{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UJT7IK6LKWIPX7RTM4QWNNKJVF","short_pith_number":"pith:UJT7IK6L","canonical_record":{"source":{"id":"0807.4006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-07-25T06:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"e2139f58a2b7acf86621bb0532e186e0e324668e7e338042f5d3935e36215398","abstract_canon_sha256":"6491eed554063f16b6185b4193b8ba06b5e24af1b885ad8aa8fcd1a478693b6a"},"schema_version":"1.0"},"canonical_sha256":"a267f42bcb5590fbfe33672166b549a95856542df7683ab48ef20a08a5d6fb42","source":{"kind":"arxiv","id":"0807.4006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4006","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4006v1","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4006","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"UJT7IK6LKWIP","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"UJT7IK6LKWIPX7RT","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"UJT7IK6L","created_at":"2026-07-04T17:11:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UJT7IK6LKWIPX7RTM4QWNNKJVF","target":"record","payload":{"canonical_record":{"source":{"id":"0807.4006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-07-25T06:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"e2139f58a2b7acf86621bb0532e186e0e324668e7e338042f5d3935e36215398","abstract_canon_sha256":"6491eed554063f16b6185b4193b8ba06b5e24af1b885ad8aa8fcd1a478693b6a"},"schema_version":"1.0"},"canonical_sha256":"a267f42bcb5590fbfe33672166b549a95856542df7683ab48ef20a08a5d6fb42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:11:58.754575Z","signature_b64":"W+XYVrv8btBGguPhZZ+od5Hi2CTt8gwOnvuv3ltwkf2RgBElvNvzj+7QSeITZL50N5iKY//w2P7rBWjpCicBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a267f42bcb5590fbfe33672166b549a95856542df7683ab48ef20a08a5d6fb42","last_reissued_at":"2026-07-04T17:11:58.754207Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:11:58.754207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.4006","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":"2026-07-04T17:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YuN9sLRlWI/G2dNqEJIo+rmFsG01z4Et8oPrp8uH443UzNIGpAT9ZxxQs0bftQMvoPgp2EyC5FxYu7KVhL8qAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:06:25.191828Z"},"content_sha256":"e92ce7723a80d933896334aae7fbbcac1aebfc0f7411665da2efc59165b0947a","schema_version":"1.0","event_id":"sha256:e92ce7723a80d933896334aae7fbbcac1aebfc0f7411665da2efc59165b0947a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UJT7IK6LKWIPX7RTM4QWNNKJVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical Calculation of Critical Perturbation Amplitudes and Critical Densities by Non-Linear Stability Analysis of a Simple Traffic Flow Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Dirk Helbing, Mehdi Moussaid","submitted_at":"2008-07-25T06:58:11Z","abstract_excerpt":"Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4006","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/0807.4006/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":"2026-07-04T17:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yMqXLztIBf5R+urJ7DlQy1fe3l1vxNPTp7QqR4dq7TQp5dO4BkVfR8ADxuaG1UlF+3IiBYaeWeVcqnBfVOHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:06:25.192195Z"},"content_sha256":"3350544a3390698c5c75a8dbea6a52f34495b6ed4fc6467758884819b9bcb2ae","schema_version":"1.0","event_id":"sha256:3350544a3390698c5c75a8dbea6a52f34495b6ed4fc6467758884819b9bcb2ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/bundle.json","state_url":"https://pith.science/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/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":"2026-07-05T09:06:25Z","links":{"resolver":"https://pith.science/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF","bundle":"https://pith.science/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/bundle.json","state":"https://pith.science/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJT7IK6LKWIPX7RTM4QWNNKJVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UJT7IK6LKWIPX7RTM4QWNNKJVF","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":"6491eed554063f16b6185b4193b8ba06b5e24af1b885ad8aa8fcd1a478693b6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-07-25T06:58:11Z","title_canon_sha256":"e2139f58a2b7acf86621bb0532e186e0e324668e7e338042f5d3935e36215398"},"schema_version":"1.0","source":{"id":"0807.4006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4006","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4006v1","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4006","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"UJT7IK6LKWIP","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_16","alias_value":"UJT7IK6LKWIPX7RT","created_at":"2026-07-04T17:11:58Z"},{"alias_kind":"pith_short_8","alias_value":"UJT7IK6L","created_at":"2026-07-04T17:11:58Z"}],"graph_snapshots":[{"event_id":"sha256:3350544a3390698c5c75a8dbea6a52f34495b6ed4fc6467758884819b9bcb2ae","target":"graph","created_at":"2026-07-04T17:11:58Z","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/0807.4006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerical","authors_text":"Dirk Helbing, Mehdi Moussaid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-07-25T06:58:11Z","title":"Analytical Calculation of Critical Perturbation Amplitudes and Critical Densities by Non-Linear Stability Analysis of a Simple Traffic Flow Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4006","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:e92ce7723a80d933896334aae7fbbcac1aebfc0f7411665da2efc59165b0947a","target":"record","created_at":"2026-07-04T17:11:58Z","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":"6491eed554063f16b6185b4193b8ba06b5e24af1b885ad8aa8fcd1a478693b6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-07-25T06:58:11Z","title_canon_sha256":"e2139f58a2b7acf86621bb0532e186e0e324668e7e338042f5d3935e36215398"},"schema_version":"1.0","source":{"id":"0807.4006","kind":"arxiv","version":1}},"canonical_sha256":"a267f42bcb5590fbfe33672166b549a95856542df7683ab48ef20a08a5d6fb42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a267f42bcb5590fbfe33672166b549a95856542df7683ab48ef20a08a5d6fb42","first_computed_at":"2026-07-04T17:11:58.754207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:11:58.754207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+XYVrv8btBGguPhZZ+od5Hi2CTt8gwOnvuv3ltwkf2RgBElvNvzj+7QSeITZL50N5iKY//w2P7rBWjpCicBDw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:11:58.754575Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.4006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e92ce7723a80d933896334aae7fbbcac1aebfc0f7411665da2efc59165b0947a","sha256:3350544a3390698c5c75a8dbea6a52f34495b6ed4fc6467758884819b9bcb2ae"],"state_sha256":"3741b3a36c488409246d17b2df15362127d158e49ad195be583f86dfa9ec2c63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dlVm1Eq7ZI60oCfdG6am/TFLwjQR3iFY0LISFLEeyk0yetBJhuHZPxcVZ46PVCO5n9MebsP6yQgVnjeh21i4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:06:25.194371Z","bundle_sha256":"ca485f8897d98212e4f5c2a63e92c607af4441d7a421cb2a469c2d59bc485f12"}}