{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4V5YZFRJBOJ3BRPYAL4425YKQF","short_pith_number":"pith:4V5YZFRJ","canonical_record":{"source":{"id":"1905.05537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-14T12:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"9a194bffb402dfd52943b962800d9be2dfe2f1fd33a633aceb62fa953f15c4ec","abstract_canon_sha256":"cf7966e0c7de15419c14758a9704bb4cda13d07b8676ad56a409622b1796ae0a"},"schema_version":"1.0"},"canonical_sha256":"e57b8c96290b93b0c5f802f9cd770a8171127ae8a670fb32eefe13d55221fc2a","source":{"kind":"arxiv","id":"1905.05537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05537","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05537v1","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05537","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"4V5YZFRJBOJ3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4V5YZFRJBOJ3BRPY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4V5YZFRJ","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4V5YZFRJBOJ3BRPYAL4425YKQF","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-14T12:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"9a194bffb402dfd52943b962800d9be2dfe2f1fd33a633aceb62fa953f15c4ec","abstract_canon_sha256":"cf7966e0c7de15419c14758a9704bb4cda13d07b8676ad56a409622b1796ae0a"},"schema_version":"1.0"},"canonical_sha256":"e57b8c96290b93b0c5f802f9cd770a8171127ae8a670fb32eefe13d55221fc2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:16.205832Z","signature_b64":"tT18lghMd1Kc7xL12C/MImEkxbobSJY5FKwZyN38Nr46mZ1I1NHSQWrHFnuQG/KdVi8t/+8/6OCNDu2Dvj0WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e57b8c96290b93b0c5f802f9cd770a8171127ae8a670fb32eefe13d55221fc2a","last_reissued_at":"2026-05-17T23:46:16.205110Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:16.205110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05537","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":"2026-05-17T23:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E8mfkOY6TTjMSqiPmKU546zDwvtw6BJo05HombKY8xhSUtIwqnaEufZQd84HDJyMFrKFz8A0RMIgYonv0VXsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:56:22.359236Z"},"content_sha256":"22d170b4ee6c8b8feb3831e9f295fc6aadc6ec8fe58788b57826c65026bceb96","schema_version":"1.0","event_id":"sha256:22d170b4ee6c8b8feb3831e9f295fc6aadc6ec8fe58788b57826c65026bceb96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4V5YZFRJBOJ3BRPYAL4425YKQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-Run Average Behavior of Vector Addition Systems with States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Jan Otop, Krishnendu Chatterjee, Thomas A. Henzinger","submitted_at":"2019-05-14T12:05:54Z","abstract_excerpt":"A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05537","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":"2026-05-17T23:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSFcbG37S2IO8X+JuVeReMJE10pY/jmCGUT/9xWmi+/y+7Mt/ICVS6NbKiIEzmox1qlF90C4OAL1AHbuYMlKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:56:22.359967Z"},"content_sha256":"d8464be33dcf4e389bd52028260e588cabdacc3778c498452539c3a74237f533","schema_version":"1.0","event_id":"sha256:d8464be33dcf4e389bd52028260e588cabdacc3778c498452539c3a74237f533"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/bundle.json","state_url":"https://pith.science/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/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":"2026-05-26T00:56:22Z","links":{"resolver":"https://pith.science/pith/4V5YZFRJBOJ3BRPYAL4425YKQF","bundle":"https://pith.science/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/bundle.json","state":"https://pith.science/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4V5YZFRJBOJ3BRPYAL4425YKQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4V5YZFRJBOJ3BRPYAL4425YKQF","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":"cf7966e0c7de15419c14758a9704bb4cda13d07b8676ad56a409622b1796ae0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-14T12:05:54Z","title_canon_sha256":"9a194bffb402dfd52943b962800d9be2dfe2f1fd33a633aceb62fa953f15c4ec"},"schema_version":"1.0","source":{"id":"1905.05537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05537","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05537v1","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05537","created_at":"2026-05-17T23:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"4V5YZFRJBOJ3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4V5YZFRJBOJ3BRPY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4V5YZFRJ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:d8464be33dcf4e389bd52028260e588cabdacc3778c498452539c3a74237f533","target":"graph","created_at":"2026-05-17T23:46:16Z","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":"A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all","authors_text":"Jan Otop, Krishnendu Chatterjee, Thomas A. Henzinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-14T12:05:54Z","title":"Long-Run Average Behavior of Vector Addition Systems with States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05537","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":"sha256:22d170b4ee6c8b8feb3831e9f295fc6aadc6ec8fe58788b57826c65026bceb96","target":"record","created_at":"2026-05-17T23:46:16Z","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":"cf7966e0c7de15419c14758a9704bb4cda13d07b8676ad56a409622b1796ae0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2019-05-14T12:05:54Z","title_canon_sha256":"9a194bffb402dfd52943b962800d9be2dfe2f1fd33a633aceb62fa953f15c4ec"},"schema_version":"1.0","source":{"id":"1905.05537","kind":"arxiv","version":1}},"canonical_sha256":"e57b8c96290b93b0c5f802f9cd770a8171127ae8a670fb32eefe13d55221fc2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e57b8c96290b93b0c5f802f9cd770a8171127ae8a670fb32eefe13d55221fc2a","first_computed_at":"2026-05-17T23:46:16.205110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:16.205110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tT18lghMd1Kc7xL12C/MImEkxbobSJY5FKwZyN38Nr46mZ1I1NHSQWrHFnuQG/KdVi8t/+8/6OCNDu2Dvj0WCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:16.205832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d170b4ee6c8b8feb3831e9f295fc6aadc6ec8fe58788b57826c65026bceb96","sha256:d8464be33dcf4e389bd52028260e588cabdacc3778c498452539c3a74237f533"],"state_sha256":"23cdd26866ac6d724d37e240cbfe9e754aad16dd57992fe541b22cf181a90307"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nziSMO2jTkmzlJ2fCze4zSnxshCxQsoGzw6gxcA+H+ILlGJJ0walMbHBD7KkcBSXd1lb9JBXqSa3a2E+y2ylCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:56:22.363705Z","bundle_sha256":"96b2884fa9705575f3d066921ef8df3640260eebfdedff3d173b135d07352642"}}