{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FFEIV5RY3YMSXXOW3PLSCHZYOW","short_pith_number":"pith:FFEIV5RY","canonical_record":{"source":{"id":"1702.08697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-28T08:53:22Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"950d22458dff5fa3a7d1e27c52f7be404e1a0a8d1dec67ab82d656331e6e2692","abstract_canon_sha256":"e4be4fa762dd17e43da6591236884219ff3c9635b526db2db99ee3155f96d5d0"},"schema_version":"1.0"},"canonical_sha256":"29488af638de192bddd6dbd7211f3875ba6a7da236b5334a4f8c60c43cd77e45","source":{"kind":"arxiv","id":"1702.08697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08697","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08697v2","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08697","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"pith_short_12","alias_value":"FFEIV5RY3YMS","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FFEIV5RY3YMSXXOW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FFEIV5RY","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FFEIV5RY3YMSXXOW3PLSCHZYOW","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-28T08:53:22Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"950d22458dff5fa3a7d1e27c52f7be404e1a0a8d1dec67ab82d656331e6e2692","abstract_canon_sha256":"e4be4fa762dd17e43da6591236884219ff3c9635b526db2db99ee3155f96d5d0"},"schema_version":"1.0"},"canonical_sha256":"29488af638de192bddd6dbd7211f3875ba6a7da236b5334a4f8c60c43cd77e45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:35.049468Z","signature_b64":"pmbSasVXStSogrvJJx2CyaiT/zHWMIT7BtYGQxhOqp7M/ADjAeQrb1kFL0nykVQ7A5itg/47nhX1f7RD/r7yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29488af638de192bddd6dbd7211f3875ba6a7da236b5334a4f8c60c43cd77e45","last_reissued_at":"2026-05-18T00:44:35.048800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:35.048800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08697","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":"2026-05-18T00:44:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjjGg7TV/faJhWIJchhR3gtACMiexNPGjWPOnRgK/d7s52vCMysqhpPpBI++f6K77RZPAgK9Le55TDi8TQJQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:53.567053Z"},"content_sha256":"08cd5b68d3675210a70e3f55ac0627eab2842ff88640f2cf48b4ffbd73519036","schema_version":"1.0","event_id":"sha256:08cd5b68d3675210a70e3f55ac0627eab2842ff88640f2cf48b4ffbd73519036"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FFEIV5RY3YMSXXOW3PLSCHZYOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A differential model for growing sandpiles on networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Fabio Camilli, Lucilla Corrias, Simone Cacace","submitted_at":"2017-02-28T08:53:22Z","abstract_excerpt":"We consider a system of differential equations of Monge-Kantorovich type which describes the equilibrium configurations of granular material poured by a constant source on a network. Relying on the definition of viscosity solution for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions and P. E. Souganidis, we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08697","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":"2026-05-18T00:44:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ap6fG48yfB9ZFccL1kE7dBxWLyK9NQOB5XXZZKUTNOMxL3671PXiEwNuKOqR/ioyV9GvRSDe4idDfAl2xVEgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:53.567421Z"},"content_sha256":"7b0ee1f32827a97a64e6ce0966ed76567eb2d4c0cbe2d0cf55eddefab463f921","schema_version":"1.0","event_id":"sha256:7b0ee1f32827a97a64e6ce0966ed76567eb2d4c0cbe2d0cf55eddefab463f921"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/bundle.json","state_url":"https://pith.science/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/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":"2026-06-09T19:22:53Z","links":{"resolver":"https://pith.science/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW","bundle":"https://pith.science/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/bundle.json","state":"https://pith.science/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFEIV5RY3YMSXXOW3PLSCHZYOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FFEIV5RY3YMSXXOW3PLSCHZYOW","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":"e4be4fa762dd17e43da6591236884219ff3c9635b526db2db99ee3155f96d5d0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-28T08:53:22Z","title_canon_sha256":"950d22458dff5fa3a7d1e27c52f7be404e1a0a8d1dec67ab82d656331e6e2692"},"schema_version":"1.0","source":{"id":"1702.08697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08697","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08697v2","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08697","created_at":"2026-05-18T00:44:35Z"},{"alias_kind":"pith_short_12","alias_value":"FFEIV5RY3YMS","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FFEIV5RY3YMSXXOW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FFEIV5RY","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:7b0ee1f32827a97a64e6ce0966ed76567eb2d4c0cbe2d0cf55eddefab463f921","target":"graph","created_at":"2026-05-18T00:44:35Z","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 a system of differential equations of Monge-Kantorovich type which describes the equilibrium configurations of granular material poured by a constant source on a network. Relying on the definition of viscosity solution for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions and P. E. Souganidis, we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out.","authors_text":"Fabio Camilli, Lucilla Corrias, Simone Cacace","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-28T08:53:22Z","title":"A differential model for growing sandpiles on networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08697","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":"sha256:08cd5b68d3675210a70e3f55ac0627eab2842ff88640f2cf48b4ffbd73519036","target":"record","created_at":"2026-05-18T00:44:35Z","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":"e4be4fa762dd17e43da6591236884219ff3c9635b526db2db99ee3155f96d5d0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-28T08:53:22Z","title_canon_sha256":"950d22458dff5fa3a7d1e27c52f7be404e1a0a8d1dec67ab82d656331e6e2692"},"schema_version":"1.0","source":{"id":"1702.08697","kind":"arxiv","version":2}},"canonical_sha256":"29488af638de192bddd6dbd7211f3875ba6a7da236b5334a4f8c60c43cd77e45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29488af638de192bddd6dbd7211f3875ba6a7da236b5334a4f8c60c43cd77e45","first_computed_at":"2026-05-18T00:44:35.048800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:35.048800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pmbSasVXStSogrvJJx2CyaiT/zHWMIT7BtYGQxhOqp7M/ADjAeQrb1kFL0nykVQ7A5itg/47nhX1f7RD/r7yDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:35.049468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08cd5b68d3675210a70e3f55ac0627eab2842ff88640f2cf48b4ffbd73519036","sha256:7b0ee1f32827a97a64e6ce0966ed76567eb2d4c0cbe2d0cf55eddefab463f921"],"state_sha256":"85002e679553a12ad15d798fb9292a68131c29ff40fbae4b6fbfcb9f99cd46d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FsqV9XrjFJKX1pzmcjcfI8xxXLt7Zrje+Gwaz2jHibiNH9/TQFfUrG3nscuAChieRYCl2vQJ8K+wD6WuzkMzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:22:53.570690Z","bundle_sha256":"22ceb86959e11c7b09b6b9a38158a30a6d7b673f98c25260d9828874e4e85e36"}}