{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4XGU77AWPDNEXGYWXCYWCTVV6P","short_pith_number":"pith:4XGU77AW","canonical_record":{"source":{"id":"1007.3109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-07-19T10:16:31Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"5ffb4f0cb1ba76e9d4e1c4d1a4a3770534f72b9bbea25d563e9039963950d08f","abstract_canon_sha256":"158cc158a5f076602829638d7a7d29854c3a5a955aa52e881b247455fd494cc2"},"schema_version":"1.0"},"canonical_sha256":"e5cd4ffc1678da4b9b16b8b1614eb5f3d7509d599ebcf26c7f993faf7ddf5635","source":{"kind":"arxiv","id":"1007.3109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3109","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3109v1","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3109","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"4XGU77AWPDNE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4XGU77AWPDNEXGYW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4XGU77AW","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4XGU77AWPDNEXGYWXCYWCTVV6P","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-07-19T10:16:31Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"5ffb4f0cb1ba76e9d4e1c4d1a4a3770534f72b9bbea25d563e9039963950d08f","abstract_canon_sha256":"158cc158a5f076602829638d7a7d29854c3a5a955aa52e881b247455fd494cc2"},"schema_version":"1.0"},"canonical_sha256":"e5cd4ffc1678da4b9b16b8b1614eb5f3d7509d599ebcf26c7f993faf7ddf5635","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:20.709187Z","signature_b64":"WYnQ3acbEzjlwHFMK8iNU9bVBfszY+6hLsUdLRIZkBvCUuqQ/TjJEiZ+w7m0p4B36ttCmoOWu7gjdrhehA8DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5cd4ffc1678da4b9b16b8b1614eb5f3d7509d599ebcf26c7f993faf7ddf5635","last_reissued_at":"2026-05-18T02:06:20.708444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:20.708444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3109","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":"2026-05-18T02:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gcqot9idfamIUW/TZhhAuT6dX1s7DLZSd60Py4LrSMumGRK+uvtvre33Ik06HwRkiorhcCoZEa6PcLL9WIPhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:26.718216Z"},"content_sha256":"9ef54baf87649ee7b35d673c0e5100272701e16778bea2186a204cb151f81275","schema_version":"1.0","event_id":"sha256:9ef54baf87649ee7b35d673c0e5100272701e16778bea2186a204cb151f81275"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4XGU77AWPDNEXGYWXCYWCTVV6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice Boltzmann study of pattern formation in reaction-diffusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.soft","authors_text":"D. Raabe, F. varnik, S.G. Ayodele","submitted_at":"2010-07-19T10:16:31Z","abstract_excerpt":"Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105 (2001)] and in developmental biology [Barkai et al. FEBS Journal 276, 1196 (2009)]. In this work, we apply the Lattice Boltzmann method (LBM) to study pattern formation in reaction-diffusion systems. As a first methodological step, we consider the case of a single species undergoing transformation reaction and diffusion. In this case, we perform a third-order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3109","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":"2026-05-18T02:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6ZUU/8/7WDusUKG71Q2+Gp8daaHd8K1Zn0+8I3D0ylC5KDbKyO936qiCovLa5pD21ZyDei132P30y1vHQjtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:26.718590Z"},"content_sha256":"bfaa62fa6a88f7ce7ac33b135bb0f42e881763b643e7d882c7349c1e81b37ce9","schema_version":"1.0","event_id":"sha256:bfaa62fa6a88f7ce7ac33b135bb0f42e881763b643e7d882c7349c1e81b37ce9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/bundle.json","state_url":"https://pith.science/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/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":"2026-05-30T06:54:26Z","links":{"resolver":"https://pith.science/pith/4XGU77AWPDNEXGYWXCYWCTVV6P","bundle":"https://pith.science/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/bundle.json","state":"https://pith.science/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XGU77AWPDNEXGYWXCYWCTVV6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4XGU77AWPDNEXGYWXCYWCTVV6P","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":"158cc158a5f076602829638d7a7d29854c3a5a955aa52e881b247455fd494cc2","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-07-19T10:16:31Z","title_canon_sha256":"5ffb4f0cb1ba76e9d4e1c4d1a4a3770534f72b9bbea25d563e9039963950d08f"},"schema_version":"1.0","source":{"id":"1007.3109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3109","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3109v1","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3109","created_at":"2026-05-18T02:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"4XGU77AWPDNE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4XGU77AWPDNEXGYW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4XGU77AW","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:bfaa62fa6a88f7ce7ac33b135bb0f42e881763b643e7d882c7349c1e81b37ce9","target":"graph","created_at":"2026-05-18T02:06:20Z","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":"Pattern formation in reaction-diffusion systems is of great importance in surface micro-patterning [Grzybowski et al. Soft Matter. 1, 114 (2005)], self-organization of cellular micro-organisms [Schulz et al. Annu. Rev. Microbiol. 55, 105 (2001)] and in developmental biology [Barkai et al. FEBS Journal 276, 1196 (2009)]. In this work, we apply the Lattice Boltzmann method (LBM) to study pattern formation in reaction-diffusion systems. As a first methodological step, we consider the case of a single species undergoing transformation reaction and diffusion. In this case, we perform a third-order ","authors_text":"D. Raabe, F. varnik, S.G. Ayodele","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-07-19T10:16:31Z","title":"Lattice Boltzmann study of pattern formation in reaction-diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3109","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":"sha256:9ef54baf87649ee7b35d673c0e5100272701e16778bea2186a204cb151f81275","target":"record","created_at":"2026-05-18T02:06:20Z","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":"158cc158a5f076602829638d7a7d29854c3a5a955aa52e881b247455fd494cc2","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-07-19T10:16:31Z","title_canon_sha256":"5ffb4f0cb1ba76e9d4e1c4d1a4a3770534f72b9bbea25d563e9039963950d08f"},"schema_version":"1.0","source":{"id":"1007.3109","kind":"arxiv","version":1}},"canonical_sha256":"e5cd4ffc1678da4b9b16b8b1614eb5f3d7509d599ebcf26c7f993faf7ddf5635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5cd4ffc1678da4b9b16b8b1614eb5f3d7509d599ebcf26c7f993faf7ddf5635","first_computed_at":"2026-05-18T02:06:20.708444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:20.708444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYnQ3acbEzjlwHFMK8iNU9bVBfszY+6hLsUdLRIZkBvCUuqQ/TjJEiZ+w7m0p4B36ttCmoOWu7gjdrhehA8DAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:20.709187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ef54baf87649ee7b35d673c0e5100272701e16778bea2186a204cb151f81275","sha256:bfaa62fa6a88f7ce7ac33b135bb0f42e881763b643e7d882c7349c1e81b37ce9"],"state_sha256":"de8d0d30c055579a7b9dee896f5a8d31045f3dbbf32db7783c26794e9dc09528"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXwEeneecnzJN1OrbayK0M8fRCqyqyqS6Ul+5hB9H3lYGd6HirN9/Ca5K/G+lEFMilFvnI3JuCJlgjJtHvMCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:54:26.720520Z","bundle_sha256":"832ac21c8c6f234f25c6cb38b49b42014f216af5ba79db3e17e8e32bcf8d82d1"}}