{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6UV675MGV5MVZ7XJNCNR37XNWX","short_pith_number":"pith:6UV675MG","canonical_record":{"source":{"id":"1706.04108","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-13T14:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"1de221725d301ba8bd2d6d4bc6e54cbec2399bd3753177324d83fe01c384105c","abstract_canon_sha256":"ce4e5a93834930f29e0bab6c20b23aa71a30019fd7dddcbad7958a6526aaed25"},"schema_version":"1.0"},"canonical_sha256":"f52beff586af595cfee9689b1dfeedb5fcf0bd31d5353489c4ba8edf1d81cca4","source":{"kind":"arxiv","id":"1706.04108","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04108","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04108v3","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04108","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"6UV675MGV5MV","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UV675MGV5MVZ7XJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UV675MG","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6UV675MGV5MVZ7XJNCNR37XNWX","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04108","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-13T14:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"1de221725d301ba8bd2d6d4bc6e54cbec2399bd3753177324d83fe01c384105c","abstract_canon_sha256":"ce4e5a93834930f29e0bab6c20b23aa71a30019fd7dddcbad7958a6526aaed25"},"schema_version":"1.0"},"canonical_sha256":"f52beff586af595cfee9689b1dfeedb5fcf0bd31d5353489c4ba8edf1d81cca4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:02.573979Z","signature_b64":"KuyHuQVp1VRWopp7Pchvd9uP/6ZxYgJwlGpvZGpczQkIFJRUIJ+G5ePeoRFImQVjNS/EkR6kjsWxgN6K7Q2SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f52beff586af595cfee9689b1dfeedb5fcf0bd31d5353489c4ba8edf1d81cca4","last_reissued_at":"2026-05-18T00:00:02.573503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:02.573503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04108","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vgm+klhJRKCDlHegOUNirh3ss3MjTJDsM34aX3CiJD5yJIonvArBrRUYhwtM/oOB8fGvwOnVZO4OMEIOYuYPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:40:11.478554Z"},"content_sha256":"00fba5a9c6de0368a70d85c84e06f9526fc6bbeefd6ebe0f2d664216f186708b","schema_version":"1.0","event_id":"sha256:00fba5a9c6de0368a70d85c84e06f9526fc6bbeefd6ebe0f2d664216f186708b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6UV675MGV5MVZ7XJNCNR37XNWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On complexity of propositional Linear-time Temporal Logic with finitely many variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Dmitry Shkatov, Mikhail Rybakov","submitted_at":"2017-06-13T14:58:23Z","abstract_excerpt":"It is known [DemriSchnoebelen02] that both satisfiability and model-checking problems for propositional Linear-time Temporal Logic, LTL, with only a single propositional variable in the language are PSPACE-complete, which coincides with the complexity of these problems for LTL with an arbitrary number of propositional variables [SislaClarke85]. In the present paper, we show that the same result can be obtained by modifying the original proof of SPACE-hardness for LTL from [SislaClarke85]; i.e., we show how to modify the construction from [SislaClarke85] to model the computations of polynomiall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04108","kind":"arxiv","version":3},"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":"2026-05-18T00:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2YAPI7MjZ6KOkX519XdinN4Kg/iD5nu47wWJL+q122n3LRsp/HaSx9fVBToUiRXpy64OqLL/uNJLLPtDeVxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:40:11.478902Z"},"content_sha256":"94c4ae415bf37a611c7408c42c4d21785e7b2526dd9d6c37b39af293195e2fee","schema_version":"1.0","event_id":"sha256:94c4ae415bf37a611c7408c42c4d21785e7b2526dd9d6c37b39af293195e2fee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UV675MGV5MVZ7XJNCNR37XNWX/bundle.json","state_url":"https://pith.science/pith/6UV675MGV5MVZ7XJNCNR37XNWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UV675MGV5MVZ7XJNCNR37XNWX/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":"2026-06-22T21:40:11Z","links":{"resolver":"https://pith.science/pith/6UV675MGV5MVZ7XJNCNR37XNWX","bundle":"https://pith.science/pith/6UV675MGV5MVZ7XJNCNR37XNWX/bundle.json","state":"https://pith.science/pith/6UV675MGV5MVZ7XJNCNR37XNWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UV675MGV5MVZ7XJNCNR37XNWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6UV675MGV5MVZ7XJNCNR37XNWX","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":"ce4e5a93834930f29e0bab6c20b23aa71a30019fd7dddcbad7958a6526aaed25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-13T14:58:23Z","title_canon_sha256":"1de221725d301ba8bd2d6d4bc6e54cbec2399bd3753177324d83fe01c384105c"},"schema_version":"1.0","source":{"id":"1706.04108","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04108","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04108v3","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04108","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"6UV675MGV5MV","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UV675MGV5MVZ7XJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UV675MG","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:94c4ae415bf37a611c7408c42c4d21785e7b2526dd9d6c37b39af293195e2fee","target":"graph","created_at":"2026-05-18T00:00:02Z","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 known [DemriSchnoebelen02] that both satisfiability and model-checking problems for propositional Linear-time Temporal Logic, LTL, with only a single propositional variable in the language are PSPACE-complete, which coincides with the complexity of these problems for LTL with an arbitrary number of propositional variables [SislaClarke85]. In the present paper, we show that the same result can be obtained by modifying the original proof of SPACE-hardness for LTL from [SislaClarke85]; i.e., we show how to modify the construction from [SislaClarke85] to model the computations of polynomiall","authors_text":"Dmitry Shkatov, Mikhail Rybakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-13T14:58:23Z","title":"On complexity of propositional Linear-time Temporal Logic with finitely many variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04108","kind":"arxiv","version":3},"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":"sha256:00fba5a9c6de0368a70d85c84e06f9526fc6bbeefd6ebe0f2d664216f186708b","target":"record","created_at":"2026-05-18T00:00:02Z","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":"ce4e5a93834930f29e0bab6c20b23aa71a30019fd7dddcbad7958a6526aaed25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-06-13T14:58:23Z","title_canon_sha256":"1de221725d301ba8bd2d6d4bc6e54cbec2399bd3753177324d83fe01c384105c"},"schema_version":"1.0","source":{"id":"1706.04108","kind":"arxiv","version":3}},"canonical_sha256":"f52beff586af595cfee9689b1dfeedb5fcf0bd31d5353489c4ba8edf1d81cca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f52beff586af595cfee9689b1dfeedb5fcf0bd31d5353489c4ba8edf1d81cca4","first_computed_at":"2026-05-18T00:00:02.573503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:02.573503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuyHuQVp1VRWopp7Pchvd9uP/6ZxYgJwlGpvZGpczQkIFJRUIJ+G5ePeoRFImQVjNS/EkR6kjsWxgN6K7Q2SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:02.573979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04108","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00fba5a9c6de0368a70d85c84e06f9526fc6bbeefd6ebe0f2d664216f186708b","sha256:94c4ae415bf37a611c7408c42c4d21785e7b2526dd9d6c37b39af293195e2fee"],"state_sha256":"7461a8a27824fbaf6420bb1d648238b1612b2eb2a0a66326950a0726adf46af0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXTThMZXN3NEcWZW/4LUJIf59hfWS06sxMF9/YTMrNBblwhoEhzyKL1OtQcn7Xs8uQMX5DlNuRtq+CcNFWg6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:40:11.480954Z","bundle_sha256":"5c6193d353bdd6a08d3de3edbe6caa2033232139bd0013abea1bac559bdf89ae"}}