{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q3YQHM4RCIP3S6KGZVDKYFVTGS","short_pith_number":"pith:Q3YQHM4R","canonical_record":{"source":{"id":"1402.4992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T13:18:00Z","cross_cats_sorted":[],"title_canon_sha256":"abb19d07705d48c8cfad548a8b47936b4815161933791f7d526815b8572d80ef","abstract_canon_sha256":"033fac7f782f0df19cddc837fff3f42957c27101181e7b6dd3b39a4e1867c8ce"},"schema_version":"1.0"},"canonical_sha256":"86f103b391121fb97946cd46ac16b334bd4cff475a42dd5ec1e18eb4375a5495","source":{"kind":"arxiv","id":"1402.4992","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4992","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4992v1","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4992","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"Q3YQHM4RCIP3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3YQHM4RCIP3S6KG","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3YQHM4R","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q3YQHM4RCIP3S6KGZVDKYFVTGS","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T13:18:00Z","cross_cats_sorted":[],"title_canon_sha256":"abb19d07705d48c8cfad548a8b47936b4815161933791f7d526815b8572d80ef","abstract_canon_sha256":"033fac7f782f0df19cddc837fff3f42957c27101181e7b6dd3b39a4e1867c8ce"},"schema_version":"1.0"},"canonical_sha256":"86f103b391121fb97946cd46ac16b334bd4cff475a42dd5ec1e18eb4375a5495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:31.433950Z","signature_b64":"L0SejDkWEh0s7VwA7bQkMMn3Cz9aNfyIO4pidZYdN9dr93hM8onL2HT9RG/a+0DN9io3Fn6eMwWrsEGd68oLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f103b391121fb97946cd46ac16b334bd4cff475a42dd5ec1e18eb4375a5495","last_reissued_at":"2026-05-18T02:58:31.433379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:31.433379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4992","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":"2026-05-18T02:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7YEO/LGYCsYs0qpnnmePbXPw3ZPsinj1XWFZRagJPXyn09fCWV4kUSNnATvjgSZD5apTe0biPHu9pEc8fIrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:44:53.531589Z"},"content_sha256":"6cddfb16893d0abee9504fbb13237190e0b17e1f5106d13a8f3fff6d29cad8eb","schema_version":"1.0","event_id":"sha256:6cddfb16893d0abee9504fbb13237190e0b17e1f5106d13a8f3fff6d29cad8eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q3YQHM4RCIP3S6KGZVDKYFVTGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structural parameterizations for boxicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Joos, Henning Bruhn, Morgan Chopin, Oliver Schaudt","submitted_at":"2014-02-20T13:18:00Z","abstract_excerpt":"The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \\ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number.\n  Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4992","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":"2026-05-18T02:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fqSlp+PKP21AMWaGLwqfbu3Ywf/yr6jOI4/fPJsnPfcsLnhWhMXQpZ5dB6IH8pUMRnnS311/cwBbOJuAGZjcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:44:53.532231Z"},"content_sha256":"46d4cff7d1643b44098339ac041b8dde1e168c4d035edeb6b036f8825da0ec9f","schema_version":"1.0","event_id":"sha256:46d4cff7d1643b44098339ac041b8dde1e168c4d035edeb6b036f8825da0ec9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/bundle.json","state_url":"https://pith.science/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/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":"2026-06-04T04:44:53Z","links":{"resolver":"https://pith.science/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS","bundle":"https://pith.science/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/bundle.json","state":"https://pith.science/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3YQHM4RCIP3S6KGZVDKYFVTGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q3YQHM4RCIP3S6KGZVDKYFVTGS","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":"033fac7f782f0df19cddc837fff3f42957c27101181e7b6dd3b39a4e1867c8ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T13:18:00Z","title_canon_sha256":"abb19d07705d48c8cfad548a8b47936b4815161933791f7d526815b8572d80ef"},"schema_version":"1.0","source":{"id":"1402.4992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4992","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4992v1","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4992","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"Q3YQHM4RCIP3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3YQHM4RCIP3S6KG","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3YQHM4R","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:46d4cff7d1643b44098339ac041b8dde1e168c4d035edeb6b036f8825da0ec9f","target":"graph","created_at":"2026-05-18T02:58:31Z","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":"The boxicity of a graph $G$ is the least integer $d$ such that $G$ has an intersection model of axis-aligned $d$-dimensional boxes. Boxicity, the problem of deciding whether a given graph $G$ has boxicity at most $d$, is NP-complete for every fixed $d \\ge 2$. We show that boxicity is fixed-parameter tractable when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Adiga et al., that boxicity is fixed-parameter tractable in the vertex cover number.\n  Moreover, we show that boxicity admits an additive $1$-approximation when parameterized by the","authors_text":"Felix Joos, Henning Bruhn, Morgan Chopin, Oliver Schaudt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T13:18:00Z","title":"Structural parameterizations for boxicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4992","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":"sha256:6cddfb16893d0abee9504fbb13237190e0b17e1f5106d13a8f3fff6d29cad8eb","target":"record","created_at":"2026-05-18T02:58:31Z","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":"033fac7f782f0df19cddc837fff3f42957c27101181e7b6dd3b39a4e1867c8ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-20T13:18:00Z","title_canon_sha256":"abb19d07705d48c8cfad548a8b47936b4815161933791f7d526815b8572d80ef"},"schema_version":"1.0","source":{"id":"1402.4992","kind":"arxiv","version":1}},"canonical_sha256":"86f103b391121fb97946cd46ac16b334bd4cff475a42dd5ec1e18eb4375a5495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86f103b391121fb97946cd46ac16b334bd4cff475a42dd5ec1e18eb4375a5495","first_computed_at":"2026-05-18T02:58:31.433379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:31.433379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L0SejDkWEh0s7VwA7bQkMMn3Cz9aNfyIO4pidZYdN9dr93hM8onL2HT9RG/a+0DN9io3Fn6eMwWrsEGd68oLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:31.433950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cddfb16893d0abee9504fbb13237190e0b17e1f5106d13a8f3fff6d29cad8eb","sha256:46d4cff7d1643b44098339ac041b8dde1e168c4d035edeb6b036f8825da0ec9f"],"state_sha256":"454fbb42eac0363df22f3ec3f3d5b7b5f1e3500298692f27ea25249585a7ec5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qv5BNGwOXjQAWcXhG5XuQFOckmf+QCpKDxb6sCdC75aeox1c8H2Zv3eQt2AFVjqpPH2RkA33ve7TwuL/y0k+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:44:53.535436Z","bundle_sha256":"45a1c36e411ff0f26a82bdf4fcd661a9022dd4c389f0acbfead0c5bec895dcea"}}