{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MAT2BZI7LDJHP5ZBVOMSKSULI2","short_pith_number":"pith:MAT2BZI7","canonical_record":{"source":{"id":"1903.10706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-03-26T06:52:34Z","cross_cats_sorted":["cs.CC","cs.DB"],"title_canon_sha256":"10605dda973827fcd6f37e135b13dcc59b980111f894efe0fdbf45f2ed262260","abstract_canon_sha256":"fbb902b853a13afabf41ba7c8e7931d38c1c7cf7d3ba22af4e2f6e736815bd75"},"schema_version":"1.0"},"canonical_sha256":"6027a0e51f58d277f721ab99254a8b46bcb955fb4f1a9412eb41501fd59335c4","source":{"kind":"arxiv","id":"1903.10706","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10706","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10706v1","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10706","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"MAT2BZI7LDJH","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MAT2BZI7LDJHP5ZB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MAT2BZI7","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MAT2BZI7LDJHP5ZBVOMSKSULI2","target":"record","payload":{"canonical_record":{"source":{"id":"1903.10706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-03-26T06:52:34Z","cross_cats_sorted":["cs.CC","cs.DB"],"title_canon_sha256":"10605dda973827fcd6f37e135b13dcc59b980111f894efe0fdbf45f2ed262260","abstract_canon_sha256":"fbb902b853a13afabf41ba7c8e7931d38c1c7cf7d3ba22af4e2f6e736815bd75"},"schema_version":"1.0"},"canonical_sha256":"6027a0e51f58d277f721ab99254a8b46bcb955fb4f1a9412eb41501fd59335c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:17.956952Z","signature_b64":"L7+A3DqAPhepvL+oR6jLawIZiN9pi43wohU6s5/kKMynDICUdbMVAyy6S0Y4me2aw1CpcF+b6lUrXKvHj5aKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6027a0e51f58d277f721ab99254a8b46bcb955fb4f1a9412eb41501fd59335c4","last_reissued_at":"2026-05-17T23:50:17.956256Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:17.956256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.10706","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":"2026-05-17T23:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26rgFdyDPbkr0UdSLK4YzTUQSmqpzol7tb55XNIdvEG3A8OWHVNDti3o/kkQNWD2l5L8PsEu4WQH6XolYkxXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:04.406665Z"},"content_sha256":"ac9eff6cdc5faf944834a35c11b6306da3fdef170f330ab8ad2af3ed72abbcd1","schema_version":"1.0","event_id":"sha256:ac9eff6cdc5faf944834a35c11b6306da3fdef170f330ab8ad2af3ed72abbcd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MAT2BZI7LDJHP5ZBVOMSKSULI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity Thresholds in Inclusion Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DB"],"primary_cat":"cs.LO","authors_text":"Lauri Hella, Miika Hannula","submitted_at":"2019-03-26T06:52:34Z","abstract_excerpt":"Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic polynomial time in ordered models. In this article we examine connections between syntactical fragments of inclusion logic and different complexity classes in terms of two computational problems: "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10706","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":"2026-05-17T23:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISLhe1ylodIk3SuU2nTD230bI/RkoK6I8c7J3aZHlULt2L/m7KcSlJhpfc8yozw3x4BlwVFVMWyGgYct/FXDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:04.407015Z"},"content_sha256":"1d071f7cc16619a5459f166b0aa0d6bf287b003b747e9af657836176ff94b30c","schema_version":"1.0","event_id":"sha256:1d071f7cc16619a5459f166b0aa0d6bf287b003b747e9af657836176ff94b30c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/bundle.json","state_url":"https://pith.science/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/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":"2026-06-01T06:48:04Z","links":{"resolver":"https://pith.science/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2","bundle":"https://pith.science/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/bundle.json","state":"https://pith.science/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MAT2BZI7LDJHP5ZBVOMSKSULI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MAT2BZI7LDJHP5ZBVOMSKSULI2","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":"fbb902b853a13afabf41ba7c8e7931d38c1c7cf7d3ba22af4e2f6e736815bd75","cross_cats_sorted":["cs.CC","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-03-26T06:52:34Z","title_canon_sha256":"10605dda973827fcd6f37e135b13dcc59b980111f894efe0fdbf45f2ed262260"},"schema_version":"1.0","source":{"id":"1903.10706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10706","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10706v1","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10706","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"MAT2BZI7LDJH","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MAT2BZI7LDJHP5ZB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MAT2BZI7","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:1d071f7cc16619a5459f166b0aa0d6bf287b003b747e9af657836176ff94b30c","target":"graph","created_at":"2026-05-17T23:50:17Z","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":"Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic polynomial time in ordered models. In this article we examine connections between syntactical fragments of inclusion logic and different complexity classes in terms of two computational problems: ","authors_text":"Lauri Hella, Miika Hannula","cross_cats":["cs.CC","cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-03-26T06:52:34Z","title":"Complexity Thresholds in Inclusion Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10706","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:ac9eff6cdc5faf944834a35c11b6306da3fdef170f330ab8ad2af3ed72abbcd1","target":"record","created_at":"2026-05-17T23:50:17Z","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":"fbb902b853a13afabf41ba7c8e7931d38c1c7cf7d3ba22af4e2f6e736815bd75","cross_cats_sorted":["cs.CC","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-03-26T06:52:34Z","title_canon_sha256":"10605dda973827fcd6f37e135b13dcc59b980111f894efe0fdbf45f2ed262260"},"schema_version":"1.0","source":{"id":"1903.10706","kind":"arxiv","version":1}},"canonical_sha256":"6027a0e51f58d277f721ab99254a8b46bcb955fb4f1a9412eb41501fd59335c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6027a0e51f58d277f721ab99254a8b46bcb955fb4f1a9412eb41501fd59335c4","first_computed_at":"2026-05-17T23:50:17.956256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:17.956256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L7+A3DqAPhepvL+oR6jLawIZiN9pi43wohU6s5/kKMynDICUdbMVAyy6S0Y4me2aw1CpcF+b6lUrXKvHj5aKDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:17.956952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac9eff6cdc5faf944834a35c11b6306da3fdef170f330ab8ad2af3ed72abbcd1","sha256:1d071f7cc16619a5459f166b0aa0d6bf287b003b747e9af657836176ff94b30c"],"state_sha256":"a9141479a44e3393ff02edafca48e914409d565b92e4ab887b2db46f7a1343e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oWuWvT8EmXYa8xmMmIOxQk3cEVfGfM1YF8bR+MolrstKT/OF9K+M9omh4sH3ST7tZBoX9PflESoggsdePwQjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:48:04.409063Z","bundle_sha256":"20da84736b7067a970ba1e0295ad358b4895a1ea651b0f8b27608069e2fb6aff"}}