{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YVMHXDVBY5O3NTXNKERUNUXV3U","short_pith_number":"pith:YVMHXDVB","canonical_record":{"source":{"id":"2302.07558","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-15T09:52:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"17f901479d6e7193c235850d3283bc73ff3fff6b7977f11460cf689a9316dcd7","abstract_canon_sha256":"a7dd708c7040eb1c1e62ceb9b89e27ef3d8d0456b8136b88268330653d59f403"},"schema_version":"1.0"},"canonical_sha256":"c5587b8ea1c75db6ceed512346d2f5dd38de617ce1f170ba072c641d6d97720d","source":{"kind":"arxiv","id":"2302.07558","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.07558","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"2302.07558v5","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.07558","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"YVMHXDVBY5O3","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_16","alias_value":"YVMHXDVBY5O3NTXN","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_8","alias_value":"YVMHXDVB","created_at":"2026-07-05T07:49:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YVMHXDVBY5O3NTXNKERUNUXV3U","target":"record","payload":{"canonical_record":{"source":{"id":"2302.07558","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-15T09:52:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"17f901479d6e7193c235850d3283bc73ff3fff6b7977f11460cf689a9316dcd7","abstract_canon_sha256":"a7dd708c7040eb1c1e62ceb9b89e27ef3d8d0456b8136b88268330653d59f403"},"schema_version":"1.0"},"canonical_sha256":"c5587b8ea1c75db6ceed512346d2f5dd38de617ce1f170ba072c641d6d97720d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:49:30.176343Z","signature_b64":"Ca/TuTW1vO47Sc8ytIK/pDusnrOX8vss0r00zuReZ+80RtE3riQpVrO3O2Bv60O6M3H9kAFRqD7kA8hfaVs5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5587b8ea1c75db6ceed512346d2f5dd38de617ce1f170ba072c641d6d97720d","last_reissued_at":"2026-07-05T07:49:30.175909Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:49:30.175909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.07558","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4SL+893LxVygAJM/2BXg6w9TQMENR2kiTL5guPERncaLm1VdheD1ZWj3zKkEx4wcHS4b86K+fNm9XNaktUYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:38:25.155305Z"},"content_sha256":"b56d52738996ffb76ef57ba1daa40796bfc0b6b691883a3558b2c49f4fec6f28","schema_version":"1.0","event_id":"sha256:b56d52738996ffb76ef57ba1daa40796bfc0b6b691883a3558b2c49f4fec6f28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YVMHXDVBY5O3NTXNKERUNUXV3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Initialisation from lattice Boltzmann to multi-step Finite Difference methods: modified equations and discrete observability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas Bellotti (CMAP)","submitted_at":"2023-02-15T09:52:59Z","abstract_excerpt":"Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numerical so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07558","kind":"arxiv","version":5},"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/2302.07558/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":"2026-07-05T07:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3brXe9HAEk7cS8G5kt0KQJLmN6vyBtIwM1uxVPTtjLZtc/q3J4sethz16fNSBr0b72j1yQZWHTBA87ywEF/2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:38:25.157197Z"},"content_sha256":"4e6a5959ce4ab8e5437778f1bccf7e8c7d31f33d95346e1309c7a508c1bd8902","schema_version":"1.0","event_id":"sha256:4e6a5959ce4ab8e5437778f1bccf7e8c7d31f33d95346e1309c7a508c1bd8902"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/bundle.json","state_url":"https://pith.science/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/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":"2026-08-03T15:38:25Z","links":{"resolver":"https://pith.science/pith/YVMHXDVBY5O3NTXNKERUNUXV3U","bundle":"https://pith.science/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/bundle.json","state":"https://pith.science/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVMHXDVBY5O3NTXNKERUNUXV3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YVMHXDVBY5O3NTXNKERUNUXV3U","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":"a7dd708c7040eb1c1e62ceb9b89e27ef3d8d0456b8136b88268330653d59f403","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-15T09:52:59Z","title_canon_sha256":"17f901479d6e7193c235850d3283bc73ff3fff6b7977f11460cf689a9316dcd7"},"schema_version":"1.0","source":{"id":"2302.07558","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.07558","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"2302.07558v5","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.07558","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"YVMHXDVBY5O3","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_16","alias_value":"YVMHXDVBY5O3NTXN","created_at":"2026-07-05T07:49:30Z"},{"alias_kind":"pith_short_8","alias_value":"YVMHXDVB","created_at":"2026-07-05T07:49:30Z"}],"graph_snapshots":[{"event_id":"sha256:4e6a5959ce4ab8e5437778f1bccf7e8c7d31f33d95346e1309c7a508c1bd8902","target":"graph","created_at":"2026-07-05T07:49:30Z","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/2302.07558/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numerical so","authors_text":"Thomas Bellotti (CMAP)","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-15T09:52:59Z","title":"Initialisation from lattice Boltzmann to multi-step Finite Difference methods: modified equations and discrete observability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07558","kind":"arxiv","version":5},"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:b56d52738996ffb76ef57ba1daa40796bfc0b6b691883a3558b2c49f4fec6f28","target":"record","created_at":"2026-07-05T07:49:30Z","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":"a7dd708c7040eb1c1e62ceb9b89e27ef3d8d0456b8136b88268330653d59f403","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-15T09:52:59Z","title_canon_sha256":"17f901479d6e7193c235850d3283bc73ff3fff6b7977f11460cf689a9316dcd7"},"schema_version":"1.0","source":{"id":"2302.07558","kind":"arxiv","version":5}},"canonical_sha256":"c5587b8ea1c75db6ceed512346d2f5dd38de617ce1f170ba072c641d6d97720d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5587b8ea1c75db6ceed512346d2f5dd38de617ce1f170ba072c641d6d97720d","first_computed_at":"2026-07-05T07:49:30.175909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:49:30.175909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ca/TuTW1vO47Sc8ytIK/pDusnrOX8vss0r00zuReZ+80RtE3riQpVrO3O2Bv60O6M3H9kAFRqD7kA8hfaVs5DA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:49:30.176343Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.07558","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b56d52738996ffb76ef57ba1daa40796bfc0b6b691883a3558b2c49f4fec6f28","sha256:4e6a5959ce4ab8e5437778f1bccf7e8c7d31f33d95346e1309c7a508c1bd8902"],"state_sha256":"b6d73649d7616edd7e3dac25e402c88901adb1363ce536ddc0f9fab5a3482bec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yBod1DXZmjdmDo5FKh7ZRoO6vZZmg2xm6ZbSbEhkah6DmlqLFWqpkfwy2ydvl7BT6H7/XQrUQ61uQCqdN/u4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:38:25.166239Z","bundle_sha256":"fc11a3ca79746fc51cde0c1daf501c336516b0f7a822d7ede01b6d91bc2aba66"}}