{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QEQGXBPWYKTVHU7Y2J7ZQV7ITZ","short_pith_number":"pith:QEQGXBPW","canonical_record":{"source":{"id":"1011.0496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2010-11-02T01:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"1b6e183bd43459e320c6b34a74a71b4f3a040ea728c06ce022c42633425833e5","abstract_canon_sha256":"3e7a707362a5025aeeccd1405e264efac150c72ab5296ba76c20f1ae1a77f329"},"schema_version":"1.0"},"canonical_sha256":"81206b85f6c2a753d3f8d27f9857e89e56789daa10ab2d97bb1138da2dfbbef7","source":{"kind":"arxiv","id":"1011.0496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0496","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0496v1","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0496","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"QEQGXBPWYKTV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QEQGXBPWYKTVHU7Y","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QEQGXBPW","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QEQGXBPWYKTVHU7Y2J7ZQV7ITZ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2010-11-02T01:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"1b6e183bd43459e320c6b34a74a71b4f3a040ea728c06ce022c42633425833e5","abstract_canon_sha256":"3e7a707362a5025aeeccd1405e264efac150c72ab5296ba76c20f1ae1a77f329"},"schema_version":"1.0"},"canonical_sha256":"81206b85f6c2a753d3f8d27f9857e89e56789daa10ab2d97bb1138da2dfbbef7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:21.524625Z","signature_b64":"XtimV7JQIzJIl/0YMuAHZi/1xfgOLAmhj946tpazFEcqj0EHGA59iWFBkhUJiu/SZUH9GMaDfZVWAcLCYUxgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81206b85f6c2a753d3f8d27f9857e89e56789daa10ab2d97bb1138da2dfbbef7","last_reissued_at":"2026-05-18T04:37:21.523830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:21.523830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0496","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":"2026-05-18T04:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUL3J/sYLCrnp9Ztlk/1DUSn9Nf9wsor7FEx7UfMa58XpP6G5hrgIaW8aBPt/IOL7HbGzkb7XyEZ9SBjC7gICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:19:34.727914Z"},"content_sha256":"4a15cc8c528a4bf8963e51bbf5364e9fc4175df818cd0d1440ba59af8eb1fc4e","schema_version":"1.0","event_id":"sha256:4a15cc8c528a4bf8963e51bbf5364e9fc4175df818cd0d1440ba59af8eb1fc4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QEQGXBPWYKTVHU7Y2J7ZQV7ITZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lumpability Abstractions of Rule-based Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CE","authors_text":"Austria), France), Heinz Koeppl (EPFL, Jerome Feret (INRIA, Lausanne, Paris, Switzerland), Tatjana Petrov (EPFL, Technology, Thomas Henzinger (Institute of Science, Vienna","submitted_at":"2010-11-02T01:30:06Z","abstract_excerpt":"The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins.  To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology.  Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit.  Recently we proposed a quotie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0496","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":"2026-05-18T04:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDW1QBG7UX1+tvaZL9W/4GFioRoE1lMO1ST+g+gg8aeb1smUWW5Jgvjv9ETrU2stYYWJ0VsGUhx+jnm5J0LgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:19:34.728286Z"},"content_sha256":"bc6f131acfbf696e2a8854e926d903c7e7cbe6e350a9198d08c02fc9c1165b67","schema_version":"1.0","event_id":"sha256:bc6f131acfbf696e2a8854e926d903c7e7cbe6e350a9198d08c02fc9c1165b67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/bundle.json","state_url":"https://pith.science/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/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":"2026-06-11T12:19:34Z","links":{"resolver":"https://pith.science/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ","bundle":"https://pith.science/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/bundle.json","state":"https://pith.science/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEQGXBPWYKTVHU7Y2J7ZQV7ITZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QEQGXBPWYKTVHU7Y2J7ZQV7ITZ","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":"3e7a707362a5025aeeccd1405e264efac150c72ab5296ba76c20f1ae1a77f329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2010-11-02T01:30:06Z","title_canon_sha256":"1b6e183bd43459e320c6b34a74a71b4f3a040ea728c06ce022c42633425833e5"},"schema_version":"1.0","source":{"id":"1011.0496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0496","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0496v1","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0496","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"QEQGXBPWYKTV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QEQGXBPWYKTVHU7Y","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QEQGXBPW","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:bc6f131acfbf696e2a8854e926d903c7e7cbe6e350a9198d08c02fc9c1165b67","target":"graph","created_at":"2026-05-18T04:37:21Z","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":"The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins.  To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology.  Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit.  Recently we proposed a quotie","authors_text":"Austria), France), Heinz Koeppl (EPFL, Jerome Feret (INRIA, Lausanne, Paris, Switzerland), Tatjana Petrov (EPFL, Technology, Thomas Henzinger (Institute of Science, Vienna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2010-11-02T01:30:06Z","title":"Lumpability Abstractions of Rule-based Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0496","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":"sha256:4a15cc8c528a4bf8963e51bbf5364e9fc4175df818cd0d1440ba59af8eb1fc4e","target":"record","created_at":"2026-05-18T04:37:21Z","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":"3e7a707362a5025aeeccd1405e264efac150c72ab5296ba76c20f1ae1a77f329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2010-11-02T01:30:06Z","title_canon_sha256":"1b6e183bd43459e320c6b34a74a71b4f3a040ea728c06ce022c42633425833e5"},"schema_version":"1.0","source":{"id":"1011.0496","kind":"arxiv","version":1}},"canonical_sha256":"81206b85f6c2a753d3f8d27f9857e89e56789daa10ab2d97bb1138da2dfbbef7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81206b85f6c2a753d3f8d27f9857e89e56789daa10ab2d97bb1138da2dfbbef7","first_computed_at":"2026-05-18T04:37:21.523830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:21.523830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XtimV7JQIzJIl/0YMuAHZi/1xfgOLAmhj946tpazFEcqj0EHGA59iWFBkhUJiu/SZUH9GMaDfZVWAcLCYUxgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:21.524625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a15cc8c528a4bf8963e51bbf5364e9fc4175df818cd0d1440ba59af8eb1fc4e","sha256:bc6f131acfbf696e2a8854e926d903c7e7cbe6e350a9198d08c02fc9c1165b67"],"state_sha256":"aeb5cedf4e72dcabf439431e6e847dc669db8ad1b6b6ba2b2bf3dd9ae96e5d3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcD0ts4tJYIR4OyQPbYeTcyyubB0ZRe4dNIJMrewzvDRvMSYG7A8TJXWdFt7jf25GIPVh1IWAzLpSZfF8qBlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:19:34.730259Z","bundle_sha256":"fd1d551d8aa22ced9ffa13db0d0802f1d79644156cd6c0d4ab86a5411ffdaafd"}}