{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5HZCQLDTSR3EXSRJC3L7TQNCMA","short_pith_number":"pith:5HZCQLDT","canonical_record":{"source":{"id":"1010.4669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-22T10:58:16Z","cross_cats_sorted":[],"title_canon_sha256":"0af601adeb8da3b5875a95bc80ac073d5ad8c324749b9630851155e3bf6c8291","abstract_canon_sha256":"05b25b9ead81742cadf111f3ad4ec25c5f8bebce59943efc30956125e6facae9"},"schema_version":"1.0"},"canonical_sha256":"e9f2282c7394764bca2916d7f9c1a2602ec267e510023994817205baf087ebe6","source":{"kind":"arxiv","id":"1010.4669","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4669","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4669v3","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4669","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"5HZCQLDTSR3E","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5HZCQLDTSR3EXSRJ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5HZCQLDT","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5HZCQLDTSR3EXSRJC3L7TQNCMA","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-22T10:58:16Z","cross_cats_sorted":[],"title_canon_sha256":"0af601adeb8da3b5875a95bc80ac073d5ad8c324749b9630851155e3bf6c8291","abstract_canon_sha256":"05b25b9ead81742cadf111f3ad4ec25c5f8bebce59943efc30956125e6facae9"},"schema_version":"1.0"},"canonical_sha256":"e9f2282c7394764bca2916d7f9c1a2602ec267e510023994817205baf087ebe6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:39.231705Z","signature_b64":"FtDc7rRjQSGzk21rRNaB/7bEvbJkyJqeCkwDO6F7qyvbatw73F3EbDVrOf7OFV1nxTA62yjHjNPPKSxKzlLRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f2282c7394764bca2916d7f9c1a2602ec267e510023994817205baf087ebe6","last_reissued_at":"2026-05-18T04:38:39.230798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:39.230798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4669","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEjEDFqfS6vi2jXYDp/YlvzttIaKR+HOIXE8V1ueLkD6NXkLpvzxw4UPD12Gs7zhbyTtCCP5a6v6NODlZAp2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:55.830414Z"},"content_sha256":"7a75386c93c9a05a29e381730231ef077b38420df3ca1550f76f8175dcb6d813","schema_version":"1.0","event_id":"sha256:7a75386c93c9a05a29e381730231ef077b38420df3ca1550f76f8175dcb6d813"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5HZCQLDTSR3EXSRJC3L7TQNCMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling and analysis of pooled stepped chutes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Marcellini, Graziano Guerra, Michael Herty","submitted_at":"2010-10-22T10:58:16Z","abstract_excerpt":"We consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. We present the solution to a Riemann problem in the large and also a well--posedness result for the coupled problem. We finally report on some numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4669","kind":"arxiv","version":3},"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":"2026-05-18T04:38:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+U4vfYPTzKHaAr7SMsCnIVXokQIAcWokD9eGMxMgCYWBW0lE47q5M/qkOsoV1+0ns22jnYKo82JD/3Gxx6HDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:55.830799Z"},"content_sha256":"432cf979aa07f46f644a107ead4eb0aa774394fbc1569ee52545cc3dae47216c","schema_version":"1.0","event_id":"sha256:432cf979aa07f46f644a107ead4eb0aa774394fbc1569ee52545cc3dae47216c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/bundle.json","state_url":"https://pith.science/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/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":"2026-06-11T23:02:55Z","links":{"resolver":"https://pith.science/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA","bundle":"https://pith.science/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/bundle.json","state":"https://pith.science/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HZCQLDTSR3EXSRJC3L7TQNCMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5HZCQLDTSR3EXSRJC3L7TQNCMA","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":"05b25b9ead81742cadf111f3ad4ec25c5f8bebce59943efc30956125e6facae9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-22T10:58:16Z","title_canon_sha256":"0af601adeb8da3b5875a95bc80ac073d5ad8c324749b9630851155e3bf6c8291"},"schema_version":"1.0","source":{"id":"1010.4669","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4669","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4669v3","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4669","created_at":"2026-05-18T04:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"5HZCQLDTSR3E","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5HZCQLDTSR3EXSRJ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5HZCQLDT","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:432cf979aa07f46f644a107ead4eb0aa774394fbc1569ee52545cc3dae47216c","target":"graph","created_at":"2026-05-18T04:38:39Z","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 consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. We present the solution to a Riemann problem in the large and also a well--posedness result for the coupled problem. We finally report on some numerical experiments.","authors_text":"Francesca Marcellini, Graziano Guerra, Michael Herty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-22T10:58:16Z","title":"Modeling and analysis of pooled stepped chutes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4669","kind":"arxiv","version":3},"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":"sha256:7a75386c93c9a05a29e381730231ef077b38420df3ca1550f76f8175dcb6d813","target":"record","created_at":"2026-05-18T04:38:39Z","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":"05b25b9ead81742cadf111f3ad4ec25c5f8bebce59943efc30956125e6facae9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-22T10:58:16Z","title_canon_sha256":"0af601adeb8da3b5875a95bc80ac073d5ad8c324749b9630851155e3bf6c8291"},"schema_version":"1.0","source":{"id":"1010.4669","kind":"arxiv","version":3}},"canonical_sha256":"e9f2282c7394764bca2916d7f9c1a2602ec267e510023994817205baf087ebe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9f2282c7394764bca2916d7f9c1a2602ec267e510023994817205baf087ebe6","first_computed_at":"2026-05-18T04:38:39.230798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:39.230798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FtDc7rRjQSGzk21rRNaB/7bEvbJkyJqeCkwDO6F7qyvbatw73F3EbDVrOf7OFV1nxTA62yjHjNPPKSxKzlLRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:39.231705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4669","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a75386c93c9a05a29e381730231ef077b38420df3ca1550f76f8175dcb6d813","sha256:432cf979aa07f46f644a107ead4eb0aa774394fbc1569ee52545cc3dae47216c"],"state_sha256":"21994e5aa0fad8906ed8043d89bcc20ae10ef8d06ae358875bc39f5408dbcf23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BwltrbS4InAW05Tg74w2efvh8+T1Nn7IbrTImFevI/BNhegJJ3wL8fSzhSIcoU3tVFZeJ+HnbT/vNLXqhHuuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:02:55.832908Z","bundle_sha256":"6526468a3d699e30a77d88c35ab4fcd647a4e1b32de2ec97b98efdd02582c1ce"}}