{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FWOMUNLZIXB66VY2C37GJ6ZP5P","short_pith_number":"pith:FWOMUNLZ","canonical_record":{"source":{"id":"1610.01397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-10-05T13:06:02Z","cross_cats_sorted":[],"title_canon_sha256":"2baa15c37a079c206036b384dddb5ecd0564b7e9c49f02179046b29e1e2aea09","abstract_canon_sha256":"5f20d28fad0f8a12f734ad7e45747820ff49213afbe634f42e958ead4c0670ab"},"schema_version":"1.0"},"canonical_sha256":"2d9cca357945c3ef571a16fe64fb2febd2566bae06e8379f6ea9306d9c61e7f1","source":{"kind":"arxiv","id":"1610.01397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01397","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01397v1","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01397","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"FWOMUNLZIXB6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FWOMUNLZIXB66VY2","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FWOMUNLZ","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FWOMUNLZIXB66VY2C37GJ6ZP5P","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-10-05T13:06:02Z","cross_cats_sorted":[],"title_canon_sha256":"2baa15c37a079c206036b384dddb5ecd0564b7e9c49f02179046b29e1e2aea09","abstract_canon_sha256":"5f20d28fad0f8a12f734ad7e45747820ff49213afbe634f42e958ead4c0670ab"},"schema_version":"1.0"},"canonical_sha256":"2d9cca357945c3ef571a16fe64fb2febd2566bae06e8379f6ea9306d9c61e7f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:10.955713Z","signature_b64":"znM9RSeCK9ceoWePrhA08NH4rwy27Xo6pB6avZEI3odQ4q5r1wM01hRcNvy6/CwFb9A3cy0Flz+ilO6TKPjUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d9cca357945c3ef571a16fe64fb2febd2566bae06e8379f6ea9306d9c61e7f1","last_reissued_at":"2026-05-18T01:03:10.955117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:10.955117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01397","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":"2026-05-18T01:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ypccUz3N/J4rFureK2D0BzzlgNZhTWDm8iiHDaQf7Dv1IDu1I6gcbBjESu/s6povYx3gApEuS+K0ab9TmE4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:05:07.660518Z"},"content_sha256":"4bae4c7bb1357c850d8a089b27d664960aeba47fc184d58af74fcab238f18882","schema_version":"1.0","event_id":"sha256:4bae4c7bb1357c850d8a089b27d664960aeba47fc184d58af74fcab238f18882"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FWOMUNLZIXB66VY2C37GJ6ZP5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decision problems on unary probabilistic and quantum automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Abuzer Yakary{\\i}lmaz, Mika Hirvensalo","submitted_at":"2016-10-05T13:06:02Z","abstract_excerpt":"It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems. We also introduce the concept of linear recurrence automata in order to show the connection naturally. Then, we also give possible generalizations of linear recurrence relations and automata on vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01397","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":"2026-05-18T01:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Is0IlBHgZVYr0nIRTFUezt8o5yYX7g/EF9ioV0ENqrNNK7925PauopXrynAF4PvJBrDLJ+Yh42eVc9PCT06lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:05:07.660855Z"},"content_sha256":"9582d2a09311b2f5902cbd39bf933d2ae94be01219e4b31632f39c4fb1ab279e","schema_version":"1.0","event_id":"sha256:9582d2a09311b2f5902cbd39bf933d2ae94be01219e4b31632f39c4fb1ab279e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/bundle.json","state_url":"https://pith.science/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/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":"2026-06-24T04:05:07Z","links":{"resolver":"https://pith.science/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P","bundle":"https://pith.science/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/bundle.json","state":"https://pith.science/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWOMUNLZIXB66VY2C37GJ6ZP5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FWOMUNLZIXB66VY2C37GJ6ZP5P","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":"5f20d28fad0f8a12f734ad7e45747820ff49213afbe634f42e958ead4c0670ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-10-05T13:06:02Z","title_canon_sha256":"2baa15c37a079c206036b384dddb5ecd0564b7e9c49f02179046b29e1e2aea09"},"schema_version":"1.0","source":{"id":"1610.01397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01397","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01397v1","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01397","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"FWOMUNLZIXB6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FWOMUNLZIXB66VY2","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FWOMUNLZ","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:9582d2a09311b2f5902cbd39bf933d2ae94be01219e4b31632f39c4fb1ab279e","target":"graph","created_at":"2026-05-18T01:03:10Z","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":"It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems. We also introduce the concept of linear recurrence automata in order to show the connection naturally. Then, we also give possible generalizations of linear recurrence relations and automata on vectors.","authors_text":"Abuzer Yakary{\\i}lmaz, Mika Hirvensalo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-10-05T13:06:02Z","title":"Decision problems on unary probabilistic and quantum automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01397","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":"sha256:4bae4c7bb1357c850d8a089b27d664960aeba47fc184d58af74fcab238f18882","target":"record","created_at":"2026-05-18T01:03:10Z","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":"5f20d28fad0f8a12f734ad7e45747820ff49213afbe634f42e958ead4c0670ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-10-05T13:06:02Z","title_canon_sha256":"2baa15c37a079c206036b384dddb5ecd0564b7e9c49f02179046b29e1e2aea09"},"schema_version":"1.0","source":{"id":"1610.01397","kind":"arxiv","version":1}},"canonical_sha256":"2d9cca357945c3ef571a16fe64fb2febd2566bae06e8379f6ea9306d9c61e7f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d9cca357945c3ef571a16fe64fb2febd2566bae06e8379f6ea9306d9c61e7f1","first_computed_at":"2026-05-18T01:03:10.955117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:10.955117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"znM9RSeCK9ceoWePrhA08NH4rwy27Xo6pB6avZEI3odQ4q5r1wM01hRcNvy6/CwFb9A3cy0Flz+ilO6TKPjUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:10.955713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bae4c7bb1357c850d8a089b27d664960aeba47fc184d58af74fcab238f18882","sha256:9582d2a09311b2f5902cbd39bf933d2ae94be01219e4b31632f39c4fb1ab279e"],"state_sha256":"934b50576923a3c38109224c0ab3ccb41415ce15ab340ebca006dc1425d26463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d81cGd75UWIH9B+6i7pzTbyVX0XF/DqE0GtkVSWLfvUt38dx4Z1E+/l/e+yRrL7ihGioPhkbDCL8U6gUqwXWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:05:07.662940Z","bundle_sha256":"448e1ffc1d399334c8e0401c9edca94225f6f5f23bc530cd203d6b9f0f71e87c"}}