{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NT6GRINRJLSGQQ4LQDINBBA7Q4","short_pith_number":"pith:NT6GRINR","canonical_record":{"source":{"id":"1512.08559","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-28T23:30:58Z","cross_cats_sorted":[],"title_canon_sha256":"a924bf75dbfaf831bf457ebb9f25ff2b335a2677137acbcfa3d97ef77e45d465","abstract_canon_sha256":"c5da1ba51f53a87e09a8322849d3e116d489e984fce697db50b7b8ab47c60189"},"schema_version":"1.0"},"canonical_sha256":"6cfc68a1b14ae468438b80d0d0841f873f631c25e297d44c8f96d45683e815f9","source":{"kind":"arxiv","id":"1512.08559","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08559","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08559v2","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08559","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"NT6GRINRJLSG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NT6GRINRJLSGQQ4L","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NT6GRINR","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NT6GRINRJLSGQQ4LQDINBBA7Q4","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08559","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-28T23:30:58Z","cross_cats_sorted":[],"title_canon_sha256":"a924bf75dbfaf831bf457ebb9f25ff2b335a2677137acbcfa3d97ef77e45d465","abstract_canon_sha256":"c5da1ba51f53a87e09a8322849d3e116d489e984fce697db50b7b8ab47c60189"},"schema_version":"1.0"},"canonical_sha256":"6cfc68a1b14ae468438b80d0d0841f873f631c25e297d44c8f96d45683e815f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:46.862530Z","signature_b64":"EkDq+PPrv1ekxnvM8Jl9Xdc7eqG75Er9x8XxwRa+hbe1y6xfSg/nGsT6WCMWzlURkds726cP8xMDgHXyM734Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cfc68a1b14ae468438b80d0d0841f873f631c25e297d44c8f96d45683e815f9","last_reissued_at":"2026-05-18T01:17:46.861937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:46.861937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08559","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"We4NY9d38mviE5+ouILdc0Qs+U1Gwlk+5OGVL1XTD9jFho+RlRNx3FiFHeVd1LJZRtt9EifXtLlGlINr44guBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:51:03.724566Z"},"content_sha256":"3003c45b1eac9e11284a15332f6795f6dd52aea4a5ba51ff46d01d719a4303ac","schema_version":"1.0","event_id":"sha256:3003c45b1eac9e11284a15332f6795f6dd52aea4a5ba51ff46d01d719a4303ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NT6GRINRJLSGQQ4LQDINBBA7Q4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proliferating L\\'evy Walkers and Front Propagation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Helena Stage, Sergei Fedotov, Vicen\\c{c} M\\'endez","submitted_at":"2015-12-28T23:30:58Z","abstract_excerpt":"We develop non-linear integro-differential kinetic equations for proliferating L\\'{e}vy walkers with birth and death processes. A hyperbolic scaling is applied directly to the general equations to get the Hamilton-Jacobi equations that will allow to determine the rate of front propagation. We found the conditions for switching, birth and death rates under which the propagation velocity reaches the maximum value, i.e. the walker's speed. In the strong anomalous case the death rate was found to influence the velocity of propagation to fall below the walker's maximum speed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08559","kind":"arxiv","version":2},"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":"2026-05-18T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJn/3uW6HgdreG/rCP0uiOCSfcwQcbUdaSfWp55u334Z6IJsOIY0SBLRNAmvo9aPEpCi0feG9pye+MHD6/23Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:51:03.724917Z"},"content_sha256":"ba54b060d2020019a31fab0721705934cba30fc95cecc1bde2c9e7f6b0ebc06d","schema_version":"1.0","event_id":"sha256:ba54b060d2020019a31fab0721705934cba30fc95cecc1bde2c9e7f6b0ebc06d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/bundle.json","state_url":"https://pith.science/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/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":"2026-05-28T12:51:03Z","links":{"resolver":"https://pith.science/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4","bundle":"https://pith.science/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/bundle.json","state":"https://pith.science/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NT6GRINRJLSGQQ4LQDINBBA7Q4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NT6GRINRJLSGQQ4LQDINBBA7Q4","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":"c5da1ba51f53a87e09a8322849d3e116d489e984fce697db50b7b8ab47c60189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-28T23:30:58Z","title_canon_sha256":"a924bf75dbfaf831bf457ebb9f25ff2b335a2677137acbcfa3d97ef77e45d465"},"schema_version":"1.0","source":{"id":"1512.08559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08559","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08559v2","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08559","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"NT6GRINRJLSG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NT6GRINRJLSGQQ4L","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NT6GRINR","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ba54b060d2020019a31fab0721705934cba30fc95cecc1bde2c9e7f6b0ebc06d","target":"graph","created_at":"2026-05-18T01:17:46Z","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":"We develop non-linear integro-differential kinetic equations for proliferating L\\'{e}vy walkers with birth and death processes. A hyperbolic scaling is applied directly to the general equations to get the Hamilton-Jacobi equations that will allow to determine the rate of front propagation. We found the conditions for switching, birth and death rates under which the propagation velocity reaches the maximum value, i.e. the walker's speed. In the strong anomalous case the death rate was found to influence the velocity of propagation to fall below the walker's maximum speed.","authors_text":"Helena Stage, Sergei Fedotov, Vicen\\c{c} M\\'endez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-28T23:30:58Z","title":"Proliferating L\\'evy Walkers and Front Propagation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08559","kind":"arxiv","version":2},"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":"sha256:3003c45b1eac9e11284a15332f6795f6dd52aea4a5ba51ff46d01d719a4303ac","target":"record","created_at":"2026-05-18T01:17:46Z","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":"c5da1ba51f53a87e09a8322849d3e116d489e984fce697db50b7b8ab47c60189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-12-28T23:30:58Z","title_canon_sha256":"a924bf75dbfaf831bf457ebb9f25ff2b335a2677137acbcfa3d97ef77e45d465"},"schema_version":"1.0","source":{"id":"1512.08559","kind":"arxiv","version":2}},"canonical_sha256":"6cfc68a1b14ae468438b80d0d0841f873f631c25e297d44c8f96d45683e815f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cfc68a1b14ae468438b80d0d0841f873f631c25e297d44c8f96d45683e815f9","first_computed_at":"2026-05-18T01:17:46.861937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:46.861937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EkDq+PPrv1ekxnvM8Jl9Xdc7eqG75Er9x8XxwRa+hbe1y6xfSg/nGsT6WCMWzlURkds726cP8xMDgHXyM734Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:46.862530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3003c45b1eac9e11284a15332f6795f6dd52aea4a5ba51ff46d01d719a4303ac","sha256:ba54b060d2020019a31fab0721705934cba30fc95cecc1bde2c9e7f6b0ebc06d"],"state_sha256":"bad8c2ac2627853d849b0f73181288e95abd245ee9e6b23333b930605a3fdea0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRWa80LmcCcYA3uITQPYLkjn2u5I6ZUSYWgJRopWla9iEdc77qVcN/hoEdhv8jii2qBLW9HS8iXGcTrSBXyXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:51:03.726979Z","bundle_sha256":"4d19c56446baa791a4adbb10b57e8cb7cf476e2765cd7f6721bdbb3fb85c16ad"}}