{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U5FUHOA7OREOGCLNK6VWVQK632","short_pith_number":"pith:U5FUHOA7","canonical_record":{"source":{"id":"1203.3814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T20:33:28Z","cross_cats_sorted":[],"title_canon_sha256":"b915b6d9cb706eab73d9d5a768e7cbf05a947a4db4cad7f3e1cd72b568951ee3","abstract_canon_sha256":"04f504b5b03f3bf2e2a3c3618af34e033eec0534cbfa9ca0c4283d783b4ecced"},"schema_version":"1.0"},"canonical_sha256":"a74b43b81f7448e3096d57ab6ac15edeac228db84273d8a956b7e357e1d6acdc","source":{"kind":"arxiv","id":"1203.3814","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3814","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3814v2","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3814","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"U5FUHOA7OREO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U5FUHOA7OREOGCLN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U5FUHOA7","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U5FUHOA7OREOGCLNK6VWVQK632","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T20:33:28Z","cross_cats_sorted":[],"title_canon_sha256":"b915b6d9cb706eab73d9d5a768e7cbf05a947a4db4cad7f3e1cd72b568951ee3","abstract_canon_sha256":"04f504b5b03f3bf2e2a3c3618af34e033eec0534cbfa9ca0c4283d783b4ecced"},"schema_version":"1.0"},"canonical_sha256":"a74b43b81f7448e3096d57ab6ac15edeac228db84273d8a956b7e357e1d6acdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:24.096128Z","signature_b64":"TkFErfsybo6aVFk+VrX/snHLLsq8gWzk8nqU2/I+ORf99lSmMJ/eVk5w8ffWtO+sLtX7ujRLv41dWyaQso4xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a74b43b81f7448e3096d57ab6ac15edeac228db84273d8a956b7e357e1d6acdc","last_reissued_at":"2026-05-17T23:51:24.095570Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:24.095570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3814","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":"2026-05-17T23:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zlmFkNruZEDqhAzOskOz/qnnhFxYnP/JxAbbl9tu3As4EYWAJz6TWJlRuXTug6iVhTSeTmQshk7tJ3Kv9rP3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:59:29.982516Z"},"content_sha256":"7aaddfe8fa809f4bb03ea905e69b3d3721817bbb626923bece685c5ee5b91549","schema_version":"1.0","event_id":"sha256:7aaddfe8fa809f4bb03ea905e69b3d3721817bbb626923bece685c5ee5b91549"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U5FUHOA7OREOGCLNK6VWVQK632","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tree-width for first order formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Isolde Adler, Mark Weyer","submitted_at":"2012-03-16T20:33:28Z","abstract_excerpt":"We introduce tree-width for first order formulae \\phi, fotw(\\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed parameter tractable, with parameter the length of the formula. This is done by translating a formula \\phi\\ with fotw(\\phi)<k into a formula of the k-variable fragment L^k of first order logic. For fixed k, the question whether a given first order formula is equivalent to an L^k formula is undecidable. In contrast, the classes of first order formulae with bounded fot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3814","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":"2026-05-17T23:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"smV6nfirsd26zMPk0HASogDvgWxEENmPwA1qTzv7l+5mC3oGjGyy5ttYwGZff5jGoDoU++aKNcbuxLLYlzxRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:59:29.982866Z"},"content_sha256":"4cdc751c51fb1de95ac79b05b5154d9a766a6f72c3b1eddf5f091c2d78a8ed03","schema_version":"1.0","event_id":"sha256:4cdc751c51fb1de95ac79b05b5154d9a766a6f72c3b1eddf5f091c2d78a8ed03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5FUHOA7OREOGCLNK6VWVQK632/bundle.json","state_url":"https://pith.science/pith/U5FUHOA7OREOGCLNK6VWVQK632/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5FUHOA7OREOGCLNK6VWVQK632/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":"2026-06-11T08:59:29Z","links":{"resolver":"https://pith.science/pith/U5FUHOA7OREOGCLNK6VWVQK632","bundle":"https://pith.science/pith/U5FUHOA7OREOGCLNK6VWVQK632/bundle.json","state":"https://pith.science/pith/U5FUHOA7OREOGCLNK6VWVQK632/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5FUHOA7OREOGCLNK6VWVQK632/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U5FUHOA7OREOGCLNK6VWVQK632","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":"04f504b5b03f3bf2e2a3c3618af34e033eec0534cbfa9ca0c4283d783b4ecced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T20:33:28Z","title_canon_sha256":"b915b6d9cb706eab73d9d5a768e7cbf05a947a4db4cad7f3e1cd72b568951ee3"},"schema_version":"1.0","source":{"id":"1203.3814","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3814","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3814v2","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3814","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"U5FUHOA7OREO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U5FUHOA7OREOGCLN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U5FUHOA7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:4cdc751c51fb1de95ac79b05b5154d9a766a6f72c3b1eddf5f091c2d78a8ed03","target":"graph","created_at":"2026-05-17T23:51:24Z","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 introduce tree-width for first order formulae \\phi, fotw(\\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed parameter tractable, with parameter the length of the formula. This is done by translating a formula \\phi\\ with fotw(\\phi)<k into a formula of the k-variable fragment L^k of first order logic. For fixed k, the question whether a given first order formula is equivalent to an L^k formula is undecidable. In contrast, the classes of first order formulae with bounded fot","authors_text":"Isolde Adler, Mark Weyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T20:33:28Z","title":"Tree-width for first order formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3814","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":"sha256:7aaddfe8fa809f4bb03ea905e69b3d3721817bbb626923bece685c5ee5b91549","target":"record","created_at":"2026-05-17T23:51:24Z","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":"04f504b5b03f3bf2e2a3c3618af34e033eec0534cbfa9ca0c4283d783b4ecced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-03-16T20:33:28Z","title_canon_sha256":"b915b6d9cb706eab73d9d5a768e7cbf05a947a4db4cad7f3e1cd72b568951ee3"},"schema_version":"1.0","source":{"id":"1203.3814","kind":"arxiv","version":2}},"canonical_sha256":"a74b43b81f7448e3096d57ab6ac15edeac228db84273d8a956b7e357e1d6acdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a74b43b81f7448e3096d57ab6ac15edeac228db84273d8a956b7e357e1d6acdc","first_computed_at":"2026-05-17T23:51:24.095570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:24.095570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkFErfsybo6aVFk+VrX/snHLLsq8gWzk8nqU2/I+ORf99lSmMJ/eVk5w8ffWtO+sLtX7ujRLv41dWyaQso4xDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:24.096128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3814","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aaddfe8fa809f4bb03ea905e69b3d3721817bbb626923bece685c5ee5b91549","sha256:4cdc751c51fb1de95ac79b05b5154d9a766a6f72c3b1eddf5f091c2d78a8ed03"],"state_sha256":"1ee8583eee2b00b225f7cb3e106b3814316fce6f6953cd7236660d51b3961077"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2z+8buggXdY4zSqTYwYunbSK9eiGBqYXCKcip0wq5zuuNHBcvW/BfaTDFO02XuaJgmZ6gKLdYEZLZd4TjdCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:59:29.984760Z","bundle_sha256":"2307af0f66a9b040f5aec0905a303d83f76a6d4ae79c7ead248fc9f991ef42a6"}}