{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2ZMLW7KQ63CCNBRHORDN3IXPL5","short_pith_number":"pith:2ZMLW7KQ","canonical_record":{"source":{"id":"1504.06135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-04-23T12:01:22Z","cross_cats_sorted":["cs.CC","math.LO"],"title_canon_sha256":"223abc95541b97b97f5dee68069cc99403c0d3a02ec677b59b33cb2e9c812b09","abstract_canon_sha256":"c5730003cbec1e5af23d0b1462e38317ac5eccca9414606150fccc8cb3f30072"},"schema_version":"1.0"},"canonical_sha256":"d658bb7d50f6c42686277446dda2ef5f527e3c50f8d034407651abefab16777a","source":{"kind":"arxiv","id":"1504.06135","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06135","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06135v2","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06135","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"pith_short_12","alias_value":"2ZMLW7KQ63CC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZMLW7KQ63CCNBRH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZMLW7KQ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2ZMLW7KQ63CCNBRHORDN3IXPL5","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-04-23T12:01:22Z","cross_cats_sorted":["cs.CC","math.LO"],"title_canon_sha256":"223abc95541b97b97f5dee68069cc99403c0d3a02ec677b59b33cb2e9c812b09","abstract_canon_sha256":"c5730003cbec1e5af23d0b1462e38317ac5eccca9414606150fccc8cb3f30072"},"schema_version":"1.0"},"canonical_sha256":"d658bb7d50f6c42686277446dda2ef5f527e3c50f8d034407651abefab16777a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:21.169498Z","signature_b64":"cmon2QozJ5lylHy6tjCJZ5lnsCHhyZFeva6KzcZYOoV0lAObOKdtbTZBa02XgxfU1t6taxU6tv+ALDOTLI+uCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d658bb7d50f6c42686277446dda2ef5f527e3c50f8d034407651abefab16777a","last_reissued_at":"2026-05-18T00:53:21.169007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:21.169007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06135","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxRrpgXkBL5P/S52+kpw2cuvGsssgyIchVBXqOHgOENOHcdssZNX+eQgoixvKmLqvVGrZ8gbUZ+QCP5TVlxOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:17.853002Z"},"content_sha256":"05f2cc478a8ade529c99f340211fcf95454689497619928dfd211eb8ceed1480","schema_version":"1.0","event_id":"sha256:05f2cc478a8ade529c99f340211fcf95454689497619928dfd211eb8ceed1480"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2ZMLW7KQ63CCNBRHORDN3IXPL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of Propositional Logics in Team Semantics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.LO"],"primary_cat":"cs.LO","authors_text":"Heribert Vollmer, Jonni Virtema, Juha Kontinen, Miika Hannula","submitted_at":"2015-04-23T12:01:22Z","abstract_excerpt":"We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for propositional team logic are complete for alternating exponential-time with polynomially many alternations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06135","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YReDzs0zfhrL6GtJJrG+02aO2H1NTPTi1wlbYI8W0mgDzJoBeebo9FQkwAcerhNLS12lZZ8+8ZEoFEx+yoQEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:17.853376Z"},"content_sha256":"9cde59f413556899be97ef655e33e589fb6da324aa3be6b939d8b89b096d7c64","schema_version":"1.0","event_id":"sha256:9cde59f413556899be97ef655e33e589fb6da324aa3be6b939d8b89b096d7c64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/bundle.json","state_url":"https://pith.science/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/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":"2026-05-28T06:16:17Z","links":{"resolver":"https://pith.science/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5","bundle":"https://pith.science/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/bundle.json","state":"https://pith.science/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZMLW7KQ63CCNBRHORDN3IXPL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2ZMLW7KQ63CCNBRHORDN3IXPL5","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":"c5730003cbec1e5af23d0b1462e38317ac5eccca9414606150fccc8cb3f30072","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-04-23T12:01:22Z","title_canon_sha256":"223abc95541b97b97f5dee68069cc99403c0d3a02ec677b59b33cb2e9c812b09"},"schema_version":"1.0","source":{"id":"1504.06135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06135","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06135v2","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06135","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"pith_short_12","alias_value":"2ZMLW7KQ63CC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZMLW7KQ63CCNBRH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZMLW7KQ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9cde59f413556899be97ef655e33e589fb6da324aa3be6b939d8b89b096d7c64","target":"graph","created_at":"2026-05-18T00:53:21Z","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":"We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for propositional team logic are complete for alternating exponential-time with polynomially many alternations.","authors_text":"Heribert Vollmer, Jonni Virtema, Juha Kontinen, Miika Hannula","cross_cats":["cs.CC","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-04-23T12:01:22Z","title":"Complexity of Propositional Logics in Team Semantics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06135","kind":"arxiv","version":2},"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":"sha256:05f2cc478a8ade529c99f340211fcf95454689497619928dfd211eb8ceed1480","target":"record","created_at":"2026-05-18T00:53:21Z","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":"c5730003cbec1e5af23d0b1462e38317ac5eccca9414606150fccc8cb3f30072","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-04-23T12:01:22Z","title_canon_sha256":"223abc95541b97b97f5dee68069cc99403c0d3a02ec677b59b33cb2e9c812b09"},"schema_version":"1.0","source":{"id":"1504.06135","kind":"arxiv","version":2}},"canonical_sha256":"d658bb7d50f6c42686277446dda2ef5f527e3c50f8d034407651abefab16777a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d658bb7d50f6c42686277446dda2ef5f527e3c50f8d034407651abefab16777a","first_computed_at":"2026-05-18T00:53:21.169007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:21.169007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmon2QozJ5lylHy6tjCJZ5lnsCHhyZFeva6KzcZYOoV0lAObOKdtbTZBa02XgxfU1t6taxU6tv+ALDOTLI+uCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:21.169498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05f2cc478a8ade529c99f340211fcf95454689497619928dfd211eb8ceed1480","sha256:9cde59f413556899be97ef655e33e589fb6da324aa3be6b939d8b89b096d7c64"],"state_sha256":"4d8cb01afb35f9db45b82c41da815421bb54861f44a144a92a864158ce37e891"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pVo0opkh9naKo/PJvmzz8AHpH06fRM3GZUJVGT5B/a3vpdfo7ULJSl70yAHdXElQPXIst5eGRfWmpzoQ0XnECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:16:17.855526Z","bundle_sha256":"67f371da70870cfc68a5c224ca189262c6354fd0dd10168e36b2908479e46e23"}}