{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGOTMXQ2GSKB746VR4C2SQ7BG2","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":"819ba8d3ae53f88a0a2a98ec290fada5a1672974274af1c96eef18ee4c7a29a5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.OT","submitted_at":"2016-10-12T23:56:21Z","title_canon_sha256":"001d74aa7859e2f83a9f297a20ab50304e1e87f97d6deff08f27016cae6c8aa6"},"schema_version":"1.0","source":{"id":"1610.04224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04224","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04224v1","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04224","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"LGOTMXQ2GSKB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGOTMXQ2GSKB746V","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGOTMXQ2","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:86233f8ebcf249515b9bad9726be015ea586d060266dee2b57adac17508a0909","target":"graph","created_at":"2026-05-18T01:02:20Z","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":"This work gives a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, where the synthesis of the two gives rise to the emergence of function. We introduce a concept of monotonicity and prove that monotonicity together with hardwiring, defined as all cells of the same tissue having the same genome dynamics, is sufficient for the global convergence of the tissue dynamics.","authors_text":"Indika Rajapakse, Steve Smale","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.OT","submitted_at":"2016-10-12T23:56:21Z","title":"Emergence of Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04224","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":"sha256:0ac764dbe3f0df112d4a9dadeb56e10ad8f3edbf62bdd5867eb5f2971db741bf","target":"record","created_at":"2026-05-18T01:02:20Z","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":"819ba8d3ae53f88a0a2a98ec290fada5a1672974274af1c96eef18ee4c7a29a5","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.OT","submitted_at":"2016-10-12T23:56:21Z","title_canon_sha256":"001d74aa7859e2f83a9f297a20ab50304e1e87f97d6deff08f27016cae6c8aa6"},"schema_version":"1.0","source":{"id":"1610.04224","kind":"arxiv","version":1}},"canonical_sha256":"599d365e1a34941ff3d58f05a943e136bee6428315eac47ccd2d61e26a262526","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599d365e1a34941ff3d58f05a943e136bee6428315eac47ccd2d61e26a262526","first_computed_at":"2026-05-18T01:02:20.270659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:20.270659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXFeM+ShkoDp98L3hywcG+dFvkwkh1Rf6N5ByFhrswy6eW3PDJTCLa0s0ZqsnjWEJ8tuB5W0+hkof8ZmnyPMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:20.271313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ac764dbe3f0df112d4a9dadeb56e10ad8f3edbf62bdd5867eb5f2971db741bf","sha256:86233f8ebcf249515b9bad9726be015ea586d060266dee2b57adac17508a0909"],"state_sha256":"7633c0bf310e09158ff8afbde9e37198e5a48e048c9be7cd5d4bcec98b8993a2"}