"resolver":"https://pith.science/pith/P34XGTDJP35CDEMQS6VU243FJ2","bundle":"https://pith.science/pith/P34XGTDJP35CDEMQS6VU243FJ2/bundle.json","state":"https://pith.science/pith/P34XGTDJP35CDEMQS6VU243FJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P34XGTDJP35CDEMQS6VU243FJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P34XGTDJP35CDEMQS6VU243FJ2","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":"41ae3ce6f2640657769e0758a58e078fa719aed31fbd91d7dba2eeebac3b456a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T20:30:05Z","title_canon_sha256":"6f02770703b77ae568a576ee4863d376bf85dd04a262c218baa247a82f0b39be"},"schema_version":"1.0","source":{"id":"1811.09667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09667","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09667v1","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09667","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"P34XGTDJP35C","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P34XGTDJP35CDEMQ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P34XGTDJ","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:0b4613d683429dbf8b3c35508724bea676b58c7de82c976480e5a6dae5dc0f8f","target":"graph","created_at":"2026-05-17T23:45:52Z","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 propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately approximate the nonlinear term. This procedure avoids the numerical quadrature typically required for the assembly of the global matrix at each iteration in each time step, which is a computationally costly component of the standard HDG method for nonlinear PDEs. Furthermore, the Interpolatory HDG interpolation procedure yields simple explicit expressions for the no","authors_text":"Bernardo Cockburn, John Richard Singler, Yangwen Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T20:30:05Z","title":"Interpolatory HDG Method for Parabolic Semilinear PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09667","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":"sha256:235bba9f64788607deae21835686f13bf0d24ea5c299e479e7b1908d143e11de","target":"record","created_at":"2026-05-17T23:45:52Z","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":"41ae3ce6f2640657769e0758a58e078fa719aed31fbd91d7dba2eeebac3b456a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T20:30:05Z","title_canon_sha256":"6f02770703b77ae568a576ee4863d376bf85dd04a262c218baa247a82f0b39be"},"schema_version":"1.0","source":{"id":"1811.09667","kind":"arxiv","version":1}},"canonical_sha256":"7ef9734c697efa21919097ab4d73654e9ad25221d29a3dfbc68b232bc57514df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ef9734c697efa21919097ab4d73654e9ad25221d29a3dfbc68b232bc57514df","first_computed_at":"2026-05-17T23:45:52.502364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:52.502364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d0izIiH0mJhDI5bPDlzDEpeeiu+LRRv/0nTnpoLwPTrc17BIr6kZX32cbcKosKPJc1q69zUIUFeISyODyM7eBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:52.502898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:235bba9f64788607deae21835686f13bf0d24ea5c299e479e7b1908d143e11de","sha256:0b4613d683429dbf8b3c35508724bea676b58c7de82c976480e5a6dae5dc0f8f"],"state_sha256":"57a9950e55429bd737fa2a607e21b75c43d08de15fbf8b1c9969b7da62c035fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boVJZuqwGeiGJgBZbKk45clAXcfM9wivmt78Rp6lfS3k7hjezMyxk4ucm9qfBUcyiha1isJ0ln7hjdykoPIpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:36:25.199166Z","bundle_sha256":"943bb2a89d3a3dff90ced0bb0b89b380c8abfe9a2ef61621dc1e8dc58d6a5ac1"}}