{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BXD6CSM6TQD3TC3BUCVSVSANSW","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":"86cca4a64840e9e673f74b39bb9522667e3fe1989591a5d0f2993e3e5317f458","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2019-03-06T21:20:33Z","title_canon_sha256":"09b1830509d705741086aa99d65eafc55065edf3bbeefdb8be188e89551dd1d2"},"schema_version":"1.0","source":{"id":"1903.02617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02617","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02617v1","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02617","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"BXD6CSM6TQD3","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BXD6CSM6TQD3TC3B","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BXD6CSM6","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:abfada27a2642b23726a168e31b201f44e29acf080384585180690b780744586","target":"graph","created_at":"2026-05-17T23:51:51Z","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 concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We prove that oscillations persist even as the model is greatly simplified (reactions are made irreversible and intermediates are removed). Bistability, however, is much less robust -- this property is lost when intermediates are removed or even when all reactions are made irreversible. Moreover, bistabilit","authors_text":"Angelica Torres, Anne Shiu, Nida Obatake, Xiaoxian Tang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2019-03-06T21:20:33Z","title":"Oscillations and bistability in a model of ERK regulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02617","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:dac1b2ccf5f45b9657d88281548fa4e9316a9257e490b3e08b5822f9abc238cf","target":"record","created_at":"2026-05-17T23:51:51Z","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":"86cca4a64840e9e673f74b39bb9522667e3fe1989591a5d0f2993e3e5317f458","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2019-03-06T21:20:33Z","title_canon_sha256":"09b1830509d705741086aa99d65eafc55065edf3bbeefdb8be188e89551dd1d2"},"schema_version":"1.0","source":{"id":"1903.02617","kind":"arxiv","version":1}},"canonical_sha256":"0dc7e1499e9c07b98b61a0ab2ac80d95afb4da6766b92f4f33ffdb57842cef28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dc7e1499e9c07b98b61a0ab2ac80d95afb4da6766b92f4f33ffdb57842cef28","first_computed_at":"2026-05-17T23:51:51.688483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:51.688483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ofigd2r2AYTsLH6hid0H56oE/WOtdRU0SjXsmscMQs8pu6o0KrFFwIdirws99P5r/INOJUnYN0gpDAJbjH8nDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:51.689218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dac1b2ccf5f45b9657d88281548fa4e9316a9257e490b3e08b5822f9abc238cf","sha256:abfada27a2642b23726a168e31b201f44e29acf080384585180690b780744586"],"state_sha256":"8227db640113e8a857a684ea3bb612757acd05f094956ad31bb6b231fb95d3db"}