{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:37XIGL2J5TUIXFDPDC7IFQLLRD","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":"ddd50b138e12523cbe4a30d919e0576148cab5ac7db959ef7c01e025e4ea8b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-13T14:32:45Z","title_canon_sha256":"4d1f67db8842cc1008cb7f675e1d78823cb6709127298225f5df46e8fad6f871"},"schema_version":"1.0","source":{"id":"1311.3143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3143","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3143v1","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3143","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"37XIGL2J5TUI","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"37XIGL2J5TUIXFDP","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"37XIGL2J","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:eae27ec0dcc81c7707e5a431c8e5d8401cae0715e9070f1d9f322d4bb0d9a554","target":"graph","created_at":"2026-05-18T03:07:12Z","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":"We study the application of the novel tensor formats (TT, QTT, QTT-Tucker) to the solution of $d$-dimensional chemical master equations, applied mostly to gene regulating networks (signaling cascades, toggle switches, phage-$\\lambda$). For some important cases, e.g. signaling cascade models, we prove good separability properties of the system operator. The Quantized tensor representations (QTT, QTT-Tucker) are employed in both state space and time, and the global state-time $(d+1)$-dimensional system is solved in the structured form by using the ALS-type iteration. This approach leads to the l","authors_text":"Boris Khoromskij, Sergey Dolgov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-13T14:32:45Z","title":"Simultaneous state-time approximation of the chemical master equation using tensor product formats"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3143","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":"sha256:8b360c016bb973964ac6d7091e1fda4d65fe7e4f335a7ad65e690f09f385cbe1","target":"record","created_at":"2026-05-18T03:07:12Z","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":"ddd50b138e12523cbe4a30d919e0576148cab5ac7db959ef7c01e025e4ea8b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-13T14:32:45Z","title_canon_sha256":"4d1f67db8842cc1008cb7f675e1d78823cb6709127298225f5df46e8fad6f871"},"schema_version":"1.0","source":{"id":"1311.3143","kind":"arxiv","version":1}},"canonical_sha256":"dfee832f49ece88b946f18be82c16b88f41740eaa2940af674078b2e2605999e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfee832f49ece88b946f18be82c16b88f41740eaa2940af674078b2e2605999e","first_computed_at":"2026-05-18T03:07:12.974496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:12.974496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rDtBe4jTLiYzsndDEeHVl6FPkj+O0CT2YxuePuHgpKWEjauPQXn8v/nm5qtkT5r0ATo3P/86s/8yhkjGO/4+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:12.975195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b360c016bb973964ac6d7091e1fda4d65fe7e4f335a7ad65e690f09f385cbe1","sha256:eae27ec0dcc81c7707e5a431c8e5d8401cae0715e9070f1d9f322d4bb0d9a554"],"state_sha256":"af97f6d1bb0136973c1bbfadd035188e57fb3b71518f1544717799cb6adfc29b"}