{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:R4X75C4ANOTUMMJJUA7US6PP6V","short_pith_number":"pith:R4X75C4A","canonical_record":{"source":{"id":"0904.0855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-04-06T07:14:29Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"6c3bc2eb74245dcd265c260622d3ee9fa86416f2e868dee14b32f6950d36a502","abstract_canon_sha256":"2c0f9e797d0adfda619839679563e74b08db2e986eb2b784695328466b573a8a"},"schema_version":"1.0"},"canonical_sha256":"8f2ffe8b806ba7463129a03f4979eff5751826cb388a20f13cf58e6085eabc9c","source":{"kind":"arxiv","id":"0904.0855","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0855","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0855v1","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0855","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"R4X75C4ANOTU","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_16","alias_value":"R4X75C4ANOTUMMJJ","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_8","alias_value":"R4X75C4A","created_at":"2026-06-03T23:06:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:R4X75C4ANOTUMMJJUA7US6PP6V","target":"record","payload":{"canonical_record":{"source":{"id":"0904.0855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-04-06T07:14:29Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"6c3bc2eb74245dcd265c260622d3ee9fa86416f2e868dee14b32f6950d36a502","abstract_canon_sha256":"2c0f9e797d0adfda619839679563e74b08db2e986eb2b784695328466b573a8a"},"schema_version":"1.0"},"canonical_sha256":"8f2ffe8b806ba7463129a03f4979eff5751826cb388a20f13cf58e6085eabc9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:25.506766Z","signature_b64":"vF3YnPfBHwRjih7l8GO5vnqIoj7FD++XelsEXBf9L2AfW0E/TRe6ByHW1+6K30N+JNCAAtqTi1A7NHqaJNIHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f2ffe8b806ba7463129a03f4979eff5751826cb388a20f13cf58e6085eabc9c","last_reissued_at":"2026-06-03T23:06:25.506357Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:25.506357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.0855","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":"2026-06-03T23:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODP1de9qc0GYABmX1GYPF4zzactUffz61KaFs6PC9r72ToPvFTdt6uW/OfvRT7oRhlsys5Ipj0EbA3OzuMALBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:22:09.553649Z"},"content_sha256":"39f8e38dea4e3936fc97b52d7fc91fbca2d5d02b5fd31e784b3b571225a8624f","schema_version":"1.0","event_id":"sha256:39f8e38dea4e3936fc97b52d7fc91fbca2d5d02b5fd31e784b3b571225a8624f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:R4X75C4ANOTUMMJJUA7US6PP6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holistic discretisation ensures fidelity to dynamics in two spatial dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS"],"primary_cat":"math.NA","authors_text":"A. J. Roberts, Tony MacKenzie","submitted_at":"2009-04-06T07:14:29Z","abstract_excerpt":"Developments in dynamical systems theory provides new support for the discretisation of \\pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate, macroscale closures of discrete models of the \\pde. Here we explore reaction-diffusion problems in two spatial dimensions. Centre manifold theory ensures that slow manifold, holistic, discretisations exists, are quickly attractive, and are systematically approximated. Special coupling of the finite elements ensures that the resultant discretisations are consisten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0855","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/0904.0855/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":"2026-06-03T23:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/VfdlUhkymUhMsCX6XxOV+1q2CYp2n/xl0S0bWFU8oyFBuQTvEoapBWko/qDYdXXYHX2c3KwvgtsoKcoi2aBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:22:09.554517Z"},"content_sha256":"9b89bcc070a48ba3986c1d0392b1bcad22b60c1ad239887cf6787051b8e0cda6","schema_version":"1.0","event_id":"sha256:9b89bcc070a48ba3986c1d0392b1bcad22b60c1ad239887cf6787051b8e0cda6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4X75C4ANOTUMMJJUA7US6PP6V/bundle.json","state_url":"https://pith.science/pith/R4X75C4ANOTUMMJJUA7US6PP6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4X75C4ANOTUMMJJUA7US6PP6V/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":"2026-06-09T17:22:09Z","links":{"resolver":"https://pith.science/pith/R4X75C4ANOTUMMJJUA7US6PP6V","bundle":"https://pith.science/pith/R4X75C4ANOTUMMJJUA7US6PP6V/bundle.json","state":"https://pith.science/pith/R4X75C4ANOTUMMJJUA7US6PP6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4X75C4ANOTUMMJJUA7US6PP6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:R4X75C4ANOTUMMJJUA7US6PP6V","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":"2c0f9e797d0adfda619839679563e74b08db2e986eb2b784695328466b573a8a","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-04-06T07:14:29Z","title_canon_sha256":"6c3bc2eb74245dcd265c260622d3ee9fa86416f2e868dee14b32f6950d36a502"},"schema_version":"1.0","source":{"id":"0904.0855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0855","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0855v1","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0855","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"R4X75C4ANOTU","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_16","alias_value":"R4X75C4ANOTUMMJJ","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_8","alias_value":"R4X75C4A","created_at":"2026-06-03T23:06:25Z"}],"graph_snapshots":[{"event_id":"sha256:9b89bcc070a48ba3986c1d0392b1bcad22b60c1ad239887cf6787051b8e0cda6","target":"graph","created_at":"2026-06-03T23:06:25Z","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/0904.0855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Developments in dynamical systems theory provides new support for the discretisation of \\pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate, macroscale closures of discrete models of the \\pde. Here we explore reaction-diffusion problems in two spatial dimensions. Centre manifold theory ensures that slow manifold, holistic, discretisations exists, are quickly attractive, and are systematically approximated. Special coupling of the finite elements ensures that the resultant discretisations are consisten","authors_text":"A. J. Roberts, Tony MacKenzie","cross_cats":["cs.NA","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-04-06T07:14:29Z","title":"Holistic discretisation ensures fidelity to dynamics in two spatial dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0855","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":"sha256:39f8e38dea4e3936fc97b52d7fc91fbca2d5d02b5fd31e784b3b571225a8624f","target":"record","created_at":"2026-06-03T23:06:25Z","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":"2c0f9e797d0adfda619839679563e74b08db2e986eb2b784695328466b573a8a","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-04-06T07:14:29Z","title_canon_sha256":"6c3bc2eb74245dcd265c260622d3ee9fa86416f2e868dee14b32f6950d36a502"},"schema_version":"1.0","source":{"id":"0904.0855","kind":"arxiv","version":1}},"canonical_sha256":"8f2ffe8b806ba7463129a03f4979eff5751826cb388a20f13cf58e6085eabc9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f2ffe8b806ba7463129a03f4979eff5751826cb388a20f13cf58e6085eabc9c","first_computed_at":"2026-06-03T23:06:25.506357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:25.506357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vF3YnPfBHwRjih7l8GO5vnqIoj7FD++XelsEXBf9L2AfW0E/TRe6ByHW1+6K30N+JNCAAtqTi1A7NHqaJNIHCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:25.506766Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.0855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39f8e38dea4e3936fc97b52d7fc91fbca2d5d02b5fd31e784b3b571225a8624f","sha256:9b89bcc070a48ba3986c1d0392b1bcad22b60c1ad239887cf6787051b8e0cda6"],"state_sha256":"ecdf0a18986b7200bbfcdee63e4faaf9cc1101767ac13004ee783bc5a43b9dce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIv9N7A2iT2YiNJihNtP0RQS8b4pxckTSVNA/6apVjlmO2trolWyGoFSYZ2KECqcW4WTLlshjsBw8OT8JYnfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:22:09.558946Z","bundle_sha256":"301059566adbbb7697f683ecc7f31ca2b2d579a6c3d18d9efa72997b9506591e"}}