{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NV2SGNUP2WAP4R7YFVZZ726SJT","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":"a56d11de238ee68373ee3ec1cc9cf242565ecebdf139720d67f836b945a14b3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-08T07:54:24Z","title_canon_sha256":"9552c6f8d24436ca0ada0dfdc416327273be4a4be09a2a16e5641d62fd2b4fb1"},"schema_version":"1.0","source":{"id":"1412.2470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2470","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2470v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2470","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"NV2SGNUP2WAP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NV2SGNUP2WAP4R7Y","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NV2SGNUP","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:3673db254c35424c89e58aab2ae00cd87cd2ba464cb667e7c4305a461b8eb3e8","target":"graph","created_at":"2026-05-18T02:31:57Z","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":"Motivated by a recent result of Elberfeld, Jakoby and Tantau showing that $\\mathsf{MSO}$ properties are Logspace computable on graphs of bounded tree-width, we consider the complexity of computing the determinant of the adjacency matrix of a bounded tree-width graph and as our main result prove that it is in Logspace. It is important to notice that the determinant is neither an $\\mathsf{MSO}$-property nor counts the number of solutions of an $\\mathsf{MSO}$-predicate. This technique yields Logspace algorithms for counting the number of spanning arborescences and directed Euler tours in bounded ","authors_text":"Nikhil Balaji, Samir Datta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-08T07:54:24Z","title":"Bounded Treewidth and Space-Efficient Linear Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2470","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:b3f17f6393f614399092afadbda000cb10a832d8a1bc87c6f8f7e3b906c6034f","target":"record","created_at":"2026-05-18T02:31:57Z","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":"a56d11de238ee68373ee3ec1cc9cf242565ecebdf139720d67f836b945a14b3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-12-08T07:54:24Z","title_canon_sha256":"9552c6f8d24436ca0ada0dfdc416327273be4a4be09a2a16e5641d62fd2b4fb1"},"schema_version":"1.0","source":{"id":"1412.2470","kind":"arxiv","version":1}},"canonical_sha256":"6d7523368fd580fe47f82d739febd24ccd05c37962e7bcc26d7d4fbfc362c995","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d7523368fd580fe47f82d739febd24ccd05c37962e7bcc26d7d4fbfc362c995","first_computed_at":"2026-05-18T02:31:57.899537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:57.899537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXejr0Xa0hdDIpz8juWaR727YvRRY1WXbvxPobV/PBAfPbK15DgKXSV9/7MwkOtq4zLUZzGq2nEbwpS0h9n/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:57.900189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f17f6393f614399092afadbda000cb10a832d8a1bc87c6f8f7e3b906c6034f","sha256:3673db254c35424c89e58aab2ae00cd87cd2ba464cb667e7c4305a461b8eb3e8"],"state_sha256":"d382fbebba4a1a2a96cb2590e9cd8e490e6e6b1197809817ae41465f99c63f63"}