{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LGVKJA2OPTZ6KAAJFTCCP7JJ2L","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":"aea151c19c70e61edbaa70b00601a8b3a62b38b02b8fd8de5da94322ab984191","cross_cats_sorted":["q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2015-02-06T01:24:16Z","title_canon_sha256":"8cc5f391729fb893be288581ee80e6d71c46a5e1e5439a10cf135dcc18253023"},"schema_version":"1.0","source":{"id":"1502.01768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01768","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01768v1","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01768","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"LGVKJA2OPTZ6","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGVKJA2OPTZ6KAAJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGVKJA2O","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:734cb874691443441ce9900c1760a302b3b048d01972dac6f2da0041c0974e9e","target":"graph","created_at":"2026-05-18T02:27:50Z","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":"Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been observed. We develop a theoretical model of cluster- mediated concentration gradient formation based on the Becker-Doring equations of aggregation- fragmentation processes. We show that such a mechanism produces robust concentration gradients on realistic time and spatial scales so long as the process of clustering does not significantly stabilize the signal","authors_text":"Timothy E Saunders","cross_cats":["q-bio.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2015-02-06T01:24:16Z","title":"Aggregation-fragmentation model of robust concentration gradient formation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01768","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":"sha256:1aec22497deb367ba986261131226735b4b62a9d65bd7cff31f8415c78c1e6bc","target":"record","created_at":"2026-05-18T02:27:50Z","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":"aea151c19c70e61edbaa70b00601a8b3a62b38b02b8fd8de5da94322ab984191","cross_cats_sorted":["q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2015-02-06T01:24:16Z","title_canon_sha256":"8cc5f391729fb893be288581ee80e6d71c46a5e1e5439a10cf135dcc18253023"},"schema_version":"1.0","source":{"id":"1502.01768","kind":"arxiv","version":1}},"canonical_sha256":"59aaa4834e7cf3e500092cc427fd29d2d04f4bb8e3468336e405bc40c7c3c611","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59aaa4834e7cf3e500092cc427fd29d2d04f4bb8e3468336e405bc40c7c3c611","first_computed_at":"2026-05-18T02:27:50.690749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.690749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PzobazR05DRyj6kH0/Jomf4eyOHHYcKBn6HT+klbccj6b56tlPZINYyAQ065IaBZzDrF9rorOGGaeSBOCG21Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.691157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aec22497deb367ba986261131226735b4b62a9d65bd7cff31f8415c78c1e6bc","sha256:734cb874691443441ce9900c1760a302b3b048d01972dac6f2da0041c0974e9e"],"state_sha256":"cd896d893c980243246080248ee978517a42b468e1572eaf3e81d955f9a4b84f"}