{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NWG3LK7GIEOJTPYOMZQEGUND3L","short_pith_number":"pith:NWG3LK7G","canonical_record":{"source":{"id":"1212.6098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-25T23:18:15Z","cross_cats_sorted":["cs.SY","math.PR"],"title_canon_sha256":"e7c59111dced1564aa3ca0b8ad1651fabf87de3381439020edec1cadc5360889","abstract_canon_sha256":"229a47feb1eff25b1f2a791af9442d308ec40f11ea550f53dfd8cead6b514781"},"schema_version":"1.0"},"canonical_sha256":"6d8db5abe6411c99bf0e66604351a3dae2cc9b8f6689cf39307abfc18724547e","source":{"kind":"arxiv","id":"1212.6098","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6098","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6098v1","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6098","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWG3LK7GIEOJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWG3LK7GIEOJTPYO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWG3LK7G","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NWG3LK7GIEOJTPYOMZQEGUND3L","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-25T23:18:15Z","cross_cats_sorted":["cs.SY","math.PR"],"title_canon_sha256":"e7c59111dced1564aa3ca0b8ad1651fabf87de3381439020edec1cadc5360889","abstract_canon_sha256":"229a47feb1eff25b1f2a791af9442d308ec40f11ea550f53dfd8cead6b514781"},"schema_version":"1.0"},"canonical_sha256":"6d8db5abe6411c99bf0e66604351a3dae2cc9b8f6689cf39307abfc18724547e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:42.779875Z","signature_b64":"C35q5giCZL0WpiH7wNDJHL7LCF9S6L3CydGgNzNLrjiHba37J889LIdH2HnSZc2NYdLWztWLEsszOGlnIXBrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d8db5abe6411c99bf0e66604351a3dae2cc9b8f6689cf39307abfc18724547e","last_reissued_at":"2026-05-18T03:37:42.779125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:42.779125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6098","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":"2026-05-18T03:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5nAMEJ8YWu3Rvbxj8+QSJpfRsZ7WT4s5d2woNFpykYi/8bipa+V+hq7vTw5Tw4dFLIe2Rqua7Bt4h257r3jhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:59:41.282153Z"},"content_sha256":"7ef54a7bb46a4c02363c5cf19cdcd785a1e82d44f459bf9b21e789a9df66f6c5","schema_version":"1.0","event_id":"sha256:7ef54a7bb46a4c02363c5cf19cdcd785a1e82d44f459bf9b21e789a9df66f6c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NWG3LK7GIEOJTPYOMZQEGUND3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of the mean cycle time in stochastic discrete event dynamic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.PR"],"primary_cat":"math.OC","authors_text":"Nikolai Krivulin","submitted_at":"2012-12-25T23:18:15Z","abstract_excerpt":"We consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by second-order random matrices that are assumed to be independent and identically distributed. The problem of interest is to evaluate the mean growth rate of state vector, which is also referred to as the mean cycle time of the system, under various assumptions on the matrix entries. We give an overview of early results including a solution for systems determ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6098","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":"2026-05-18T03:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v1Y2rWbTzbKLasItN/RhlqxgkESaG0VNAKrVcj+g70Ki3tWjOjmDyungPVmh4y9KEjNII5SaaeKr/zIGLpZdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T22:59:41.282771Z"},"content_sha256":"028ef5080ffd09d8c87084fc94123c497343d522e979988788653e0dab5f7cb6","schema_version":"1.0","event_id":"sha256:028ef5080ffd09d8c87084fc94123c497343d522e979988788653e0dab5f7cb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/bundle.json","state_url":"https://pith.science/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/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":"2026-07-03T22:59:41Z","links":{"resolver":"https://pith.science/pith/NWG3LK7GIEOJTPYOMZQEGUND3L","bundle":"https://pith.science/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/bundle.json","state":"https://pith.science/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWG3LK7GIEOJTPYOMZQEGUND3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NWG3LK7GIEOJTPYOMZQEGUND3L","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":"229a47feb1eff25b1f2a791af9442d308ec40f11ea550f53dfd8cead6b514781","cross_cats_sorted":["cs.SY","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-25T23:18:15Z","title_canon_sha256":"e7c59111dced1564aa3ca0b8ad1651fabf87de3381439020edec1cadc5360889"},"schema_version":"1.0","source":{"id":"1212.6098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6098","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6098v1","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6098","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWG3LK7GIEOJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWG3LK7GIEOJTPYO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWG3LK7G","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:028ef5080ffd09d8c87084fc94123c497343d522e979988788653e0dab5f7cb6","target":"graph","created_at":"2026-05-18T03:37:42Z","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 consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by second-order random matrices that are assumed to be independent and identically distributed. The problem of interest is to evaluate the mean growth rate of state vector, which is also referred to as the mean cycle time of the system, under various assumptions on the matrix entries. We give an overview of early results including a solution for systems determ","authors_text":"Nikolai Krivulin","cross_cats":["cs.SY","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-25T23:18:15Z","title":"Evaluation of the mean cycle time in stochastic discrete event dynamic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6098","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":"sha256:7ef54a7bb46a4c02363c5cf19cdcd785a1e82d44f459bf9b21e789a9df66f6c5","target":"record","created_at":"2026-05-18T03:37:42Z","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":"229a47feb1eff25b1f2a791af9442d308ec40f11ea550f53dfd8cead6b514781","cross_cats_sorted":["cs.SY","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-25T23:18:15Z","title_canon_sha256":"e7c59111dced1564aa3ca0b8ad1651fabf87de3381439020edec1cadc5360889"},"schema_version":"1.0","source":{"id":"1212.6098","kind":"arxiv","version":1}},"canonical_sha256":"6d8db5abe6411c99bf0e66604351a3dae2cc9b8f6689cf39307abfc18724547e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d8db5abe6411c99bf0e66604351a3dae2cc9b8f6689cf39307abfc18724547e","first_computed_at":"2026-05-18T03:37:42.779125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:42.779125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C35q5giCZL0WpiH7wNDJHL7LCF9S6L3CydGgNzNLrjiHba37J889LIdH2HnSZc2NYdLWztWLEsszOGlnIXBrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:42.779875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ef54a7bb46a4c02363c5cf19cdcd785a1e82d44f459bf9b21e789a9df66f6c5","sha256:028ef5080ffd09d8c87084fc94123c497343d522e979988788653e0dab5f7cb6"],"state_sha256":"095bd719dd222ddcdb7e00bd5c35fe27773452a189b23326fe25c6d0882efa7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYlPcm0dwf5jOoniuhHsvPG61EyF017kfOZINV6dkyup1zLxU5UfY2Ps9SF9hmvkCWJ5NQ3jFX8yVjNMUgSuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T22:59:41.286029Z","bundle_sha256":"05016af870838a405d110e331b9bc0e4004421990bdbdc2bde52f7c79d23ac73"}}