{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7FON3YY3ARA335KR6TAOP2QXIV","short_pith_number":"pith:7FON3YY3","canonical_record":{"source":{"id":"1307.4922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-07-18T12:30:48Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"842b16b22c65b72602e0841ab7d8984ba614c5dc21c4d649aff138f0bc728dd3","abstract_canon_sha256":"a87a1a5ce002fd94ba74fe74ab9dc68092aa0446b542efc57742f2af930aecf3"},"schema_version":"1.0"},"canonical_sha256":"f95cdde31b0441bdf551f4c0e7ea174572658498b6add2cce9532d5e7c9dc041","source":{"kind":"arxiv","id":"1307.4922","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4922","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4922v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4922","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"7FON3YY3ARA3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7FON3YY3ARA335KR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7FON3YY3","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7FON3YY3ARA335KR6TAOP2QXIV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-07-18T12:30:48Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"842b16b22c65b72602e0841ab7d8984ba614c5dc21c4d649aff138f0bc728dd3","abstract_canon_sha256":"a87a1a5ce002fd94ba74fe74ab9dc68092aa0446b542efc57742f2af930aecf3"},"schema_version":"1.0"},"canonical_sha256":"f95cdde31b0441bdf551f4c0e7ea174572658498b6add2cce9532d5e7c9dc041","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:33.784194Z","signature_b64":"UOL/Fuorvnp/z5lC5zCztErCnxOtFv8e3b3aOdC0EOlwUtugmLTgiG7JpA24Xr0HOWcAoRrZB+M7WWGnNym3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f95cdde31b0441bdf551f4c0e7ea174572658498b6add2cce9532d5e7c9dc041","last_reissued_at":"2026-05-18T03:15:33.783647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:33.783647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4922","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":"2026-05-18T03:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OB1tFa58A6TgrD2ltLCnteGk+mKZYKWR0VztT3bpZy1oPcRyDzLo2LO52DFjNFV0crRH5sxc6vj7Qaz3yFK2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:07:07.406201Z"},"content_sha256":"6238ba36b4ba96a840e88690a12b65ea2b74c26543b88b10fe87c6f7a10ace6c","schema_version":"1.0","event_id":"sha256:6238ba36b4ba96a840e88690a12b65ea2b74c26543b88b10fe87c6f7a10ace6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7FON3YY3ARA335KR6TAOP2QXIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theoretical estimation of metabolic network robustness against multiple reaction knockouts using branching process approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"q-bio.MN","authors_text":"Kazuhiro Takemoto, Takeyuki Tamura, Tatsuya Akutsu","submitted_at":"2013-07-18T12:30:48Z","abstract_excerpt":"In our previous study, we showed that the branching process approximation is useful for estimating metabolic robustness, measured using the impact degree. By applying a theory of random family forests, we here extend the branching process approximation to consider the knockout of {\\it multiple} reactions, inspired by the importance of multiple knockouts reported by recent computational and experimental studies. In addition, we propose a better definition of the number of offspring of each reaction node, allowing for an improved estimation of the impact degree distribution obtained as a result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4922","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":"2026-05-18T03:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KAx5usJUrxalxIjjpKiMgqInJysffrEOU4HONxA+RAOjLQCy+tH06iDsHibDFkqx0RMtXYa2NnZ21NsqywPcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:07:07.406615Z"},"content_sha256":"8c7a73a1809264a6171155b7d1c58504387ee44459748357a6245bc3438405f6","schema_version":"1.0","event_id":"sha256:8c7a73a1809264a6171155b7d1c58504387ee44459748357a6245bc3438405f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FON3YY3ARA335KR6TAOP2QXIV/bundle.json","state_url":"https://pith.science/pith/7FON3YY3ARA335KR6TAOP2QXIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FON3YY3ARA335KR6TAOP2QXIV/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":"2026-05-25T15:07:07Z","links":{"resolver":"https://pith.science/pith/7FON3YY3ARA335KR6TAOP2QXIV","bundle":"https://pith.science/pith/7FON3YY3ARA335KR6TAOP2QXIV/bundle.json","state":"https://pith.science/pith/7FON3YY3ARA335KR6TAOP2QXIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FON3YY3ARA335KR6TAOP2QXIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7FON3YY3ARA335KR6TAOP2QXIV","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":"a87a1a5ce002fd94ba74fe74ab9dc68092aa0446b542efc57742f2af930aecf3","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-07-18T12:30:48Z","title_canon_sha256":"842b16b22c65b72602e0841ab7d8984ba614c5dc21c4d649aff138f0bc728dd3"},"schema_version":"1.0","source":{"id":"1307.4922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4922","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4922v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4922","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"7FON3YY3ARA3","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7FON3YY3ARA335KR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7FON3YY3","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8c7a73a1809264a6171155b7d1c58504387ee44459748357a6245bc3438405f6","target":"graph","created_at":"2026-05-18T03:15:33Z","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":"In our previous study, we showed that the branching process approximation is useful for estimating metabolic robustness, measured using the impact degree. By applying a theory of random family forests, we here extend the branching process approximation to consider the knockout of {\\it multiple} reactions, inspired by the importance of multiple knockouts reported by recent computational and experimental studies. In addition, we propose a better definition of the number of offspring of each reaction node, allowing for an improved estimation of the impact degree distribution obtained as a result ","authors_text":"Kazuhiro Takemoto, Takeyuki Tamura, Tatsuya Akutsu","cross_cats":["physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-07-18T12:30:48Z","title":"Theoretical estimation of metabolic network robustness against multiple reaction knockouts using branching process approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4922","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":"sha256:6238ba36b4ba96a840e88690a12b65ea2b74c26543b88b10fe87c6f7a10ace6c","target":"record","created_at":"2026-05-18T03:15:33Z","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":"a87a1a5ce002fd94ba74fe74ab9dc68092aa0446b542efc57742f2af930aecf3","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2013-07-18T12:30:48Z","title_canon_sha256":"842b16b22c65b72602e0841ab7d8984ba614c5dc21c4d649aff138f0bc728dd3"},"schema_version":"1.0","source":{"id":"1307.4922","kind":"arxiv","version":1}},"canonical_sha256":"f95cdde31b0441bdf551f4c0e7ea174572658498b6add2cce9532d5e7c9dc041","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f95cdde31b0441bdf551f4c0e7ea174572658498b6add2cce9532d5e7c9dc041","first_computed_at":"2026-05-18T03:15:33.783647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:33.783647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOL/Fuorvnp/z5lC5zCztErCnxOtFv8e3b3aOdC0EOlwUtugmLTgiG7JpA24Xr0HOWcAoRrZB+M7WWGnNym3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:33.784194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6238ba36b4ba96a840e88690a12b65ea2b74c26543b88b10fe87c6f7a10ace6c","sha256:8c7a73a1809264a6171155b7d1c58504387ee44459748357a6245bc3438405f6"],"state_sha256":"53d84bbf8cd4801d024a5aa252363e6a52ee8ec4daa9830856350313b5bfc420"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWMaBi5zT1tYIkBHS1Wi73TvPqFbhrn9cWhs8Zsew91zbcbjN6ECovK/OXYmbRu3T/wwcAcNiAzt2RWxcwkiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:07:07.410049Z","bundle_sha256":"8993aa4e2a1a915fae77f54bd435a231d4b7e9102c7dbeb232e5b498119c8a3d"}}