{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:4QCOOOYQ5SJZ46ZWUWRTKD6ARQ","short_pith_number":"pith:4QCOOOYQ","canonical_record":{"source":{"id":"0904.2960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-20T07:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"6b48d0773871e2f0d54619c0c2b278599bdd6ffbc6346c86e96775cbda8a197d","abstract_canon_sha256":"ebc6b9c131826030d48c79e0285e1ea4a44a7e40ea7fd78148492e9e3be4f3ca"},"schema_version":"1.0"},"canonical_sha256":"e404e73b10ec939e7b36a5a3350fc08c02a856d785b91b448c29a7c7c7e0c589","source":{"kind":"arxiv","id":"0904.2960","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2960","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2960v1","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2960","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"4QCOOOYQ5SJZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4QCOOOYQ5SJZ46ZW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4QCOOOYQ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:4QCOOOYQ5SJZ46ZWUWRTKD6ARQ","target":"record","payload":{"canonical_record":{"source":{"id":"0904.2960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-20T07:50:51Z","cross_cats_sorted":[],"title_canon_sha256":"6b48d0773871e2f0d54619c0c2b278599bdd6ffbc6346c86e96775cbda8a197d","abstract_canon_sha256":"ebc6b9c131826030d48c79e0285e1ea4a44a7e40ea7fd78148492e9e3be4f3ca"},"schema_version":"1.0"},"canonical_sha256":"e404e73b10ec939e7b36a5a3350fc08c02a856d785b91b448c29a7c7c7e0c589","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:06.426140Z","signature_b64":"RUpByP5ceJnha0vfWXPV8ykGvNFLt3lynY4Enp4k8FbAj+iQnwRJB2vzbGAqmkoc7bJWF46IdrvXBiVU4RrbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e404e73b10ec939e7b36a5a3350fc08c02a856d785b91b448c29a7c7c7e0c589","last_reissued_at":"2026-05-18T04:24:06.425500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:06.425500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.2960","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":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hfUiXTzv8XomR81W8kbuW0R0U8+Gl1/cZlSvtJgZIoDq4sDwIHheF+7RBWw3wV/LiLgJM2rv4u53LuqnmpUFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:08:18.458904Z"},"content_sha256":"5d989a019a01c5c6c98d4ae90bbaf8c7a962687257993dc8573d20f93e04467a","schema_version":"1.0","event_id":"sha256:5d989a019a01c5c6c98d4ae90bbaf8c7a962687257993dc8573d20f93e04467a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:4QCOOOYQ5SJZ46ZWUWRTKD6ARQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sign patterns for chemical reaction networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Igor Klep, J. William Helton, Vitaly Katsnelson","submitted_at":"2009-04-20T07:50:51Z","abstract_excerpt":"Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector consisting of real-valued functions having a special relationship to $S$. Our main interest will be in the Jacobian matrix, $f'(x)$, of $f(x)$, in particular in whether or not each entry $f'(x)_{ij}$ has the same sign for all $x$ in the orthant, i.e., the Jacobian respects a sign pattern. In other words species $x_j$ always acts on species $x_i$ in an inhibitory way "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2960","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":""},"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":"2026-05-18T04:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UWMB15IoYOckb/gmTdt2CjvJaAwjubNEs/M2qOLpRSdUEH4tdNO2wGCIss5+AMvdIotUd+SGKlnLoe8Op0s1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:08:18.459663Z"},"content_sha256":"e5f3ee674dc4231ae3e3eecb9fa7a460d07c9e828be09fb8d019ecb9c910b9ec","schema_version":"1.0","event_id":"sha256:e5f3ee674dc4231ae3e3eecb9fa7a460d07c9e828be09fb8d019ecb9c910b9ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/bundle.json","state_url":"https://pith.science/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/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":"2026-06-11T22:08:18Z","links":{"resolver":"https://pith.science/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ","bundle":"https://pith.science/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/bundle.json","state":"https://pith.science/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QCOOOYQ5SJZ46ZWUWRTKD6ARQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4QCOOOYQ5SJZ46ZWUWRTKD6ARQ","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":"ebc6b9c131826030d48c79e0285e1ea4a44a7e40ea7fd78148492e9e3be4f3ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-20T07:50:51Z","title_canon_sha256":"6b48d0773871e2f0d54619c0c2b278599bdd6ffbc6346c86e96775cbda8a197d"},"schema_version":"1.0","source":{"id":"0904.2960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2960","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2960v1","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2960","created_at":"2026-05-18T04:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"4QCOOOYQ5SJZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4QCOOOYQ5SJZ46ZW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4QCOOOYQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e5f3ee674dc4231ae3e3eecb9fa7a460d07c9e828be09fb8d019ecb9c910b9ec","target":"graph","created_at":"2026-05-18T04:24:06Z","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":"Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector consisting of real-valued functions having a special relationship to $S$. Our main interest will be in the Jacobian matrix, $f'(x)$, of $f(x)$, in particular in whether or not each entry $f'(x)_{ij}$ has the same sign for all $x$ in the orthant, i.e., the Jacobian respects a sign pattern. In other words species $x_j$ always acts on species $x_i$ in an inhibitory way ","authors_text":"Igor Klep, J. William Helton, Vitaly Katsnelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-20T07:50:51Z","title":"Sign patterns for chemical reaction networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2960","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":"sha256:5d989a019a01c5c6c98d4ae90bbaf8c7a962687257993dc8573d20f93e04467a","target":"record","created_at":"2026-05-18T04:24:06Z","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":"ebc6b9c131826030d48c79e0285e1ea4a44a7e40ea7fd78148492e9e3be4f3ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-04-20T07:50:51Z","title_canon_sha256":"6b48d0773871e2f0d54619c0c2b278599bdd6ffbc6346c86e96775cbda8a197d"},"schema_version":"1.0","source":{"id":"0904.2960","kind":"arxiv","version":1}},"canonical_sha256":"e404e73b10ec939e7b36a5a3350fc08c02a856d785b91b448c29a7c7c7e0c589","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e404e73b10ec939e7b36a5a3350fc08c02a856d785b91b448c29a7c7c7e0c589","first_computed_at":"2026-05-18T04:24:06.425500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:06.425500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUpByP5ceJnha0vfWXPV8ykGvNFLt3lynY4Enp4k8FbAj+iQnwRJB2vzbGAqmkoc7bJWF46IdrvXBiVU4RrbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:06.426140Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d989a019a01c5c6c98d4ae90bbaf8c7a962687257993dc8573d20f93e04467a","sha256:e5f3ee674dc4231ae3e3eecb9fa7a460d07c9e828be09fb8d019ecb9c910b9ec"],"state_sha256":"5824c7e1ce1d502d58789d9a3f472ca128a0757329fbab0564ce5d3d51ca374e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7D99blGmyvYAWE/UE2zzPnIoJ6dfZP/35q41bA1JalDwxhzhqSTWKBlLFaRrgRUeiQy21ksQvD37shrl55RVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:08:18.464559Z","bundle_sha256":"b48ea9aeb382a4310586572cece3babe79af7c331ed0cd10f04137ca8dfab68d"}}