{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MRTEDI44I2LLTGWD3G5V52SWJT","short_pith_number":"pith:MRTEDI44","schema_version":"1.0","canonical_sha256":"646641a39c4696b99ac3d9bb5eea564cecbf6509923bf92455500358b3a21682","source":{"kind":"arxiv","id":"1505.02655","version":2},"attestation_state":"computed","paper":{"title":"Long-Run Average Behaviour of Probabilistic Vector Addition Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Antonin Kucera, Petr Novotny, Stefan Kiefer, Tomas Brazdil","submitted_at":"2015-05-11T14:58:39Z","abstract_excerpt":"We study the pattern frequency vector for runs in probabilistic Vector Addition Systems with States (pVASS). Intuitively, each configuration of a given pVASS is assigned one of finitely many patterns, and every run can thus be seen as an infinite sequence of these patterns. The pattern frequency vector assigns to each run the limit of pattern frequencies computed for longer and longer prefixes of the run. If the limit does not exist, then the vector is undefined. We show that for one-counter pVASS, the pattern frequency vector is defined and takes only finitely many values for almost all runs."},"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":"1505.02655","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-05-11T14:58:39Z","cross_cats_sorted":[],"title_canon_sha256":"1649a79edfacab0770ed30d8d05a95a882c091c8eabbfe5fdf3617ce77f7c5cb","abstract_canon_sha256":"98fa444a03bbdbd39de271def8558ee590f09122790a06f0e98048abcacc6634"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:47.480765Z","signature_b64":"bX21B9izbvV6bPNp8qGlzUxbbpFS6CcvWu+HDVj+7m8uFcju51ZjKaosL9NaXB2gpAG9lZ00G5lpoUwdbMZXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"646641a39c4696b99ac3d9bb5eea564cecbf6509923bf92455500358b3a21682","last_reissued_at":"2026-05-18T01:42:47.480120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:47.480120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-Run Average Behaviour of Probabilistic Vector Addition Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Antonin Kucera, Petr Novotny, Stefan Kiefer, Tomas Brazdil","submitted_at":"2015-05-11T14:58:39Z","abstract_excerpt":"We study the pattern frequency vector for runs in probabilistic Vector Addition Systems with States (pVASS). Intuitively, each configuration of a given pVASS is assigned one of finitely many patterns, and every run can thus be seen as an infinite sequence of these patterns. The pattern frequency vector assigns to each run the limit of pattern frequencies computed for longer and longer prefixes of the run. If the limit does not exist, then the vector is undefined. We show that for one-counter pVASS, the pattern frequency vector is defined and takes only finitely many values for almost all runs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02655","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.02655","created_at":"2026-05-18T01:42:47.480231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.02655v2","created_at":"2026-05-18T01:42:47.480231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02655","created_at":"2026-05-18T01:42:47.480231+00:00"},{"alias_kind":"pith_short_12","alias_value":"MRTEDI44I2LL","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MRTEDI44I2LLTGWD","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MRTEDI44","created_at":"2026-05-18T12:29:32.376354+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/MRTEDI44I2LLTGWD3G5V52SWJT","json":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT.json","graph_json":"https://pith.science/api/pith-number/MRTEDI44I2LLTGWD3G5V52SWJT/graph.json","events_json":"https://pith.science/api/pith-number/MRTEDI44I2LLTGWD3G5V52SWJT/events.json","paper":"https://pith.science/paper/MRTEDI44"},"agent_actions":{"view_html":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT","download_json":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT.json","view_paper":"https://pith.science/paper/MRTEDI44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.02655&json=true","fetch_graph":"https://pith.science/api/pith-number/MRTEDI44I2LLTGWD3G5V52SWJT/graph.json","fetch_events":"https://pith.science/api/pith-number/MRTEDI44I2LLTGWD3G5V52SWJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT/action/storage_attestation","attest_author":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT/action/author_attestation","sign_citation":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT/action/citation_signature","submit_replication":"https://pith.science/pith/MRTEDI44I2LLTGWD3G5V52SWJT/action/replication_record"}},"created_at":"2026-05-18T01:42:47.480231+00:00","updated_at":"2026-05-18T01:42:47.480231+00:00"}