{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5J5NAXJKLDIFDQDSFXVCFRGH5S","short_pith_number":"pith:5J5NAXJK","canonical_record":{"source":{"id":"1303.3963","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"q-bio.MN","submitted_at":"2013-03-16T10:17:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"76dd8610123c53bfb19974a36f25a48074b34acb1b72da95c160500c9b2fda77","abstract_canon_sha256":"09445afd8ff030c3dd6f3f7c3b2af0a99d82b87d4f2ff494aca0c1cbaad6ec11"},"schema_version":"1.0"},"canonical_sha256":"ea7ad05d2a58d051c0722dea22c4c7ecb6e2811264a458b763049f499167ab64","source":{"kind":"arxiv","id":"1303.3963","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3963","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3963v2","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3963","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"5J5NAXJKLDIF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5J5NAXJKLDIFDQDS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5J5NAXJK","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5J5NAXJKLDIFDQDSFXVCFRGH5S","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3963","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"q-bio.MN","submitted_at":"2013-03-16T10:17:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"76dd8610123c53bfb19974a36f25a48074b34acb1b72da95c160500c9b2fda77","abstract_canon_sha256":"09445afd8ff030c3dd6f3f7c3b2af0a99d82b87d4f2ff494aca0c1cbaad6ec11"},"schema_version":"1.0"},"canonical_sha256":"ea7ad05d2a58d051c0722dea22c4c7ecb6e2811264a458b763049f499167ab64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:52.339573Z","signature_b64":"tsx0oSYox8WykC+M585/8OoIAqops5FE1Jca+/VuiWa8dJiZtk98ano2jcWkSm6tMs2PsmCOk+8PtfiNT/t0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea7ad05d2a58d051c0722dea22c4c7ecb6e2811264a458b763049f499167ab64","last_reissued_at":"2026-05-18T03:24:52.338987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:52.338987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3963","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ycNwv84cuhXNB6UukqChU8iTCQ66wGJtJVQu3xJshr6Zb2YcZCa+53vEN40hFCUCpSDEzb0CM6cNQuWNxDGxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:27:43.964208Z"},"content_sha256":"50b511da8b475ccf6662ffaf832887886525dd7e14ec4b95694c1ba726eb69a8","schema_version":"1.0","event_id":"sha256:50b511da8b475ccf6662ffaf832887886525dd7e14ec4b95694c1ba726eb69a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5J5NAXJKLDIFDQDSFXVCFRGH5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropicalization and tropical equilibration of chemical reactions","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.AG"],"primary_cat":"q-bio.MN","authors_text":"Dima Grigoriev, Ovidiu Radulescu, Sergei Vakulenko, Vincent Noel","submitted_at":"2013-03-16T10:17:45Z","abstract_excerpt":"Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3963","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4eMJpADbz+NnGCgHeoO0h+lU1/HxEFQKGr+0K5ZSeeJ2dRNjp3j4sthmBh4B9y8c4feO+vd5RA16wzdVvJhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:27:43.964770Z"},"content_sha256":"204c36aa89651b195849a62d0c8e6db693998173a0b11fee46d6adcf110c66fd","schema_version":"1.0","event_id":"sha256:204c36aa89651b195849a62d0c8e6db693998173a0b11fee46d6adcf110c66fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/bundle.json","state_url":"https://pith.science/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/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":"2026-05-31T22:27:43Z","links":{"resolver":"https://pith.science/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S","bundle":"https://pith.science/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/bundle.json","state":"https://pith.science/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5J5NAXJKLDIFDQDSFXVCFRGH5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5J5NAXJKLDIFDQDSFXVCFRGH5S","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":"09445afd8ff030c3dd6f3f7c3b2af0a99d82b87d4f2ff494aca0c1cbaad6ec11","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"q-bio.MN","submitted_at":"2013-03-16T10:17:45Z","title_canon_sha256":"76dd8610123c53bfb19974a36f25a48074b34acb1b72da95c160500c9b2fda77"},"schema_version":"1.0","source":{"id":"1303.3963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3963","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3963v2","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3963","created_at":"2026-05-18T03:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"5J5NAXJKLDIF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5J5NAXJKLDIFDQDS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5J5NAXJK","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:204c36aa89651b195849a62d0c8e6db693998173a0b11fee46d6adcf110c66fd","target":"graph","created_at":"2026-05-18T03:24:52Z","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":"Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated t","authors_text":"Dima Grigoriev, Ovidiu Radulescu, Sergei Vakulenko, Vincent Noel","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"q-bio.MN","submitted_at":"2013-03-16T10:17:45Z","title":"Tropicalization and tropical equilibration of chemical reactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3963","kind":"arxiv","version":2},"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":"sha256:50b511da8b475ccf6662ffaf832887886525dd7e14ec4b95694c1ba726eb69a8","target":"record","created_at":"2026-05-18T03:24:52Z","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":"09445afd8ff030c3dd6f3f7c3b2af0a99d82b87d4f2ff494aca0c1cbaad6ec11","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"q-bio.MN","submitted_at":"2013-03-16T10:17:45Z","title_canon_sha256":"76dd8610123c53bfb19974a36f25a48074b34acb1b72da95c160500c9b2fda77"},"schema_version":"1.0","source":{"id":"1303.3963","kind":"arxiv","version":2}},"canonical_sha256":"ea7ad05d2a58d051c0722dea22c4c7ecb6e2811264a458b763049f499167ab64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea7ad05d2a58d051c0722dea22c4c7ecb6e2811264a458b763049f499167ab64","first_computed_at":"2026-05-18T03:24:52.338987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:52.338987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tsx0oSYox8WykC+M585/8OoIAqops5FE1Jca+/VuiWa8dJiZtk98ano2jcWkSm6tMs2PsmCOk+8PtfiNT/t0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:52.339573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50b511da8b475ccf6662ffaf832887886525dd7e14ec4b95694c1ba726eb69a8","sha256:204c36aa89651b195849a62d0c8e6db693998173a0b11fee46d6adcf110c66fd"],"state_sha256":"417fae8c7512b048fa6fe520e648206127470c03c48f0708145369fefc5b2ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"31725B90CBJgyf0GWn22+zGXam9a/w9p5iAYzkFrHfWCC1tthQfaGvF7MdZUIvBhmP82p7uJ8LeRILfsNIQICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:27:43.968146Z","bundle_sha256":"980b695801ef3c4c46e034f8e8e6021a5b59f3f0c60fa730782657d9a9694366"}}