{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TGA3QVXK7BAZLTLUQ4L3KJWJQN","short_pith_number":"pith:TGA3QVXK","canonical_record":{"source":{"id":"1806.04317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T04:02:03Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"58b977ef0de1ec1b4d07dbdeabf6e752c60ac21563457e38b5477a799bdb8236","abstract_canon_sha256":"578fc5f37a104efbc2fd2b2f49b9983a6e49e6c07f4d13e865991da430103282"},"schema_version":"1.0"},"canonical_sha256":"9981b856eaf84195cd748717b526c98351c1c462245357c16f84a3de5667311e","source":{"kind":"arxiv","id":"1806.04317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04317","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04317v1","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04317","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"TGA3QVXK7BAZ","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"TGA3QVXK7BAZLTLU","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"TGA3QVXK","created_at":"2026-06-04T19:11:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TGA3QVXK7BAZLTLUQ4L3KJWJQN","target":"record","payload":{"canonical_record":{"source":{"id":"1806.04317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T04:02:03Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"58b977ef0de1ec1b4d07dbdeabf6e752c60ac21563457e38b5477a799bdb8236","abstract_canon_sha256":"578fc5f37a104efbc2fd2b2f49b9983a6e49e6c07f4d13e865991da430103282"},"schema_version":"1.0"},"canonical_sha256":"9981b856eaf84195cd748717b526c98351c1c462245357c16f84a3de5667311e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:58.320909Z","signature_b64":"V2GYOQG5rTQwazVF3M3XSZg6fuZBvUZ6RNw7SlxbLxAT98vAhz8lz1WLqnLH48qHFVN03PQCdS/UlQT2z6tBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9981b856eaf84195cd748717b526c98351c1c462245357c16f84a3de5667311e","last_reissued_at":"2026-06-04T19:11:58.320499Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:58.320499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.04317","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":"2026-06-04T19:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyNEIBtws2X869407+8q3gY1eCRGkVtUR+AUVmUEEUAtJuOrLZ4Ht41zXhwehw9jrWgnkc22sCRxL/BoX7GcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:41:58.760545Z"},"content_sha256":"c2e16f8267d7df59a44d7d63011fbb89aa1a067492093443f8ea13e48675aff2","schema_version":"1.0","event_id":"sha256:c2e16f8267d7df59a44d7d63011fbb89aa1a067492093443f8ea13e48675aff2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TGA3QVXK7BAZLTLUQ4L3KJWJQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Discontinuous Galerkin Methods (SDGM) Based on Fluctuation-Dissipation Balance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nathaniel Trask, Paul J. Atzberger, Will Pazner","submitted_at":"2018-06-12T04:02:03Z","abstract_excerpt":"We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We show how methods with linear-time computational complexity can be developed for handling domains with general geometry and generating stochastic terms handling both Dirichlet and Neumann boundary conditions. We demonstrate our approach on example systems and contrast with alternative approaches using direct stochastic discretizations based on random fluxes. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04317","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/1806.04317/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":"2026-06-04T19:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9xOfYTWypGz65/CgFWcK+fDlvrP9VJW983VUEI0UmyC9LGeaPBYeE5NeTOvp64RfpPxynXtQvXSQnd0amHBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:41:58.760918Z"},"content_sha256":"2e84f535cef4a33b456ed5567f0b93150c37a3523928c2edb4ac4ce47df1f45f","schema_version":"1.0","event_id":"sha256:2e84f535cef4a33b456ed5567f0b93150c37a3523928c2edb4ac4ce47df1f45f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/bundle.json","state_url":"https://pith.science/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/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":"2026-06-10T20:41:58Z","links":{"resolver":"https://pith.science/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN","bundle":"https://pith.science/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/bundle.json","state":"https://pith.science/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGA3QVXK7BAZLTLUQ4L3KJWJQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TGA3QVXK7BAZLTLUQ4L3KJWJQN","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":"578fc5f37a104efbc2fd2b2f49b9983a6e49e6c07f4d13e865991da430103282","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T04:02:03Z","title_canon_sha256":"58b977ef0de1ec1b4d07dbdeabf6e752c60ac21563457e38b5477a799bdb8236"},"schema_version":"1.0","source":{"id":"1806.04317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04317","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04317v1","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04317","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"TGA3QVXK7BAZ","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"TGA3QVXK7BAZLTLU","created_at":"2026-06-04T19:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"TGA3QVXK","created_at":"2026-06-04T19:11:58Z"}],"graph_snapshots":[{"event_id":"sha256:2e84f535cef4a33b456ed5567f0b93150c37a3523928c2edb4ac4ce47df1f45f","target":"graph","created_at":"2026-06-04T19:11:58Z","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/1806.04317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We show how methods with linear-time computational complexity can be developed for handling domains with general geometry and generating stochastic terms handling both Dirichlet and Neumann boundary conditions. We demonstrate our approach on example systems and contrast with alternative approaches using direct stochastic discretizations based on random fluxes. W","authors_text":"Nathaniel Trask, Paul J. Atzberger, Will Pazner","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T04:02:03Z","title":"Stochastic Discontinuous Galerkin Methods (SDGM) Based on Fluctuation-Dissipation Balance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04317","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:c2e16f8267d7df59a44d7d63011fbb89aa1a067492093443f8ea13e48675aff2","target":"record","created_at":"2026-06-04T19:11:58Z","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":"578fc5f37a104efbc2fd2b2f49b9983a6e49e6c07f4d13e865991da430103282","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-12T04:02:03Z","title_canon_sha256":"58b977ef0de1ec1b4d07dbdeabf6e752c60ac21563457e38b5477a799bdb8236"},"schema_version":"1.0","source":{"id":"1806.04317","kind":"arxiv","version":1}},"canonical_sha256":"9981b856eaf84195cd748717b526c98351c1c462245357c16f84a3de5667311e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9981b856eaf84195cd748717b526c98351c1c462245357c16f84a3de5667311e","first_computed_at":"2026-06-04T19:11:58.320499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:58.320499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V2GYOQG5rTQwazVF3M3XSZg6fuZBvUZ6RNw7SlxbLxAT98vAhz8lz1WLqnLH48qHFVN03PQCdS/UlQT2z6tBBQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:58.320909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2e16f8267d7df59a44d7d63011fbb89aa1a067492093443f8ea13e48675aff2","sha256:2e84f535cef4a33b456ed5567f0b93150c37a3523928c2edb4ac4ce47df1f45f"],"state_sha256":"ffd51a162972045110f9732949c8b72ce7306a995c2b536152664ce9496f003b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y27bG8/w2hEctkQp6oKvgnlVAJ8Sr57N24vF5SyDIMjLcfSAzF8c59nSDnsEZwmu7RzrK8ECSI/5izS2dxztAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:41:58.762978Z","bundle_sha256":"7d92a972c4acc88ee6ab6f4de9739635e170f42718ca7e4eef6cf925a2a2c8c4"}}