{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G4GYB7XDSAFOS6QRGOSUF33I2I","short_pith_number":"pith:G4GYB7XD","canonical_record":{"source":{"id":"1409.5509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-19T03:48:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c915c645e6e7a72135aa77c0c40e8db411a4a45e12ddaec14ab9273ad5578bc3","abstract_canon_sha256":"05e6f15bd68275f5bb89915747876cabfc1c847f6122a30b677151b2372300d0"},"schema_version":"1.0"},"canonical_sha256":"370d80fee3900ae97a1133a542ef68d21e357a5abe455c335182431378605b2a","source":{"kind":"arxiv","id":"1409.5509","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5509","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5509v1","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5509","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"G4GYB7XDSAFO","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_16","alias_value":"G4GYB7XDSAFOS6QR","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_8","alias_value":"G4GYB7XD","created_at":"2026-06-04T16:08:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G4GYB7XDSAFOS6QRGOSUF33I2I","target":"record","payload":{"canonical_record":{"source":{"id":"1409.5509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-19T03:48:19Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c915c645e6e7a72135aa77c0c40e8db411a4a45e12ddaec14ab9273ad5578bc3","abstract_canon_sha256":"05e6f15bd68275f5bb89915747876cabfc1c847f6122a30b677151b2372300d0"},"schema_version":"1.0"},"canonical_sha256":"370d80fee3900ae97a1133a542ef68d21e357a5abe455c335182431378605b2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T16:08:45.999286Z","signature_b64":"/4eXb7BjqV3s+LWHE+IEaz438iNZXTNf+LPBFvktM1sXjf1vV4xd67vWMbX9ifim2xkj6XcSfGcPX2oKPKyDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370d80fee3900ae97a1133a542ef68d21e357a5abe455c335182431378605b2a","last_reissued_at":"2026-06-04T16:08:45.998769Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T16:08:45.998769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.5509","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":"2026-06-04T16:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkQbknU0o1xNps26s/R+/8pLwWZfdczP1xOvKv2DVd3etNUr5P3Wrt7njw+jY0IRCt2kbX7PuiKpOOUs1QBVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:08:26.389167Z"},"content_sha256":"f6b9a804264fde5afda9d73cefb88312f722da60580f2aadb6c8df67a95b25e3","schema_version":"1.0","event_id":"sha256:f6b9a804264fde5afda9d73cefb88312f722da60580f2aadb6c8df67a95b25e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G4GYB7XDSAFOS6QRGOSUF33I2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A discontinuous Galerkin method on kinetic flocking models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Changhui Tan","submitted_at":"2014-09-19T03:48:19Z","abstract_excerpt":"We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic $\\delta$-singularity, and construct high order positive preserving scheme to solve kinetic flocking systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5509","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/1409.5509/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":"2026-06-04T16:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9nb48GHmwKSXbeG9y7Gnylfq1xSAF++3OJFR2buuP5CG3rUvS0J50nYiWPPrM91eswmlZtEHdgplPL+Jmm4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:08:26.389542Z"},"content_sha256":"7e420606d7ba0b87cd76b901f31e8bc0059081c2cee8df8af4582f694209bd41","schema_version":"1.0","event_id":"sha256:7e420606d7ba0b87cd76b901f31e8bc0059081c2cee8df8af4582f694209bd41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/bundle.json","state_url":"https://pith.science/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/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":"2026-06-27T04:08:26Z","links":{"resolver":"https://pith.science/pith/G4GYB7XDSAFOS6QRGOSUF33I2I","bundle":"https://pith.science/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/bundle.json","state":"https://pith.science/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4GYB7XDSAFOS6QRGOSUF33I2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G4GYB7XDSAFOS6QRGOSUF33I2I","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":"05e6f15bd68275f5bb89915747876cabfc1c847f6122a30b677151b2372300d0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-19T03:48:19Z","title_canon_sha256":"c915c645e6e7a72135aa77c0c40e8db411a4a45e12ddaec14ab9273ad5578bc3"},"schema_version":"1.0","source":{"id":"1409.5509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5509","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5509v1","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5509","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"G4GYB7XDSAFO","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_16","alias_value":"G4GYB7XDSAFOS6QR","created_at":"2026-06-04T16:08:45Z"},{"alias_kind":"pith_short_8","alias_value":"G4GYB7XD","created_at":"2026-06-04T16:08:45Z"}],"graph_snapshots":[{"event_id":"sha256:7e420606d7ba0b87cd76b901f31e8bc0059081c2cee8df8af4582f694209bd41","target":"graph","created_at":"2026-06-04T16:08:45Z","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/1409.5509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic $\\delta$-singularity, and construct high order positive preserving scheme to solve kinetic flocking systems.","authors_text":"Changhui Tan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-19T03:48:19Z","title":"A discontinuous Galerkin method on kinetic flocking models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5509","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:f6b9a804264fde5afda9d73cefb88312f722da60580f2aadb6c8df67a95b25e3","target":"record","created_at":"2026-06-04T16:08:45Z","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":"05e6f15bd68275f5bb89915747876cabfc1c847f6122a30b677151b2372300d0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-19T03:48:19Z","title_canon_sha256":"c915c645e6e7a72135aa77c0c40e8db411a4a45e12ddaec14ab9273ad5578bc3"},"schema_version":"1.0","source":{"id":"1409.5509","kind":"arxiv","version":1}},"canonical_sha256":"370d80fee3900ae97a1133a542ef68d21e357a5abe455c335182431378605b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370d80fee3900ae97a1133a542ef68d21e357a5abe455c335182431378605b2a","first_computed_at":"2026-06-04T16:08:45.998769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T16:08:45.998769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/4eXb7BjqV3s+LWHE+IEaz438iNZXTNf+LPBFvktM1sXjf1vV4xd67vWMbX9ifim2xkj6XcSfGcPX2oKPKyDDg==","signature_status":"signed_v1","signed_at":"2026-06-04T16:08:45.999286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b9a804264fde5afda9d73cefb88312f722da60580f2aadb6c8df67a95b25e3","sha256:7e420606d7ba0b87cd76b901f31e8bc0059081c2cee8df8af4582f694209bd41"],"state_sha256":"2286f4bbd3cf0411fa8abf68fa7488608a4305d22d8eeabeb2a6045f05016408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yRjRauY4KT2/EE9UEVlrQunyj0+NjUtegYB0x33aR2jh9f/241yyMOloeqWW3YGnOvuYxXewOQJGAJbsFAoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:08:26.391370Z","bundle_sha256":"de4d38ebd673ced095ae1e7d0c39779d20323b5fe36b6f613ea5b9c1654d2352"}}