{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:64IQL5LEBMXVDMWWFB6N7W27EK","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":"4ec4719732a7b7e1b9702c249e829646bc6aa5ff3474ccd7e8f219408250d6eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-07-11T17:53:30Z","title_canon_sha256":"3c75e15a802495bef11b37399634b7a659eadceb1ecd5f1c9fcaa47ef601c6bd"},"schema_version":"1.0","source":{"id":"1807.04263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04263","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04263v1","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04263","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"64IQL5LEBMXV","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"64IQL5LEBMXVDMWW","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"64IQL5LE","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:07312a3268b12ff03c09ecdc4f4a2e1b879e2c9adc13db8eb2569c5c587c4973","target":"graph","created_at":"2026-05-18T00:10:57Z","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 generalize many results concerning the tractability of SAT and #SAT on bounded treewidth CNF-formula in the context of Quantified Boolean Formulas (QBF). To this end, we start by studying the notion of width for OBDD and observe that the blow up in size while existentially or universally projecting a block of variables in an OBDD only affects its width. We then generalize this notion of width to the more general representation of structured (deterministic) DNNF and give a similar algorithm to existentially or universally project a block of variables. Using a well-known algorithm transformin","authors_text":"Florent Capelli, Stefan Mengel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-07-11T17:53:30Z","title":"Knowledge Compilation, Width and Quantification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04263","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:dd6cab62323f3be58d7145b2f5a6531752f5be12bb0d5be8bb52688737782252","target":"record","created_at":"2026-05-18T00:10:57Z","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":"4ec4719732a7b7e1b9702c249e829646bc6aa5ff3474ccd7e8f219408250d6eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-07-11T17:53:30Z","title_canon_sha256":"3c75e15a802495bef11b37399634b7a659eadceb1ecd5f1c9fcaa47ef601c6bd"},"schema_version":"1.0","source":{"id":"1807.04263","kind":"arxiv","version":1}},"canonical_sha256":"f71105f5640b2f51b2d6287cdfdb5f22853325f9958fbb61466270e74f4f23e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f71105f5640b2f51b2d6287cdfdb5f22853325f9958fbb61466270e74f4f23e4","first_computed_at":"2026-05-18T00:10:57.513311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:57.513311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZt1SJOvdZMseVEjQCVcXx7F/EOEEA2+aG7D6s7KzgbOoZiCeJet3dVO/sIYmidMlAxlJPuLqQn9rNw6KF9NDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:57.514031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd6cab62323f3be58d7145b2f5a6531752f5be12bb0d5be8bb52688737782252","sha256:07312a3268b12ff03c09ecdc4f4a2e1b879e2c9adc13db8eb2569c5c587c4973"],"state_sha256":"6f575a4891026dcd416f2e1b5e1ffed7a8e7e64244c48e49f55214a007aa4bdc"}