{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UMND4LZVCVGYZ53CLCDJC2CKJN","short_pith_number":"pith:UMND4LZV","canonical_record":{"source":{"id":"2606.02899","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T21:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"cce7c2b313fc072e2b990f52306c5feaa36e84b362016ece16b741b23cbb29f0","abstract_canon_sha256":"fd7ad03046ac6667e8c42c4295b790ff74f9240f4cdaf585d59e3b03432d0e0d"},"schema_version":"1.0"},"canonical_sha256":"a31a3e2f35154d8cf762588691684a4b7ca199f37c50b4860f8acb034f20246e","source":{"kind":"arxiv","id":"2606.02899","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02899","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02899v1","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02899","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"UMND4LZVCVGY","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"UMND4LZVCVGYZ53C","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"UMND4LZV","created_at":"2026-06-03T01:05:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UMND4LZVCVGYZ53CLCDJC2CKJN","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02899","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T21:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"cce7c2b313fc072e2b990f52306c5feaa36e84b362016ece16b741b23cbb29f0","abstract_canon_sha256":"fd7ad03046ac6667e8c42c4295b790ff74f9240f4cdaf585d59e3b03432d0e0d"},"schema_version":"1.0"},"canonical_sha256":"a31a3e2f35154d8cf762588691684a4b7ca199f37c50b4860f8acb034f20246e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:26.002587Z","signature_b64":"LmjipBcUHHQ0xcLbSW4MkMNEUR95N/GNa9aBKilWQPJ+GDS59wdZ2j32GyuS1f+Hv4N9zPlx+Xie0IM1ZH4uAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a31a3e2f35154d8cf762588691684a4b7ca199f37c50b4860f8acb034f20246e","last_reissued_at":"2026-06-03T01:05:26.002180Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:26.002180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02899","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":"2026-06-03T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xplCriED/DG4YryaHUMvGnU+PbM/99RsOxPhgDya1pXjBOEtnVMVCBe9KGAWRv2XfceunP1HuTq0vkRlQjQCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:32.164810Z"},"content_sha256":"8b68dd3e21c0810d933f1dbd9d4cd684d3b322b5930ab5470023b4309edfba12","schema_version":"1.0","event_id":"sha256:8b68dd3e21c0810d933f1dbd9d4cd684d3b322b5930ab5470023b4309edfba12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UMND4LZVCVGYZ53CLCDJC2CKJN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A coupled prediction-correction Hughes' model for congested crowd motion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ghadir Jradi, Hamza Ennaji, Jos\\'e Miguel Urbano, Noureddine Igbida","submitted_at":"2026-06-01T21:13:27Z","abstract_excerpt":"In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model \\cite{Hughes2002, Hughes2003}, which couples a nonlinear conservation law for the pedestrian density with an Eikonal equation describing the shortest path to the target. Our approach can be viewed both as a modification of Hughes' original formulation and as a refinement of the prediction-correction framework proposed in the recent work \\cite{ennaji2023prediction}. The resulting model incorporates anticipatory behavior and dynamic route adjustment, offering a more realistic representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02899","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/2606.02899/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":"2026-06-03T01:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kn0NEq5pb+clTH+Eac8oc3pycwDf55KJDTuayebsRG2qNAeLqFJxfL9nfWMp7rcyNsrcdY0LCAQPg3kKwyo1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:30:32.165272Z"},"content_sha256":"5a3395d8a16f7401bd12d3a1e37d0278d739cd5b3a8c8795e2348424cc922b4c","schema_version":"1.0","event_id":"sha256:5a3395d8a16f7401bd12d3a1e37d0278d739cd5b3a8c8795e2348424cc922b4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/bundle.json","state_url":"https://pith.science/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/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":"2026-06-23T07:30:32Z","links":{"resolver":"https://pith.science/pith/UMND4LZVCVGYZ53CLCDJC2CKJN","bundle":"https://pith.science/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/bundle.json","state":"https://pith.science/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMND4LZVCVGYZ53CLCDJC2CKJN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UMND4LZVCVGYZ53CLCDJC2CKJN","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":"fd7ad03046ac6667e8c42c4295b790ff74f9240f4cdaf585d59e3b03432d0e0d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T21:13:27Z","title_canon_sha256":"cce7c2b313fc072e2b990f52306c5feaa36e84b362016ece16b741b23cbb29f0"},"schema_version":"1.0","source":{"id":"2606.02899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02899","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02899v1","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02899","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"UMND4LZVCVGY","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_16","alias_value":"UMND4LZVCVGYZ53C","created_at":"2026-06-03T01:05:26Z"},{"alias_kind":"pith_short_8","alias_value":"UMND4LZV","created_at":"2026-06-03T01:05:26Z"}],"graph_snapshots":[{"event_id":"sha256:5a3395d8a16f7401bd12d3a1e37d0278d739cd5b3a8c8795e2348424cc922b4c","target":"graph","created_at":"2026-06-03T01:05:26Z","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/2606.02899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model \\cite{Hughes2002, Hughes2003}, which couples a nonlinear conservation law for the pedestrian density with an Eikonal equation describing the shortest path to the target. Our approach can be viewed both as a modification of Hughes' original formulation and as a refinement of the prediction-correction framework proposed in the recent work \\cite{ennaji2023prediction}. The resulting model incorporates anticipatory behavior and dynamic route adjustment, offering a more realistic representati","authors_text":"Ghadir Jradi, Hamza Ennaji, Jos\\'e Miguel Urbano, Noureddine Igbida","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T21:13:27Z","title":"A coupled prediction-correction Hughes' model for congested crowd motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02899","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":"sha256:8b68dd3e21c0810d933f1dbd9d4cd684d3b322b5930ab5470023b4309edfba12","target":"record","created_at":"2026-06-03T01:05:26Z","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":"fd7ad03046ac6667e8c42c4295b790ff74f9240f4cdaf585d59e3b03432d0e0d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T21:13:27Z","title_canon_sha256":"cce7c2b313fc072e2b990f52306c5feaa36e84b362016ece16b741b23cbb29f0"},"schema_version":"1.0","source":{"id":"2606.02899","kind":"arxiv","version":1}},"canonical_sha256":"a31a3e2f35154d8cf762588691684a4b7ca199f37c50b4860f8acb034f20246e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31a3e2f35154d8cf762588691684a4b7ca199f37c50b4860f8acb034f20246e","first_computed_at":"2026-06-03T01:05:26.002180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:26.002180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LmjipBcUHHQ0xcLbSW4MkMNEUR95N/GNa9aBKilWQPJ+GDS59wdZ2j32GyuS1f+Hv4N9zPlx+Xie0IM1ZH4uAA==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:26.002587Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b68dd3e21c0810d933f1dbd9d4cd684d3b322b5930ab5470023b4309edfba12","sha256:5a3395d8a16f7401bd12d3a1e37d0278d739cd5b3a8c8795e2348424cc922b4c"],"state_sha256":"f42f4e3006a131c8b11e61b24e4b40726f82bf185d0514a7787abc3e6cedb7e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjV0M/3oWPX9azAnvi9Sx7r8IG9azpJ4z6UrlG3X31kSx8lErBuQpPkSpskPrw8MDwzlzdBwi3BoRyY2UjbUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:30:32.167435Z","bundle_sha256":"4c6b99ff5013a6070cd7b76eb54d47fa7e4ecc038861baa5d47f86339fe8ecf4"}}