{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JQR7XK2RGZ6YXIP35TGOVJ2SRB","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":"7b304bcef9ace1e9e883fcaa0c3b48ff23f53cbda1ad56f247ce06d5d3039eda","cross_cats_sorted":["q-bio.MN"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:08:27Z","title_canon_sha256":"92726f2b5ccb18096016325c628a0e1c0d9e850e512c456ffd490aa83eb3b85c"},"schema_version":"1.0","source":{"id":"2606.30325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30325","created_at":"2026-06-30T02:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30325v1","created_at":"2026-06-30T02:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30325","created_at":"2026-06-30T02:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"JQR7XK2RGZ6Y","created_at":"2026-06-30T02:18:10Z"},{"alias_kind":"pith_short_16","alias_value":"JQR7XK2RGZ6YXIP3","created_at":"2026-06-30T02:18:10Z"},{"alias_kind":"pith_short_8","alias_value":"JQR7XK2R","created_at":"2026-06-30T02:18:10Z"}],"graph_snapshots":[{"event_id":"sha256:804ceb577ef041b7fa79da4abed9b7a0cdb8e818dc8d6b5674ebecb198bad71a","target":"graph","created_at":"2026-06-30T02:18:10Z","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/2606.30325/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we investigate the stability properties of a fundamental mechanism of biological cells called phosphorylation. The system is a chemical reaction network (CRN) for which a chemical species, {\\em the substrate}, can be sequentially transformed into two phosphorylated forms, by the activity of two types of enzymes, one type for phosphorylation, the other for dephosphorylation. We investigate a stochastic representation of this model, under the mass action kinetics. The total mass of the substrate is fixed at $N$, while the total mass of enzymes scales proportionally to $N$. The asym","authors_text":"Lucie Laurence, Philippe Robert","cross_cats":["q-bio.MN"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:08:27Z","title":"Thermodynamic Limits of Stochastic Chemical Reaction Networks with Phosphorylation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30325","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:cb5b6ece99f4b1c7bd3f3ce7d952c69481008167373a5f3a7543bd8189108964","target":"record","created_at":"2026-06-30T02:18:10Z","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":"7b304bcef9ace1e9e883fcaa0c3b48ff23f53cbda1ad56f247ce06d5d3039eda","cross_cats_sorted":["q-bio.MN"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:08:27Z","title_canon_sha256":"92726f2b5ccb18096016325c628a0e1c0d9e850e512c456ffd490aa83eb3b85c"},"schema_version":"1.0","source":{"id":"2606.30325","kind":"arxiv","version":1}},"canonical_sha256":"4c23fbab51367d8ba1fbeccceaa752885feb7b9e04927a765ed9b7c111680b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c23fbab51367d8ba1fbeccceaa752885feb7b9e04927a765ed9b7c111680b2f","first_computed_at":"2026-06-30T02:18:10.403089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:10.403089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQudNAWEcEuynn1ICFc32/6MI+jIfTT6537MK/ul0KTUYSu29RMrP6tuhIE2HGGmb8V6337VMUdnTGdPR4SVBg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:10.403696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb5b6ece99f4b1c7bd3f3ce7d952c69481008167373a5f3a7543bd8189108964","sha256:804ceb577ef041b7fa79da4abed9b7a0cdb8e818dc8d6b5674ebecb198bad71a"],"state_sha256":"5cb69dd4c750cd8cbffef2aaf862b612ea8c1bedb96ddb53e37a139270af39d5"}