{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IEMEMLY7BO2QAVTAXQJPM5F4US","short_pith_number":"pith:IEMEMLY7","canonical_record":{"source":{"id":"1004.1485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-09T07:50:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e2ee25355cdccbc641c2e5a3747b6f8fe1ce6d7180192094e990bbcfccfb2d2d","abstract_canon_sha256":"7ca191f7c39be14476ba290531aa1674520a6122e87b834d04d5b62e98823d00"},"schema_version":"1.0"},"canonical_sha256":"4118462f1f0bb5005660bc12f674bca486a88ab2a5d0b92ed5c91dc1da839161","source":{"kind":"arxiv","id":"1004.1485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1485","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1485v1","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1485","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"IEMEMLY7BO2Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IEMEMLY7BO2QAVTA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IEMEMLY7","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IEMEMLY7BO2QAVTAXQJPM5F4US","target":"record","payload":{"canonical_record":{"source":{"id":"1004.1485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-09T07:50:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e2ee25355cdccbc641c2e5a3747b6f8fe1ce6d7180192094e990bbcfccfb2d2d","abstract_canon_sha256":"7ca191f7c39be14476ba290531aa1674520a6122e87b834d04d5b62e98823d00"},"schema_version":"1.0"},"canonical_sha256":"4118462f1f0bb5005660bc12f674bca486a88ab2a5d0b92ed5c91dc1da839161","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:24.087485Z","signature_b64":"oTgMaxQcp/tZIlMIqCg0k5kXfm1pgSHhHlElCqOtBvHcvBbjOji2xpIOKF2h5giPoVncyANk5+bv2A0lGGIoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4118462f1f0bb5005660bc12f674bca486a88ab2a5d0b92ed5c91dc1da839161","last_reissued_at":"2026-05-18T01:09:24.086846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:24.086846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.1485","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":"2026-05-18T01:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"giF0rvbxPaJp5swWTrRIagtmfjfganf0YpcpQN9PUGnw7YYPgaCJ03pg6aVCN1uSulzgvN2lIDWQ9PbhCcVKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:22:50.212000Z"},"content_sha256":"f96c14ab8cd7f2eb3fba585ec4b8c35caf7bd1cba94fafa5eb6cbf5c3092352f","schema_version":"1.0","event_id":"sha256:f96c14ab8cd7f2eb3fba585ec4b8c35caf7bd1cba94fafa5eb6cbf5c3092352f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IEMEMLY7BO2QAVTAXQJPM5F4US","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Are there any good digraph width measures?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Daniel Meister, Jan Obdr\\v{z}\\'alek, Joachim Kneis, Peter Rossmanith, Petr Hlin\\v{e}n\\'y, Robert Ganian, Somnath Sikdar","submitted_at":"2010-04-09T07:50:34Z","abstract_excerpt":"Several different measures for digraph width have appeared in the last few years. However, none of them shares all the \"nice\" properties of treewidth: First, being \\emph{algorithmically useful} i.e. admitting polynomial-time algorithms for all $\\MS1$-definable problems on digraphs of bounded width. And, second, having nice \\emph{structural properties} i.e. being monotone under taking subdigraphs and some form of arc contractions. As for the former, (undirected) $\\MS1$ seems to be the least common denominator of all reasonably expressive logical languages on digraphs that can speak about the ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1485","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":"2026-05-18T01:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eXM/Ep6t1WYPpj3whnNi63ceSmbTU3Gy5Z9hIOPBGiBQqimx9To8UPQtsVRYXGCx2bpOIXLrf1dCVdgkrFKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:22:50.212391Z"},"content_sha256":"f79b03d1a1d5ce8b6125f8e3c113ff26170116f07ea04efc3c266f07460c443c","schema_version":"1.0","event_id":"sha256:f79b03d1a1d5ce8b6125f8e3c113ff26170116f07ea04efc3c266f07460c443c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/bundle.json","state_url":"https://pith.science/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/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":"2026-05-31T23:22:50Z","links":{"resolver":"https://pith.science/pith/IEMEMLY7BO2QAVTAXQJPM5F4US","bundle":"https://pith.science/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/bundle.json","state":"https://pith.science/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEMEMLY7BO2QAVTAXQJPM5F4US/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IEMEMLY7BO2QAVTAXQJPM5F4US","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":"7ca191f7c39be14476ba290531aa1674520a6122e87b834d04d5b62e98823d00","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-09T07:50:34Z","title_canon_sha256":"e2ee25355cdccbc641c2e5a3747b6f8fe1ce6d7180192094e990bbcfccfb2d2d"},"schema_version":"1.0","source":{"id":"1004.1485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1485","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1485v1","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1485","created_at":"2026-05-18T01:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"IEMEMLY7BO2Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IEMEMLY7BO2QAVTA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IEMEMLY7","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:f79b03d1a1d5ce8b6125f8e3c113ff26170116f07ea04efc3c266f07460c443c","target":"graph","created_at":"2026-05-18T01:09:24Z","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":"Several different measures for digraph width have appeared in the last few years. However, none of them shares all the \"nice\" properties of treewidth: First, being \\emph{algorithmically useful} i.e. admitting polynomial-time algorithms for all $\\MS1$-definable problems on digraphs of bounded width. And, second, having nice \\emph{structural properties} i.e. being monotone under taking subdigraphs and some form of arc contractions. As for the former, (undirected) $\\MS1$ seems to be the least common denominator of all reasonably expressive logical languages on digraphs that can speak about the ed","authors_text":"Daniel Meister, Jan Obdr\\v{z}\\'alek, Joachim Kneis, Peter Rossmanith, Petr Hlin\\v{e}n\\'y, Robert Ganian, Somnath Sikdar","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-09T07:50:34Z","title":"Are there any good digraph width measures?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1485","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:f96c14ab8cd7f2eb3fba585ec4b8c35caf7bd1cba94fafa5eb6cbf5c3092352f","target":"record","created_at":"2026-05-18T01:09:24Z","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":"7ca191f7c39be14476ba290531aa1674520a6122e87b834d04d5b62e98823d00","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-09T07:50:34Z","title_canon_sha256":"e2ee25355cdccbc641c2e5a3747b6f8fe1ce6d7180192094e990bbcfccfb2d2d"},"schema_version":"1.0","source":{"id":"1004.1485","kind":"arxiv","version":1}},"canonical_sha256":"4118462f1f0bb5005660bc12f674bca486a88ab2a5d0b92ed5c91dc1da839161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4118462f1f0bb5005660bc12f674bca486a88ab2a5d0b92ed5c91dc1da839161","first_computed_at":"2026-05-18T01:09:24.086846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:24.086846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oTgMaxQcp/tZIlMIqCg0k5kXfm1pgSHhHlElCqOtBvHcvBbjOji2xpIOKF2h5giPoVncyANk5+bv2A0lGGIoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:24.087485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f96c14ab8cd7f2eb3fba585ec4b8c35caf7bd1cba94fafa5eb6cbf5c3092352f","sha256:f79b03d1a1d5ce8b6125f8e3c113ff26170116f07ea04efc3c266f07460c443c"],"state_sha256":"47b1f9ccee8a95f91c8beeac0b5ef19bd07f6ebd2910ff82bf1e4083b01b33be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uzh1/UR4MfeCWrrlYY8WG4W/BDh2KBKCWrMDJGInIOO53Zgdl0xICWXkUcL9AMblKLcVikib10OEz1w8tKLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:22:50.214862Z","bundle_sha256":"5eea3e50ace719346db4cb4793a63caefda6680f09adca8de63e23c76e76fe95"}}