{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ID6HOCANXOFFXRYMOYFGUOJGR5","short_pith_number":"pith:ID6HOCAN","canonical_record":{"source":{"id":"1411.2896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2014-11-11T17:38:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"918c89426c3dce80940f47c5053757ea31dbbfe0faad059068c1c69093a325d0","abstract_canon_sha256":"b7dcf148a00123159f52759439256a8e0a6c3cc986317ab0bae33558ebf4f3be"},"schema_version":"1.0"},"canonical_sha256":"40fc77080dbb8a5bc70c760a6a39268f767c9f81ff5c647ed56a06cb9cce956f","source":{"kind":"arxiv","id":"1411.2896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2896","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2896v1","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2896","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"ID6HOCANXOFF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ID6HOCANXOFFXRYM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ID6HOCAN","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ID6HOCANXOFFXRYMOYFGUOJGR5","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2014-11-11T17:38:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"918c89426c3dce80940f47c5053757ea31dbbfe0faad059068c1c69093a325d0","abstract_canon_sha256":"b7dcf148a00123159f52759439256a8e0a6c3cc986317ab0bae33558ebf4f3be"},"schema_version":"1.0"},"canonical_sha256":"40fc77080dbb8a5bc70c760a6a39268f767c9f81ff5c647ed56a06cb9cce956f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:52.773621Z","signature_b64":"geWe1VoXzQrtl+jvtdy2afsqyME6quYV8J9HOzvs3gijUwEm6uSrpe9HmT8/0XjJH37zH0E7B7rvvPUZGbDRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40fc77080dbb8a5bc70c760a6a39268f767c9f81ff5c647ed56a06cb9cce956f","last_reissued_at":"2026-05-18T02:37:52.773152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:52.773152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2896","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":"2026-05-18T02:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeOI7KLWBrzeHl672byKqoXr89EzL0N7cvEnnocA3y0iTLEyX77G646QDngZHhDrUF2waFjisi0hqqdmaOM6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T15:46:03.056871Z"},"content_sha256":"96ee93b4fe2948e9713fb639164ce1e57d7ed87756cfc5119ab59a4c05503a83","schema_version":"1.0","event_id":"sha256:96ee93b4fe2948e9713fb639164ce1e57d7ed87756cfc5119ab59a4c05503a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ID6HOCANXOFFXRYMOYFGUOJGR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph-theoretic analysis of multistationarity using degree theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.MN","authors_text":"Carsten Conradi, Maya Mincheva","submitted_at":"2014-11-11T17:38:25Z","abstract_excerpt":"Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be represented by a directed bipartite graph with species and reaction nodes. Graph-theoretic methods can then be used to assess the potential of a given biochemical mechanism for multistationarity by identifying structures in the bipartite graph referr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2896","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":"2026-05-18T02:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i+PW5xfDG5rXT2kXhSZIHml5CWSQmTg/s9pkUeAQgtqvBnEW57Ha1PVOLqYLCOj5XvDqaI4k30Z0l22Q9QWPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T15:46:03.057577Z"},"content_sha256":"0aa1b49c8b4e350207fab2e03ffb99c90df3bc6d9041b7ea9c8cbc2ca6305aeb","schema_version":"1.0","event_id":"sha256:0aa1b49c8b4e350207fab2e03ffb99c90df3bc6d9041b7ea9c8cbc2ca6305aeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/bundle.json","state_url":"https://pith.science/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/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":"2026-05-23T15:46:03Z","links":{"resolver":"https://pith.science/pith/ID6HOCANXOFFXRYMOYFGUOJGR5","bundle":"https://pith.science/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/bundle.json","state":"https://pith.science/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ID6HOCANXOFFXRYMOYFGUOJGR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ID6HOCANXOFFXRYMOYFGUOJGR5","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":"b7dcf148a00123159f52759439256a8e0a6c3cc986317ab0bae33558ebf4f3be","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2014-11-11T17:38:25Z","title_canon_sha256":"918c89426c3dce80940f47c5053757ea31dbbfe0faad059068c1c69093a325d0"},"schema_version":"1.0","source":{"id":"1411.2896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2896","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2896v1","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2896","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"ID6HOCANXOFF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ID6HOCANXOFFXRYM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ID6HOCAN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:0aa1b49c8b4e350207fab2e03ffb99c90df3bc6d9041b7ea9c8cbc2ca6305aeb","target":"graph","created_at":"2026-05-18T02:37:52Z","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":"Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be represented by a directed bipartite graph with species and reaction nodes. Graph-theoretic methods can then be used to assess the potential of a given biochemical mechanism for multistationarity by identifying structures in the bipartite graph referr","authors_text":"Carsten Conradi, Maya Mincheva","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2014-11-11T17:38:25Z","title":"Graph-theoretic analysis of multistationarity using degree theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2896","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":"sha256:96ee93b4fe2948e9713fb639164ce1e57d7ed87756cfc5119ab59a4c05503a83","target":"record","created_at":"2026-05-18T02:37:52Z","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":"b7dcf148a00123159f52759439256a8e0a6c3cc986317ab0bae33558ebf4f3be","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2014-11-11T17:38:25Z","title_canon_sha256":"918c89426c3dce80940f47c5053757ea31dbbfe0faad059068c1c69093a325d0"},"schema_version":"1.0","source":{"id":"1411.2896","kind":"arxiv","version":1}},"canonical_sha256":"40fc77080dbb8a5bc70c760a6a39268f767c9f81ff5c647ed56a06cb9cce956f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40fc77080dbb8a5bc70c760a6a39268f767c9f81ff5c647ed56a06cb9cce956f","first_computed_at":"2026-05-18T02:37:52.773152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:52.773152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"geWe1VoXzQrtl+jvtdy2afsqyME6quYV8J9HOzvs3gijUwEm6uSrpe9HmT8/0XjJH37zH0E7B7rvvPUZGbDRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:52.773621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96ee93b4fe2948e9713fb639164ce1e57d7ed87756cfc5119ab59a4c05503a83","sha256:0aa1b49c8b4e350207fab2e03ffb99c90df3bc6d9041b7ea9c8cbc2ca6305aeb"],"state_sha256":"56de34f5ce1fefb28c6e13e847ac9ebf01f8d8f821133d9acf77177a3f8f84b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gnKCHbDA/Vy4IqiuSiJs9nS0I5KZifhmINCU11VjnNYY6EvL/gYJ0vsanMC30hZpLMJrzALS2xip68y4rvmIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T15:46:03.061186Z","bundle_sha256":"f2a088a8d1b38633506b3307e2a04257cc1a29f57c7dd43aad11a26bdc39e54a"}}