{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BQDDXOOQONGZOHFDY5FG6ZAJZB","short_pith_number":"pith:BQDDXOOQ","canonical_record":{"source":{"id":"1304.5169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-18T15:58:28Z","cross_cats_sorted":[],"title_canon_sha256":"e826f54e6f71dd585d54ce79853a7993062c3386ddcf33ba40229cdcc7da2475","abstract_canon_sha256":"f4caf62e2f466b2ab962138e832c175d0ef9f0ce1fb58ed7690b2e390be6e404"},"schema_version":"1.0"},"canonical_sha256":"0c063bb9d0734d971ca3c74a6f6409c877946ba5e6a45eb54e1e0ca6fa607f33","source":{"kind":"arxiv","id":"1304.5169","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5169","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5169v2","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5169","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"BQDDXOOQONGZ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQDDXOOQONGZOHFD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQDDXOOQ","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BQDDXOOQONGZOHFDY5FG6ZAJZB","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-18T15:58:28Z","cross_cats_sorted":[],"title_canon_sha256":"e826f54e6f71dd585d54ce79853a7993062c3386ddcf33ba40229cdcc7da2475","abstract_canon_sha256":"f4caf62e2f466b2ab962138e832c175d0ef9f0ce1fb58ed7690b2e390be6e404"},"schema_version":"1.0"},"canonical_sha256":"0c063bb9d0734d971ca3c74a6f6409c877946ba5e6a45eb54e1e0ca6fa607f33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.067066Z","signature_b64":"8+C06dfvsdt3TrOhgvUkXKpYkd7YDJGUDAA+lk0bSiOOItuadZhf1FPucUXhN/gvKs7LOi+bwdMmUfMCebiFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c063bb9d0734d971ca3c74a6f6409c877946ba5e6a45eb54e1e0ca6fa607f33","last_reissued_at":"2026-05-18T02:28:21.066447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.066447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5169","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8DNJ8lQDbI2vm5cbu3OwxkxO0Vb4VJkvUIyxqh7PWA5/4T2SxwymUcyr5sXcb0fz8aypE/RvVA7rX53UqzpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:28:36.254182Z"},"content_sha256":"bebee7c10049a11a0dbe5cffcbc5ecf9a17319ffd3fadc3051e4539647d9584e","schema_version":"1.0","event_id":"sha256:bebee7c10049a11a0dbe5cffcbc5ecf9a17319ffd3fadc3051e4539647d9584e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BQDDXOOQONGZOHFDY5FG6ZAJZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moment growth bounds on continuous time Markov processes on non-negative integer lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Muruhan Rathinam","submitted_at":"2013-04-18T15:58:28Z","abstract_excerpt":"We consider Markov processes in continuous time with state space $\\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\\|X(t)\\|^r)$ of all orders $r \\in \\nat$ for all $t \\geq 0$. The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied have finitely many state independent jumpsize vectors $\\nu_1,\\dots,\\nu_M$. This class of processes arise naturally in many applications such as stochastic models of chemical kinetics, population dynamics and queueing theory for example. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5169","kind":"arxiv","version":2},"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":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwCaE05zrYJEcf6xWy6djHqu5Pa/ZCpjyfBSV0VPCE6oCrg/rQSU+QixCFAkJAULD02phJ42gw1YQ8Wzjb5cDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:28:36.254855Z"},"content_sha256":"399c32cd8a85d0e4ca6d5853c8edce7f72075656e7ea81f185fe007b179ad2eb","schema_version":"1.0","event_id":"sha256:399c32cd8a85d0e4ca6d5853c8edce7f72075656e7ea81f185fe007b179ad2eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/bundle.json","state_url":"https://pith.science/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/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":"2026-05-28T23:28:36Z","links":{"resolver":"https://pith.science/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB","bundle":"https://pith.science/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/bundle.json","state":"https://pith.science/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQDDXOOQONGZOHFDY5FG6ZAJZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BQDDXOOQONGZOHFDY5FG6ZAJZB","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":"f4caf62e2f466b2ab962138e832c175d0ef9f0ce1fb58ed7690b2e390be6e404","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-18T15:58:28Z","title_canon_sha256":"e826f54e6f71dd585d54ce79853a7993062c3386ddcf33ba40229cdcc7da2475"},"schema_version":"1.0","source":{"id":"1304.5169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5169","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5169v2","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5169","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"BQDDXOOQONGZ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQDDXOOQONGZOHFD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQDDXOOQ","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:399c32cd8a85d0e4ca6d5853c8edce7f72075656e7ea81f185fe007b179ad2eb","target":"graph","created_at":"2026-05-18T02:28:21Z","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":"We consider Markov processes in continuous time with state space $\\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\\|X(t)\\|^r)$ of all orders $r \\in \\nat$ for all $t \\geq 0$. The sufficient conditions also guarantee an exponential in time growth bound for the moments. The class of processes studied have finitely many state independent jumpsize vectors $\\nu_1,\\dots,\\nu_M$. This class of processes arise naturally in many applications such as stochastic models of chemical kinetics, population dynamics and queueing theory for example. We ","authors_text":"Muruhan Rathinam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-18T15:58:28Z","title":"Moment growth bounds on continuous time Markov processes on non-negative integer lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5169","kind":"arxiv","version":2},"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:bebee7c10049a11a0dbe5cffcbc5ecf9a17319ffd3fadc3051e4539647d9584e","target":"record","created_at":"2026-05-18T02:28:21Z","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":"f4caf62e2f466b2ab962138e832c175d0ef9f0ce1fb58ed7690b2e390be6e404","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-18T15:58:28Z","title_canon_sha256":"e826f54e6f71dd585d54ce79853a7993062c3386ddcf33ba40229cdcc7da2475"},"schema_version":"1.0","source":{"id":"1304.5169","kind":"arxiv","version":2}},"canonical_sha256":"0c063bb9d0734d971ca3c74a6f6409c877946ba5e6a45eb54e1e0ca6fa607f33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c063bb9d0734d971ca3c74a6f6409c877946ba5e6a45eb54e1e0ca6fa607f33","first_computed_at":"2026-05-18T02:28:21.066447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:21.066447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+C06dfvsdt3TrOhgvUkXKpYkd7YDJGUDAA+lk0bSiOOItuadZhf1FPucUXhN/gvKs7LOi+bwdMmUfMCebiFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:21.067066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bebee7c10049a11a0dbe5cffcbc5ecf9a17319ffd3fadc3051e4539647d9584e","sha256:399c32cd8a85d0e4ca6d5853c8edce7f72075656e7ea81f185fe007b179ad2eb"],"state_sha256":"a90f7f57e66a5e861da40af724732bccf3a0a42563cdc12f56503b66b0fc863f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sepuNj3q22upd2Iz7YCr04OMqtOUkZk/f3s5PBJwG4J+aaiCdkWdRRIoth093UFAouhFQ3ZHnOWf+osuUVSECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:28:36.258259Z","bundle_sha256":"7690b1eb1cb0c5d1a30b1d08ba525ef33676730a0cc304a6e10d5e3e53ff451f"}}