{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JQR7XK2RGZ6YXIP35TGOVJ2SRB","short_pith_number":"pith:JQR7XK2R","canonical_record":{"source":{"id":"2606.30325","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:08:27Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"92726f2b5ccb18096016325c628a0e1c0d9e850e512c456ffd490aa83eb3b85c","abstract_canon_sha256":"7b304bcef9ace1e9e883fcaa0c3b48ff23f53cbda1ad56f247ce06d5d3039eda"},"schema_version":"1.0"},"canonical_sha256":"4c23fbab51367d8ba1fbeccceaa752885feb7b9e04927a765ed9b7c111680b2f","source":{"kind":"arxiv","id":"2606.30325","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JQR7XK2RGZ6YXIP35TGOVJ2SRB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30325","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T14:08:27Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"92726f2b5ccb18096016325c628a0e1c0d9e850e512c456ffd490aa83eb3b85c","abstract_canon_sha256":"7b304bcef9ace1e9e883fcaa0c3b48ff23f53cbda1ad56f247ce06d5d3039eda"},"schema_version":"1.0"},"canonical_sha256":"4c23fbab51367d8ba1fbeccceaa752885feb7b9e04927a765ed9b7c111680b2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:10.403696Z","signature_b64":"cQudNAWEcEuynn1ICFc32/6MI+jIfTT6537MK/ul0KTUYSu29RMrP6tuhIE2HGGmb8V6337VMUdnTGdPR4SVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c23fbab51367d8ba1fbeccceaa752885feb7b9e04927a765ed9b7c111680b2f","last_reissued_at":"2026-06-30T02:18:10.403089Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:10.403089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30325","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":"2026-06-30T02:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKPS+cVyd2uIlaNAE2BASOzY9n08sdVvghZ6mw8sTuslGbI2mHyTBoi5VsAVWyiOMkSntcbe1ejV0dabpXtDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:20:32.422469Z"},"content_sha256":"cb5b6ece99f4b1c7bd3f3ce7d952c69481008167373a5f3a7543bd8189108964","schema_version":"1.0","event_id":"sha256:cb5b6ece99f4b1c7bd3f3ce7d952c69481008167373a5f3a7543bd8189108964"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JQR7XK2RGZ6YXIP35TGOVJ2SRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamic Limits of Stochastic Chemical Reaction Networks with Phosphorylation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["q-bio.MN"],"primary_cat":"math.PR","authors_text":"Lucie Laurence, Philippe Robert","submitted_at":"2026-06-29T14:08:27Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30325","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/2606.30325/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":"2026-06-30T02:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRropQ4Pz3ztri/rKnYXn74h06AlTbavhcd+Qd0IX8jmFThgUUXrTEdz3UZxfWjD4VaZFxsLvBp9bQ2uOv2wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:20:32.423407Z"},"content_sha256":"804ceb577ef041b7fa79da4abed9b7a0cdb8e818dc8d6b5674ebecb198bad71a","schema_version":"1.0","event_id":"sha256:804ceb577ef041b7fa79da4abed9b7a0cdb8e818dc8d6b5674ebecb198bad71a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/bundle.json","state_url":"https://pith.science/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/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":"2026-08-15T17:20:32Z","links":{"resolver":"https://pith.science/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB","bundle":"https://pith.science/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/bundle.json","state":"https://pith.science/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQR7XK2RGZ6YXIP35TGOVJ2SRB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWvJSXd4r9KZBpb5y5zlnDQbKHPd/YjnEC4oDGOACnJddxfhvpA/9Z+LWa3+Q6gilhs72q6cmfEPH8O/fgI5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T17:20:32.428899Z","bundle_sha256":"0f840f5f59eebf85ab4c67bbea3ba779cd5bc23f561c36566af98055ee239642"}}