{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GTMTXC4ZULNESOERP5AJZF3AJH","short_pith_number":"pith:GTMTXC4Z","canonical_record":{"source":{"id":"1603.03790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-11T21:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"af0e6fbdd467f1b5f4dcbe8b1d830d736774029d4eea3b01d119c8ebbb0c4b86","abstract_canon_sha256":"87474ff4e1858e08b94e4734406a1108853ea93f155db66cd42135b6b68358c1"},"schema_version":"1.0"},"canonical_sha256":"34d93b8b99a2da4938917f409c976049f9ccd7c50d4c7f6065aca46a8e77a965","source":{"kind":"arxiv","id":"1603.03790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03790","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03790v1","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03790","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"GTMTXC4ZULNE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GTMTXC4ZULNESOER","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GTMTXC4Z","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GTMTXC4ZULNESOERP5AJZF3AJH","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-11T21:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"af0e6fbdd467f1b5f4dcbe8b1d830d736774029d4eea3b01d119c8ebbb0c4b86","abstract_canon_sha256":"87474ff4e1858e08b94e4734406a1108853ea93f155db66cd42135b6b68358c1"},"schema_version":"1.0"},"canonical_sha256":"34d93b8b99a2da4938917f409c976049f9ccd7c50d4c7f6065aca46a8e77a965","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:25.137926Z","signature_b64":"wlhz3d5uExf4cKVGMDCoO+UZUtMK2piuQc3YJfDLLxg+P7s3b20kmEBkIGvHirGgmAjLoOSteBvRloJqimafAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34d93b8b99a2da4938917f409c976049f9ccd7c50d4c7f6065aca46a8e77a965","last_reissued_at":"2026-05-18T00:35:25.137293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:25.137293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03790","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":"2026-05-18T00:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Da1DuH/8Htq/5VYNhFYq5oi1BKB09QL3ZBwb90B3YYAW+a17O3PJq1++gtWgANceOVcZ+7GwShwZwb0sC+pdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:20:06.263661Z"},"content_sha256":"0120dde3cb721ee9961fb95bafa83e5739568a9749b07fc66ec57d247c0b990a","schema_version":"1.0","event_id":"sha256:0120dde3cb721ee9961fb95bafa83e5739568a9749b07fc66ec57d247c0b990a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GTMTXC4ZULNESOERP5AJZF3AJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congested aggregation via Newtonian interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inwon Kim, Katy Craig, Yao Yao","submitted_at":"2016-03-11T21:26:43Z","abstract_excerpt":"We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our model as the Wasserstein gradient flow of an interaction energy, with a penalization to enforce the constraint on the height of the density. From this perspective, the problem can be seen as a singular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03790","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":"2026-05-18T00:35:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxtFETcXZlDSQf5kDjDx68BJ27dbuoWm5HsqW1cJ/XzE9iK7GaqZCW3f8aE76W05iauGTb3RQVxj+Q7Qi5pnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:20:06.264009Z"},"content_sha256":"444e4c81dccd3b22eee878f4d36186b39795aa5f383b593dd34a408957f75b7e","schema_version":"1.0","event_id":"sha256:444e4c81dccd3b22eee878f4d36186b39795aa5f383b593dd34a408957f75b7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTMTXC4ZULNESOERP5AJZF3AJH/bundle.json","state_url":"https://pith.science/pith/GTMTXC4ZULNESOERP5AJZF3AJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTMTXC4ZULNESOERP5AJZF3AJH/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":"2026-06-01T00:20:06Z","links":{"resolver":"https://pith.science/pith/GTMTXC4ZULNESOERP5AJZF3AJH","bundle":"https://pith.science/pith/GTMTXC4ZULNESOERP5AJZF3AJH/bundle.json","state":"https://pith.science/pith/GTMTXC4ZULNESOERP5AJZF3AJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTMTXC4ZULNESOERP5AJZF3AJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GTMTXC4ZULNESOERP5AJZF3AJH","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":"87474ff4e1858e08b94e4734406a1108853ea93f155db66cd42135b6b68358c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-11T21:26:43Z","title_canon_sha256":"af0e6fbdd467f1b5f4dcbe8b1d830d736774029d4eea3b01d119c8ebbb0c4b86"},"schema_version":"1.0","source":{"id":"1603.03790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03790","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03790v1","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03790","created_at":"2026-05-18T00:35:25Z"},{"alias_kind":"pith_short_12","alias_value":"GTMTXC4ZULNE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GTMTXC4ZULNESOER","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GTMTXC4Z","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:444e4c81dccd3b22eee878f4d36186b39795aa5f383b593dd34a408957f75b7e","target":"graph","created_at":"2026-05-18T00:35:25Z","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 congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our model as the Wasserstein gradient flow of an interaction energy, with a penalization to enforce the constraint on the height of the density. From this perspective, the problem can be seen as a singular ","authors_text":"Inwon Kim, Katy Craig, Yao Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-11T21:26:43Z","title":"Congested aggregation via Newtonian interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03790","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":"sha256:0120dde3cb721ee9961fb95bafa83e5739568a9749b07fc66ec57d247c0b990a","target":"record","created_at":"2026-05-18T00:35:25Z","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":"87474ff4e1858e08b94e4734406a1108853ea93f155db66cd42135b6b68358c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-11T21:26:43Z","title_canon_sha256":"af0e6fbdd467f1b5f4dcbe8b1d830d736774029d4eea3b01d119c8ebbb0c4b86"},"schema_version":"1.0","source":{"id":"1603.03790","kind":"arxiv","version":1}},"canonical_sha256":"34d93b8b99a2da4938917f409c976049f9ccd7c50d4c7f6065aca46a8e77a965","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34d93b8b99a2da4938917f409c976049f9ccd7c50d4c7f6065aca46a8e77a965","first_computed_at":"2026-05-18T00:35:25.137293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:25.137293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wlhz3d5uExf4cKVGMDCoO+UZUtMK2piuQc3YJfDLLxg+P7s3b20kmEBkIGvHirGgmAjLoOSteBvRloJqimafAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:25.137926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0120dde3cb721ee9961fb95bafa83e5739568a9749b07fc66ec57d247c0b990a","sha256:444e4c81dccd3b22eee878f4d36186b39795aa5f383b593dd34a408957f75b7e"],"state_sha256":"86cbfe557dd0b3b5a6712d850f6784d8a50d2df1d3cdc174eafacbe487da925a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyuv8UIQ/mzvc7ckIZ6imD5iajrJyeQd1hvlunvCIkaG6NzNd7H/FOXt8HkJmN3jnESf6WbOcyXGqPrcVzyCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:20:06.266075Z","bundle_sha256":"125605d16d4bc998a4d85466422a2531dd5039e05a071a1b953b6b625cda3eb0"}}