{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YJDGLA45FJ7MNLFTHZ4IH2JU6U","short_pith_number":"pith:YJDGLA45","canonical_record":{"source":{"id":"1203.1611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-07T09:20:03Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"85784fa76a2fdc611dc65a931a9596c71016ec02d3bb80c8e0aec438f486ec04","abstract_canon_sha256":"004920f8d0b64e3302aaff00a4725c6206a4c6701bdab52afef4720e6aa3f591"},"schema_version":"1.0"},"canonical_sha256":"c24665839d2a7ec6acb33e7883e934f53fc1d0738b306aac36338cde2d99022d","source":{"kind":"arxiv","id":"1203.1611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1611","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1611v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1611","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"YJDGLA45FJ7M","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJDGLA45FJ7MNLFT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJDGLA45","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YJDGLA45FJ7MNLFTHZ4IH2JU6U","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-07T09:20:03Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"85784fa76a2fdc611dc65a931a9596c71016ec02d3bb80c8e0aec438f486ec04","abstract_canon_sha256":"004920f8d0b64e3302aaff00a4725c6206a4c6701bdab52afef4720e6aa3f591"},"schema_version":"1.0"},"canonical_sha256":"c24665839d2a7ec6acb33e7883e934f53fc1d0738b306aac36338cde2d99022d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:37.485449Z","signature_b64":"MUW/rE2qmrxxXsaCAi6l6+15nM1RTPLO+FY0JRh7Fh6uonVVUUNZ9FtqXfVvn3if/9zBAxz6SsqLZHuiuIuMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24665839d2a7ec6acb33e7883e934f53fc1d0738b306aac36338cde2d99022d","last_reissued_at":"2026-05-18T04:00:37.484739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:37.484739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1611","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":"2026-05-18T04:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVQQwUk6eXHb4tzrrv+k8PLXI1ShRw4FBzpEFjTaki0ZPD/EIxYpgqFQgN+sZdR00z2R6TH1pPkqfTy6MiOdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:19:26.907550Z"},"content_sha256":"497a8340153567303e34204825a3e9406a61980bc6a476ebf17eee13f59fdb8e","schema_version":"1.0","event_id":"sha256:497a8340153567303e34204825a3e9406a61980bc6a476ebf17eee13f59fdb8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YJDGLA45FJ7MNLFTHZ4IH2JU6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quasi-Variational Inequality Problem Arising in the Modeling of Growing Sandpiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"John W. Barrett, Leonid Prigozhin","submitted_at":"2012-03-07T09:20:03Z","abstract_excerpt":"Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized mixed formulation involving both the primal (sand surface) and dual (sand flux) variables. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1611","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":"2026-05-18T04:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7m1Tltq48zql8o6pVEIyG+k2ALTuZUINh6NJn8dqgTxkukcI8bUhtMfMFAzjHFUzdvq2cFcr9corrEQ1HQXWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:19:26.907896Z"},"content_sha256":"2001d908833328e3417f6f1d49a667bf7c4f681f54e2a5680d70b634aa708d50","schema_version":"1.0","event_id":"sha256:2001d908833328e3417f6f1d49a667bf7c4f681f54e2a5680d70b634aa708d50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/bundle.json","state_url":"https://pith.science/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/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":"2026-06-24T03:19:26Z","links":{"resolver":"https://pith.science/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U","bundle":"https://pith.science/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/bundle.json","state":"https://pith.science/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJDGLA45FJ7MNLFTHZ4IH2JU6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YJDGLA45FJ7MNLFTHZ4IH2JU6U","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":"004920f8d0b64e3302aaff00a4725c6206a4c6701bdab52afef4720e6aa3f591","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-07T09:20:03Z","title_canon_sha256":"85784fa76a2fdc611dc65a931a9596c71016ec02d3bb80c8e0aec438f486ec04"},"schema_version":"1.0","source":{"id":"1203.1611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1611","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1611v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1611","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"YJDGLA45FJ7M","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJDGLA45FJ7MNLFT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJDGLA45","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:2001d908833328e3417f6f1d49a667bf7c4f681f54e2a5680d70b634aa708d50","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized mixed formulation involving both the primal (sand surface) and dual (sand flux) variables. W","authors_text":"John W. Barrett, Leonid Prigozhin","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-07T09:20:03Z","title":"A Quasi-Variational Inequality Problem Arising in the Modeling of Growing Sandpiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1611","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":"sha256:497a8340153567303e34204825a3e9406a61980bc6a476ebf17eee13f59fdb8e","target":"record","created_at":"2026-05-18T04:00:37Z","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":"004920f8d0b64e3302aaff00a4725c6206a4c6701bdab52afef4720e6aa3f591","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-07T09:20:03Z","title_canon_sha256":"85784fa76a2fdc611dc65a931a9596c71016ec02d3bb80c8e0aec438f486ec04"},"schema_version":"1.0","source":{"id":"1203.1611","kind":"arxiv","version":1}},"canonical_sha256":"c24665839d2a7ec6acb33e7883e934f53fc1d0738b306aac36338cde2d99022d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c24665839d2a7ec6acb33e7883e934f53fc1d0738b306aac36338cde2d99022d","first_computed_at":"2026-05-18T04:00:37.484739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.484739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MUW/rE2qmrxxXsaCAi6l6+15nM1RTPLO+FY0JRh7Fh6uonVVUUNZ9FtqXfVvn3if/9zBAxz6SsqLZHuiuIuMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.485449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:497a8340153567303e34204825a3e9406a61980bc6a476ebf17eee13f59fdb8e","sha256:2001d908833328e3417f6f1d49a667bf7c4f681f54e2a5680d70b634aa708d50"],"state_sha256":"d9e69c62f437672d4cf5537a8e395ee60dcfc47defee76c7f8112678d97d5f73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jOBk0+fWBtFLsFlfcNLwGRLmC0BT4Bijwz/xFMpu3HBwe3QRxxdR6qQ+MPuGzU9L4oyNxpqP65NrXnBK7FJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:19:26.909917Z","bundle_sha256":"da624dbed563e5d534ad2ab8bd5481c3ec2ef395d01e54d4e294b7c75d69da60"}}