{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:74Z63J3ZZQQHQIZDXL6JTFZ6RO","short_pith_number":"pith:74Z63J3Z","canonical_record":{"source":{"id":"2606.18592","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T01:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"d9762a545c0e57b37c6ea1671a5d6aea82fb94780e8b44536596086ee4c1ef76","abstract_canon_sha256":"c9531bca810e959b03f21780f4187b4316a7c5fd56f1d6c79964fe7e9543ecf0"},"schema_version":"1.0"},"canonical_sha256":"ff33eda779cc20782323bafc99973e8b9ddcfb92caf799fff862f7e5985932da","source":{"kind":"arxiv","id":"2606.18592","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18592","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18592v1","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18592","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"74Z63J3ZZQQH","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_16","alias_value":"74Z63J3ZZQQHQIZD","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_8","alias_value":"74Z63J3Z","created_at":"2026-06-19T16:11:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:74Z63J3ZZQQHQIZDXL6JTFZ6RO","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18592","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T01:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"d9762a545c0e57b37c6ea1671a5d6aea82fb94780e8b44536596086ee4c1ef76","abstract_canon_sha256":"c9531bca810e959b03f21780f4187b4316a7c5fd56f1d6c79964fe7e9543ecf0"},"schema_version":"1.0"},"canonical_sha256":"ff33eda779cc20782323bafc99973e8b9ddcfb92caf799fff862f7e5985932da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:41.918368Z","signature_b64":"9Kp9Qe/lL9it/ikwGPbvPpcshNQsVkjYPeh4CAYLIcx4pr1WzgSRP8/+pMkGc/aybCmYSqXEHlHsXMi0B3XIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff33eda779cc20782323bafc99973e8b9ddcfb92caf799fff862f7e5985932da","last_reissued_at":"2026-06-19T16:11:41.917965Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:41.917965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18592","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":"2026-06-19T16:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GmeecQIan5GmSAMFOqgHNyHrv5SFb6leEZrPQ+rZyIn27KenivclNbDVZbYCympC0ZAj864/3KFZPlKPMxvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:29:02.586847Z"},"content_sha256":"1c43a677c2f73e594ebddb5d0b96a9d150cdccb62220d68aafa48390fd0d379a","schema_version":"1.0","event_id":"sha256:1c43a677c2f73e594ebddb5d0b96a9d150cdccb62220d68aafa48390fd0d379a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:74Z63J3ZZQQHQIZDXL6JTFZ6RO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global bounded solutions for a class of generalized Hillen-Painter models near Couette flow in $\\mathbb{R}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guoxu Yang, Wendong Wang, Yi Zhang, Yubo Chen","submitted_at":"2026-06-17T01:39:36Z","abstract_excerpt":"We investigate the global well-posedness of a class of generalized Hillen--Painter systems -- specifically, supercritical volume-filling chemotaxis models -- in $\\mathbb{R}^2$ under the influence of Couette flow. It is well established that, in the absence of fluid flow, solutions to this system may develop finite-time singularities (blow-up) for arbitrary initial cell mass. It is proved that the introduction of a Couette flow with sufficiently large amplitude guarantees the global existence of solutions for all initial masses. By employing a novel frequency decomposition technique, we success"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18592","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaRS2OQkXRCh/DZhBtuUz5ZksVdxpA6A10zl+HFVOsniqtByHYqtEtRRRyVGzFkGoNLVGX9Gk7S0QFaGS3MeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:29:02.587224Z"},"content_sha256":"3ed720b863b00ad7910d6d68418cb17506ae69e23539ee01d07148757a296918","schema_version":"1.0","event_id":"sha256:3ed720b863b00ad7910d6d68418cb17506ae69e23539ee01d07148757a296918"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/bundle.json","state_url":"https://pith.science/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/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":"2026-06-24T07:29:02Z","links":{"resolver":"https://pith.science/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO","bundle":"https://pith.science/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/bundle.json","state":"https://pith.science/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74Z63J3ZZQQHQIZDXL6JTFZ6RO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:74Z63J3ZZQQHQIZDXL6JTFZ6RO","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":"c9531bca810e959b03f21780f4187b4316a7c5fd56f1d6c79964fe7e9543ecf0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T01:39:36Z","title_canon_sha256":"d9762a545c0e57b37c6ea1671a5d6aea82fb94780e8b44536596086ee4c1ef76"},"schema_version":"1.0","source":{"id":"2606.18592","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18592","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18592v1","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18592","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"74Z63J3ZZQQH","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_16","alias_value":"74Z63J3ZZQQHQIZD","created_at":"2026-06-19T16:11:41Z"},{"alias_kind":"pith_short_8","alias_value":"74Z63J3Z","created_at":"2026-06-19T16:11:41Z"}],"graph_snapshots":[{"event_id":"sha256:3ed720b863b00ad7910d6d68418cb17506ae69e23539ee01d07148757a296918","target":"graph","created_at":"2026-06-19T16:11:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18592/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the global well-posedness of a class of generalized Hillen--Painter systems -- specifically, supercritical volume-filling chemotaxis models -- in $\\mathbb{R}^2$ under the influence of Couette flow. It is well established that, in the absence of fluid flow, solutions to this system may develop finite-time singularities (blow-up) for arbitrary initial cell mass. It is proved that the introduction of a Couette flow with sufficiently large amplitude guarantees the global existence of solutions for all initial masses. By employing a novel frequency decomposition technique, we success","authors_text":"Guoxu Yang, Wendong Wang, Yi Zhang, Yubo Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T01:39:36Z","title":"Global bounded solutions for a class of generalized Hillen-Painter models near Couette flow in $\\mathbb{R}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18592","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":"sha256:1c43a677c2f73e594ebddb5d0b96a9d150cdccb62220d68aafa48390fd0d379a","target":"record","created_at":"2026-06-19T16:11:41Z","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":"c9531bca810e959b03f21780f4187b4316a7c5fd56f1d6c79964fe7e9543ecf0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T01:39:36Z","title_canon_sha256":"d9762a545c0e57b37c6ea1671a5d6aea82fb94780e8b44536596086ee4c1ef76"},"schema_version":"1.0","source":{"id":"2606.18592","kind":"arxiv","version":1}},"canonical_sha256":"ff33eda779cc20782323bafc99973e8b9ddcfb92caf799fff862f7e5985932da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff33eda779cc20782323bafc99973e8b9ddcfb92caf799fff862f7e5985932da","first_computed_at":"2026-06-19T16:11:41.917965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:41.917965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Kp9Qe/lL9it/ikwGPbvPpcshNQsVkjYPeh4CAYLIcx4pr1WzgSRP8/+pMkGc/aybCmYSqXEHlHsXMi0B3XIBQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:41.918368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18592","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c43a677c2f73e594ebddb5d0b96a9d150cdccb62220d68aafa48390fd0d379a","sha256:3ed720b863b00ad7910d6d68418cb17506ae69e23539ee01d07148757a296918"],"state_sha256":"35654720aa63e0b1c607cee76889a524c37bd95be338ef73229fcace3f7a1d97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WsimjcEsI73bXLiCwaydsY0M0SaVGv0esCcQFH5OSpc5eHu1VRgjZWHv3bHXfRl7cgLe8JDEa9f2vqIeZdO7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:29:02.589213Z","bundle_sha256":"853cd689620867926b8c6f7b94ede07bd6a1bc9b0e6b552dd6f3cbdf7418b9bd"}}