{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FA2LBYJUQW4V5KMKIMRNVEX7KT","short_pith_number":"pith:FA2LBYJU","canonical_record":{"source":{"id":"0908.2752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-19T14:27:44Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"fe4d34547efc9128ff71d7eb0bb55f6cc7dceec6166f6285992536e9066060b9","abstract_canon_sha256":"c75d06008ca2b8034870eebcc71e76fc2f42614f16e96132a45e7e288438fef9"},"schema_version":"1.0"},"canonical_sha256":"2834b0e13485b95ea98a4322da92ff54d842ff859be329e7146d0013f291946d","source":{"kind":"arxiv","id":"0908.2752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2752","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2752v1","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2752","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"FA2LBYJUQW4V","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"FA2LBYJUQW4V5KMK","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"FA2LBYJU","created_at":"2026-06-03T23:06:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FA2LBYJUQW4V5KMKIMRNVEX7KT","target":"record","payload":{"canonical_record":{"source":{"id":"0908.2752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-19T14:27:44Z","cross_cats_sorted":["cs.NA","math.DS"],"title_canon_sha256":"fe4d34547efc9128ff71d7eb0bb55f6cc7dceec6166f6285992536e9066060b9","abstract_canon_sha256":"c75d06008ca2b8034870eebcc71e76fc2f42614f16e96132a45e7e288438fef9"},"schema_version":"1.0"},"canonical_sha256":"2834b0e13485b95ea98a4322da92ff54d842ff859be329e7146d0013f291946d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:28.337851Z","signature_b64":"KcvfdxGI4q4jn2C98EH5qGSovnQcuduSmYkTLKd5ifCNcN2qH/OxTg1Zipfm34qfoKyIh8Ex5QL3c1dkUCOFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2834b0e13485b95ea98a4322da92ff54d842ff859be329e7146d0013f291946d","last_reissued_at":"2026-06-03T23:06:28.337443Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:28.337443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.2752","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":"2026-06-03T23:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxfyNCApn6jdmyLSY0FZQQhjc2xelyOPE8iJSo1Aamy06oX6gXuf7T0pt+LfHKqGwd8HCd5dAvEY+lfAWxC0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:12:55.805619Z"},"content_sha256":"3c44827d9fa28dce47f82a87311cc8b0f43fb867abe62c3aead109c18341d854","schema_version":"1.0","event_id":"sha256:3c44827d9fa28dce47f82a87311cc8b0f43fb867abe62c3aead109c18341d854"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FA2LBYJUQW4V5KMKIMRNVEX7KT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis and Computation of a Discrete KdV-Burgers Type Equation with Fast Dispersion and Slow Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS"],"primary_cat":"math.NA","authors_text":"C. William Gear, Edriss S. Titi, Ioannis G. Kevrekidis, Marshall Slemrod, Zvi Artstein","submitted_at":"2009-08-19T14:27:44Z","abstract_excerpt":"The long time behavior of the dynamics of a fast-slow system of ordinary differential equations is examined. The system is derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion. The discretization is based on a model developed by Goodman and Lax, that is composed of a fast system drifted by a slow forcing term. A natural split to fast and slow state variables is, however, not available. Our approach views the limit behavior as an invariant measure of the fast motion drifted by the slow component, where the known constants of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2752","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/0908.2752/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":"2026-06-03T23:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pb9Y8f3/9hr5MK0ildXVYHT8kTN4QxIwTAaBijZ4Rsz0uCQWV8Fn0Lna1dHi/EptLu9uPP+XzN+uNYv0DSV2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:12:55.805991Z"},"content_sha256":"fca17253512b0e6f09f76a23b914e9e6cd2fc991fd149a030a7555ea45f0b0df","schema_version":"1.0","event_id":"sha256:fca17253512b0e6f09f76a23b914e9e6cd2fc991fd149a030a7555ea45f0b0df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/bundle.json","state_url":"https://pith.science/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/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":"2026-06-21T20:12:55Z","links":{"resolver":"https://pith.science/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT","bundle":"https://pith.science/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/bundle.json","state":"https://pith.science/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FA2LBYJUQW4V5KMKIMRNVEX7KT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FA2LBYJUQW4V5KMKIMRNVEX7KT","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":"c75d06008ca2b8034870eebcc71e76fc2f42614f16e96132a45e7e288438fef9","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-19T14:27:44Z","title_canon_sha256":"fe4d34547efc9128ff71d7eb0bb55f6cc7dceec6166f6285992536e9066060b9"},"schema_version":"1.0","source":{"id":"0908.2752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2752","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2752v1","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2752","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"FA2LBYJUQW4V","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"FA2LBYJUQW4V5KMK","created_at":"2026-06-03T23:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"FA2LBYJU","created_at":"2026-06-03T23:06:28Z"}],"graph_snapshots":[{"event_id":"sha256:fca17253512b0e6f09f76a23b914e9e6cd2fc991fd149a030a7555ea45f0b0df","target":"graph","created_at":"2026-06-03T23:06:28Z","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/0908.2752/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The long time behavior of the dynamics of a fast-slow system of ordinary differential equations is examined. The system is derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion. The discretization is based on a model developed by Goodman and Lax, that is composed of a fast system drifted by a slow forcing term. A natural split to fast and slow state variables is, however, not available. Our approach views the limit behavior as an invariant measure of the fast motion drifted by the slow component, where the known constants of","authors_text":"C. William Gear, Edriss S. Titi, Ioannis G. Kevrekidis, Marshall Slemrod, Zvi Artstein","cross_cats":["cs.NA","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-19T14:27:44Z","title":"Analysis and Computation of a Discrete KdV-Burgers Type Equation with Fast Dispersion and Slow Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2752","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":"sha256:3c44827d9fa28dce47f82a87311cc8b0f43fb867abe62c3aead109c18341d854","target":"record","created_at":"2026-06-03T23:06:28Z","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":"c75d06008ca2b8034870eebcc71e76fc2f42614f16e96132a45e7e288438fef9","cross_cats_sorted":["cs.NA","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-08-19T14:27:44Z","title_canon_sha256":"fe4d34547efc9128ff71d7eb0bb55f6cc7dceec6166f6285992536e9066060b9"},"schema_version":"1.0","source":{"id":"0908.2752","kind":"arxiv","version":1}},"canonical_sha256":"2834b0e13485b95ea98a4322da92ff54d842ff859be329e7146d0013f291946d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2834b0e13485b95ea98a4322da92ff54d842ff859be329e7146d0013f291946d","first_computed_at":"2026-06-03T23:06:28.337443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:28.337443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KcvfdxGI4q4jn2C98EH5qGSovnQcuduSmYkTLKd5ifCNcN2qH/OxTg1Zipfm34qfoKyIh8Ex5QL3c1dkUCOFAA==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:28.337851Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c44827d9fa28dce47f82a87311cc8b0f43fb867abe62c3aead109c18341d854","sha256:fca17253512b0e6f09f76a23b914e9e6cd2fc991fd149a030a7555ea45f0b0df"],"state_sha256":"8b07190586fb1be4e613938996098ba808ab96e21ebae54ba6e5ea67d82dfcb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qYxb4Ais3kgxDmqCkotnLwqs0fGIQbYoMIalo3sPp0pHXnE6zORBERAEZnP8MzyRrPnRURBqrLAB7DhEAPPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:12:55.807923Z","bundle_sha256":"21833993253b4d4264d7b0c1ab80eb4f830728d7a3e840d11d489704834fb667"}}