{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4HQIIPRVMFKQFYNYFEAII7NSEZ","short_pith_number":"pith:4HQIIPRV","schema_version":"1.0","canonical_sha256":"e1e0843e35615502e1b82900847db2266754fa6603398e190bd45af0ad24e2d3","source":{"kind":"arxiv","id":"2607.07283","version":1},"attestation_state":"computed","paper":{"title":"Multi-time Markov renewal chains and stratified renewal theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Leonidas Kordalis, Samis Trevezas","submitted_at":"2026-07-08T11:21:16Z","abstract_excerpt":"We develop a discrete Markov renewal theory on a standard Borel state space, with vector-valued sojourn times and lower-rectangle observation on $\\N^d$. The Markov renewal potential is a kernel-valued convolution resolvent and yields unified representations for semi-Markov transitions, first-passage laws, occupation measures and rewards. The semi-Markov field observed on the partially ordered lattice is generally not Markov. We identify its canonical Markovian augmentation through the backward recurrence vector and give a lumpability criterion for the exceptional cases in which the augmentatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.07283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-08T11:21:16Z","cross_cats_sorted":[],"title_canon_sha256":"7effe7efcae17e9b50d5d4c5c04c7a1f61c3b89b00b14d05f7bc312c30ccdb19","abstract_canon_sha256":"b1a70d1efb5484755aa9d753b84e0e8a3a20753ae971e6897bffe8ee1485a659"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:19.857332Z","signature_b64":"6WY39uYGBjMHihow+mYAHmrnHHNe760q06h9csNZc7s3N8PyJiNvX0siQRK9pAgiu3Jf2MDLb8U9Pm6r2SH3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1e0843e35615502e1b82900847db2266754fa6603398e190bd45af0ad24e2d3","last_reissued_at":"2026-07-09T01:20:19.856927Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:19.856927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-time Markov renewal chains and stratified renewal theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Leonidas Kordalis, Samis Trevezas","submitted_at":"2026-07-08T11:21:16Z","abstract_excerpt":"We develop a discrete Markov renewal theory on a standard Borel state space, with vector-valued sojourn times and lower-rectangle observation on $\\N^d$. The Markov renewal potential is a kernel-valued convolution resolvent and yields unified representations for semi-Markov transitions, first-passage laws, occupation measures and rewards. The semi-Markov field observed on the partially ordered lattice is generally not Markov. We identify its canonical Markovian augmentation through the backward recurrence vector and give a lumpability criterion for the exceptional cases in which the augmentatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07283","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07283/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.07283","created_at":"2026-07-09T01:20:19.856987+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07283v1","created_at":"2026-07-09T01:20:19.856987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07283","created_at":"2026-07-09T01:20:19.856987+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HQIIPRVMFKQ","created_at":"2026-07-09T01:20:19.856987+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HQIIPRVMFKQFYNY","created_at":"2026-07-09T01:20:19.856987+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HQIIPRV","created_at":"2026-07-09T01:20:19.856987+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ","json":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ.json","graph_json":"https://pith.science/api/pith-number/4HQIIPRVMFKQFYNYFEAII7NSEZ/graph.json","events_json":"https://pith.science/api/pith-number/4HQIIPRVMFKQFYNYFEAII7NSEZ/events.json","paper":"https://pith.science/paper/4HQIIPRV"},"agent_actions":{"view_html":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ","download_json":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ.json","view_paper":"https://pith.science/paper/4HQIIPRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07283&json=true","fetch_graph":"https://pith.science/api/pith-number/4HQIIPRVMFKQFYNYFEAII7NSEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4HQIIPRVMFKQFYNYFEAII7NSEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ/action/storage_attestation","attest_author":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ/action/author_attestation","sign_citation":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ/action/citation_signature","submit_replication":"https://pith.science/pith/4HQIIPRVMFKQFYNYFEAII7NSEZ/action/replication_record"}},"created_at":"2026-07-09T01:20:19.856987+00:00","updated_at":"2026-07-09T01:20:19.856987+00:00"}