{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XSJ3LZUIU7QWFX5RLXQS5LE647","short_pith_number":"pith:XSJ3LZUI","canonical_record":{"source":{"id":"1101.2131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T14:11:21Z","cross_cats_sorted":[],"title_canon_sha256":"ab25cbc31d33c5b1af44449c43b043966e1b7dae8b69aeef18949658be306708","abstract_canon_sha256":"0cbc12408fd318866304056c29319312c65f9350710d95200f5966bd78c29311"},"schema_version":"1.0"},"canonical_sha256":"bc93b5e688a7e162dfb15de12eac9ee7f7b9aeb1974d93ffc59c500ca7037e79","source":{"kind":"arxiv","id":"1101.2131","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2131","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2131v1","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2131","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"XSJ3LZUIU7QW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XSJ3LZUIU7QWFX5R","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XSJ3LZUI","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XSJ3LZUIU7QWFX5RLXQS5LE647","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T14:11:21Z","cross_cats_sorted":[],"title_canon_sha256":"ab25cbc31d33c5b1af44449c43b043966e1b7dae8b69aeef18949658be306708","abstract_canon_sha256":"0cbc12408fd318866304056c29319312c65f9350710d95200f5966bd78c29311"},"schema_version":"1.0"},"canonical_sha256":"bc93b5e688a7e162dfb15de12eac9ee7f7b9aeb1974d93ffc59c500ca7037e79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:58.828095Z","signature_b64":"XFQRowT1u8nytwDRR2JYqfd2uClxjufKESxjcr49LjJ4PVgOsO0s+1ALRLA85Rn2JT1rW8myPXnRxkCXnrNyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc93b5e688a7e162dfb15de12eac9ee7f7b9aeb1974d93ffc59c500ca7037e79","last_reissued_at":"2026-05-18T02:22:58.827452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:58.827452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2131","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":"2026-05-18T02:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tfm5VTnirxj3V4+r3VS2A9S2ARnusWtgG4uLeIhLUYwvAL7QoTKGnActEtCoN7fco3G0J+Uciwxnx7R3zNDnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:08:34.742012Z"},"content_sha256":"14ad6ad1dd618ddf016f9448eb49ee35c7ab20df1f958cf20f0df08d747857c1","schema_version":"1.0","event_id":"sha256:14ad6ad1dd618ddf016f9448eb49ee35c7ab20df1f958cf20f0df08d747857c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XSJ3LZUIU7QWFX5RLXQS5LE647","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Integro-Differential Conservation Law arising in a Model of Granular Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"D. Amadori, W. Shen","submitted_at":"2011-01-11T14:11:21Z","abstract_excerpt":"We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A-priori L^\\infty bounds and BV estimates yield convergence and global existence of BV solutions. Furthermore, we present a well-posedness analysis, showing that the solutions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2131","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":""},"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":"2026-05-18T02:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLXE3o6Bzvr6P0as67VsdNOR46e5Vx81c6Xas1ZpB8CtvJq/JJl+XNRkqsV7nZmGuO/a8KHpY6y/iSYjQWUVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:08:34.742375Z"},"content_sha256":"75ed2657c838606cfb2aa3bf304bb5a50354b50a36dc51085525554019180c9d","schema_version":"1.0","event_id":"sha256:75ed2657c838606cfb2aa3bf304bb5a50354b50a36dc51085525554019180c9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/bundle.json","state_url":"https://pith.science/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/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":"2026-06-03T16:08:34Z","links":{"resolver":"https://pith.science/pith/XSJ3LZUIU7QWFX5RLXQS5LE647","bundle":"https://pith.science/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/bundle.json","state":"https://pith.science/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSJ3LZUIU7QWFX5RLXQS5LE647/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XSJ3LZUIU7QWFX5RLXQS5LE647","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":"0cbc12408fd318866304056c29319312c65f9350710d95200f5966bd78c29311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T14:11:21Z","title_canon_sha256":"ab25cbc31d33c5b1af44449c43b043966e1b7dae8b69aeef18949658be306708"},"schema_version":"1.0","source":{"id":"1101.2131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2131","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2131v1","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2131","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"XSJ3LZUIU7QW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XSJ3LZUIU7QWFX5R","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XSJ3LZUI","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:75ed2657c838606cfb2aa3bf304bb5a50354b50a36dc51085525554019180c9d","target":"graph","created_at":"2026-05-18T02:22:58Z","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"},"paper":{"abstract_excerpt":"We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A-priori L^\\infty bounds and BV estimates yield convergence and global existence of BV solutions. Furthermore, we present a well-posedness analysis, showing that the solutions ","authors_text":"D. Amadori, W. Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T14:11:21Z","title":"An Integro-Differential Conservation Law arising in a Model of Granular Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2131","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":"sha256:14ad6ad1dd618ddf016f9448eb49ee35c7ab20df1f958cf20f0df08d747857c1","target":"record","created_at":"2026-05-18T02:22:58Z","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":"0cbc12408fd318866304056c29319312c65f9350710d95200f5966bd78c29311","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-11T14:11:21Z","title_canon_sha256":"ab25cbc31d33c5b1af44449c43b043966e1b7dae8b69aeef18949658be306708"},"schema_version":"1.0","source":{"id":"1101.2131","kind":"arxiv","version":1}},"canonical_sha256":"bc93b5e688a7e162dfb15de12eac9ee7f7b9aeb1974d93ffc59c500ca7037e79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc93b5e688a7e162dfb15de12eac9ee7f7b9aeb1974d93ffc59c500ca7037e79","first_computed_at":"2026-05-18T02:22:58.827452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:58.827452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFQRowT1u8nytwDRR2JYqfd2uClxjufKESxjcr49LjJ4PVgOsO0s+1ALRLA85Rn2JT1rW8myPXnRxkCXnrNyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:58.828095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14ad6ad1dd618ddf016f9448eb49ee35c7ab20df1f958cf20f0df08d747857c1","sha256:75ed2657c838606cfb2aa3bf304bb5a50354b50a36dc51085525554019180c9d"],"state_sha256":"4bb604676066661ee88fa3a089e20558760852df5ba947d568e6b0bf0598be2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34ED3u1hTGqqhE2ON27NCg/Oq0etQ0dp6yO1aqi8LX9Ivg5S42kcAi9H1zD7uFGOLt4XRUaQQwcTC3K5REBTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:08:34.744336Z","bundle_sha256":"c9c7d6dae608ee8061d95d98441a33f194f96849a7b2cc6e335b2754ead861f7"}}