{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O5BWHZ47I6UXOWCMIDPKL7PSXE","short_pith_number":"pith:O5BWHZ47","canonical_record":{"source":{"id":"1312.1636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T18:13:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c73a9deac49749457c45b8c0b5ff62bae2247051b31ee883ff6382b73065fd68","abstract_canon_sha256":"9ddbd7b9091c966d5c0a93114944f4d63a8314eee27d3edcfd676577271f3f41"},"schema_version":"1.0"},"canonical_sha256":"774363e79f47a977584c40dea5fdf2b90c9f5b541e4abb23d32f40d391a69232","source":{"kind":"arxiv","id":"1312.1636","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1636","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1636v1","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1636","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"O5BWHZ47I6UX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O5BWHZ47I6UXOWCM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O5BWHZ47","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O5BWHZ47I6UXOWCMIDPKL7PSXE","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T18:13:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c73a9deac49749457c45b8c0b5ff62bae2247051b31ee883ff6382b73065fd68","abstract_canon_sha256":"9ddbd7b9091c966d5c0a93114944f4d63a8314eee27d3edcfd676577271f3f41"},"schema_version":"1.0"},"canonical_sha256":"774363e79f47a977584c40dea5fdf2b90c9f5b541e4abb23d32f40d391a69232","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:26.636066Z","signature_b64":"ctdq1usw8hLfTq8jZ0S1zLd9tWK2qSmTO/OOUV7cE6C4i0RL4vaO5AZBTe2T/UxJKlYKUDlgI1LpDeHMtp13DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"774363e79f47a977584c40dea5fdf2b90c9f5b541e4abb23d32f40d391a69232","last_reissued_at":"2026-05-18T03:05:26.635564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:26.635564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1636","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":"2026-05-18T03:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DU1ALTupJUnGhwn4OK3+rvKOp3p6ZUXRIOld2WFMKBkTkNtiuqPk8qL0U0z7nGKhqq66izWl/rvvhbNXea0pBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:22:33.403867Z"},"content_sha256":"b2a3a4467479e423d70cb65b7c649c11a79042f44b490b966715494ccafaecba","schema_version":"1.0","event_id":"sha256:b2a3a4467479e423d70cb65b7c649c11a79042f44b490b966715494ccafaecba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O5BWHZ47I6UXOWCMIDPKL7PSXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-existence and Non-uniqueness for Multidimensional Sticky Particle Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alberto Bressan, Truyen Nguyen","submitted_at":"2013-12-05T18:13:40Z","abstract_excerpt":"The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is continuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1636","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":"2026-05-18T03:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ak+vpuONcWLff8dXhk5quM9ySoFnRm0QBsaWUfFNaVCC/RUZGcIxhTvvq6wmhxv/sFF48ZOlzItvpskIbHUiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:22:33.404215Z"},"content_sha256":"a98fe38ff3d47c3a79bf2ddb06f059d4ff61340f790bba517e21d4213f8825ec","schema_version":"1.0","event_id":"sha256:a98fe38ff3d47c3a79bf2ddb06f059d4ff61340f790bba517e21d4213f8825ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/bundle.json","state_url":"https://pith.science/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/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":"2026-06-21T19:22:33Z","links":{"resolver":"https://pith.science/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE","bundle":"https://pith.science/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/bundle.json","state":"https://pith.science/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5BWHZ47I6UXOWCMIDPKL7PSXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O5BWHZ47I6UXOWCMIDPKL7PSXE","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":"9ddbd7b9091c966d5c0a93114944f4d63a8314eee27d3edcfd676577271f3f41","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T18:13:40Z","title_canon_sha256":"c73a9deac49749457c45b8c0b5ff62bae2247051b31ee883ff6382b73065fd68"},"schema_version":"1.0","source":{"id":"1312.1636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1636","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1636v1","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1636","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"O5BWHZ47I6UX","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O5BWHZ47I6UXOWCM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O5BWHZ47","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:a98fe38ff3d47c3a79bf2ddb06f059d4ff61340f790bba517e21d4213f8825ec","target":"graph","created_at":"2026-05-18T03:05:26Z","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"},"paper":{"abstract_excerpt":"The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is continuous.","authors_text":"Alberto Bressan, Truyen Nguyen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T18:13:40Z","title":"Non-existence and Non-uniqueness for Multidimensional Sticky Particle Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1636","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:b2a3a4467479e423d70cb65b7c649c11a79042f44b490b966715494ccafaecba","target":"record","created_at":"2026-05-18T03:05:26Z","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":"9ddbd7b9091c966d5c0a93114944f4d63a8314eee27d3edcfd676577271f3f41","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-05T18:13:40Z","title_canon_sha256":"c73a9deac49749457c45b8c0b5ff62bae2247051b31ee883ff6382b73065fd68"},"schema_version":"1.0","source":{"id":"1312.1636","kind":"arxiv","version":1}},"canonical_sha256":"774363e79f47a977584c40dea5fdf2b90c9f5b541e4abb23d32f40d391a69232","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774363e79f47a977584c40dea5fdf2b90c9f5b541e4abb23d32f40d391a69232","first_computed_at":"2026-05-18T03:05:26.635564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:26.635564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ctdq1usw8hLfTq8jZ0S1zLd9tWK2qSmTO/OOUV7cE6C4i0RL4vaO5AZBTe2T/UxJKlYKUDlgI1LpDeHMtp13DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:26.636066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2a3a4467479e423d70cb65b7c649c11a79042f44b490b966715494ccafaecba","sha256:a98fe38ff3d47c3a79bf2ddb06f059d4ff61340f790bba517e21d4213f8825ec"],"state_sha256":"4e195063ba1c0f09bfb4730324c8cddaab979c6b2dfa221e21ac36d50e961670"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gyopL/3mDtRrYyTCOMwSKSV7XG+b1f+Vgg6Ht398djdpfsIIUyvU0GtoVqTj72JUHc37BNC/DDIoVrBnU+FAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:22:33.406140Z","bundle_sha256":"0dac2b3f3351ea55be3e8e38a55b834abbdd9200f753befe1e00250e0700939f"}}