{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RGO4FJEJKQURIFGPOLE42FUO35","short_pith_number":"pith:RGO4FJEJ","canonical_record":{"source":{"id":"1810.03455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-08T13:50:31Z","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"aeefd48bec2773fb3d954e0feb1d8956268d58f16707ddd67abfa769d8eac422","abstract_canon_sha256":"e0262236eb3f53706f1a0dbd97daab307bcef5593cb62f6561c555e9bf8acf11"},"schema_version":"1.0"},"canonical_sha256":"899dc2a48954291414cf72c9cd168edf599dcd32944a16e8a7548b787def26a0","source":{"kind":"arxiv","id":"1810.03455","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03455","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03455v3","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03455","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"RGO4FJEJKQUR","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_16","alias_value":"RGO4FJEJKQURIFGP","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_8","alias_value":"RGO4FJEJ","created_at":"2026-07-05T00:00:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RGO4FJEJKQURIFGPOLE42FUO35","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-08T13:50:31Z","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"aeefd48bec2773fb3d954e0feb1d8956268d58f16707ddd67abfa769d8eac422","abstract_canon_sha256":"e0262236eb3f53706f1a0dbd97daab307bcef5593cb62f6561c555e9bf8acf11"},"schema_version":"1.0"},"canonical_sha256":"899dc2a48954291414cf72c9cd168edf599dcd32944a16e8a7548b787def26a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:23.464911Z","signature_b64":"ZUZUx+Tv91Dp7fC4iIkgJoMNgSOD7S8Dd22Rw3Hoj0u0I/O1JAkgJ+Fu8iwhvZY8hv4bZ3LZ0f3NfWNxWI13Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"899dc2a48954291414cf72c9cd168edf599dcd32944a16e8a7548b787def26a0","last_reissued_at":"2026-07-05T00:00:23.464482Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:23.464482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03455","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":"2026-07-05T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dMbfQsSRqEvoCUj5yCPmR+Hj17NkoRfUcfGhWQI1+S8cR4I9/bq4Cvt+kJugNZY+BOzy8GwBef0lkmGj5RLEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:39:27.985841Z"},"content_sha256":"2d0223f650eda90f32242eebd405a4bc8c6f83319cbde23fbefd731872c31cb6","schema_version":"1.0","event_id":"sha256:2d0223f650eda90f32242eebd405a4bc8c6f83319cbde23fbefd731872c31cb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RGO4FJEJKQURIFGPOLE42FUO35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Adjoint Petrov-Galerkin Method for Non-Linear Model Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.DS","authors_text":"Christopher Wentland, Eric J. Parish, Karthik Duraisamy","submitted_at":"2018-10-08T13:50:31Z","abstract_excerpt":"We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori-Zwanzig formalism is then used to develop a reduced-order representation of the coarse-scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03455","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/1810.03455/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":"2026-07-05T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xw6kSENrtgIGjD1DBLjb0fMG8tmQaROhYfOkMBFvaobd8P8KGnBSwuEF1BPADvc+fkvNPvtfHbertVvU5BETAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:39:27.986341Z"},"content_sha256":"c77c0d7d11b200b3b8fe7177e0819a77ff7cd0124cffe4ef8d984b2ce9bfa048","schema_version":"1.0","event_id":"sha256:c77c0d7d11b200b3b8fe7177e0819a77ff7cd0124cffe4ef8d984b2ce9bfa048"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGO4FJEJKQURIFGPOLE42FUO35/bundle.json","state_url":"https://pith.science/pith/RGO4FJEJKQURIFGPOLE42FUO35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGO4FJEJKQURIFGPOLE42FUO35/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":"2026-08-04T00:39:27Z","links":{"resolver":"https://pith.science/pith/RGO4FJEJKQURIFGPOLE42FUO35","bundle":"https://pith.science/pith/RGO4FJEJKQURIFGPOLE42FUO35/bundle.json","state":"https://pith.science/pith/RGO4FJEJKQURIFGPOLE42FUO35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGO4FJEJKQURIFGPOLE42FUO35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RGO4FJEJKQURIFGPOLE42FUO35","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":"e0262236eb3f53706f1a0dbd97daab307bcef5593cb62f6561c555e9bf8acf11","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-08T13:50:31Z","title_canon_sha256":"aeefd48bec2773fb3d954e0feb1d8956268d58f16707ddd67abfa769d8eac422"},"schema_version":"1.0","source":{"id":"1810.03455","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03455","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03455v3","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03455","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"RGO4FJEJKQUR","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_16","alias_value":"RGO4FJEJKQURIFGP","created_at":"2026-07-05T00:00:23Z"},{"alias_kind":"pith_short_8","alias_value":"RGO4FJEJ","created_at":"2026-07-05T00:00:23Z"}],"graph_snapshots":[{"event_id":"sha256:c77c0d7d11b200b3b8fe7177e0819a77ff7cd0124cffe4ef8d984b2ce9bfa048","target":"graph","created_at":"2026-07-05T00:00:23Z","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/1810.03455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori-Zwanzig formalism is then used to develop a reduced-order representation of the coarse-scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization metho","authors_text":"Christopher Wentland, Eric J. Parish, Karthik Duraisamy","cross_cats":["physics.comp-ph","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-08T13:50:31Z","title":"The Adjoint Petrov-Galerkin Method for Non-Linear Model Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03455","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":"sha256:2d0223f650eda90f32242eebd405a4bc8c6f83319cbde23fbefd731872c31cb6","target":"record","created_at":"2026-07-05T00:00:23Z","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":"e0262236eb3f53706f1a0dbd97daab307bcef5593cb62f6561c555e9bf8acf11","cross_cats_sorted":["physics.comp-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-08T13:50:31Z","title_canon_sha256":"aeefd48bec2773fb3d954e0feb1d8956268d58f16707ddd67abfa769d8eac422"},"schema_version":"1.0","source":{"id":"1810.03455","kind":"arxiv","version":3}},"canonical_sha256":"899dc2a48954291414cf72c9cd168edf599dcd32944a16e8a7548b787def26a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"899dc2a48954291414cf72c9cd168edf599dcd32944a16e8a7548b787def26a0","first_computed_at":"2026-07-05T00:00:23.464482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:00:23.464482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZUZUx+Tv91Dp7fC4iIkgJoMNgSOD7S8Dd22Rw3Hoj0u0I/O1JAkgJ+Fu8iwhvZY8hv4bZ3LZ0f3NfWNxWI13Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:00:23.464911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03455","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d0223f650eda90f32242eebd405a4bc8c6f83319cbde23fbefd731872c31cb6","sha256:c77c0d7d11b200b3b8fe7177e0819a77ff7cd0124cffe4ef8d984b2ce9bfa048"],"state_sha256":"842dd3f3b0f423648d98116a2a758edf1570c7c921cb5ba141d53064810843ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ictuxY/6vnNcORa//LAkpOCJGD6aFKkfEMEj6lNnaZzs8fOXXgGnyWlsb0YSCXVz03vuGAp4Nt54QdwipqD/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T00:39:27.990028Z","bundle_sha256":"829c77809140ad4085c7e0321f697481fc3382d618aa0e1da790b29624807acc"}}