{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KPY5SZ2SPGEIRF7IWUBMUVSLDE","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":"71360493a0d73da49acb9c3b951dc08b5d952bd663599dc0b987d000e3dc107b","cross_cats_sorted":["cs.CC","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-17T20:38:28Z","title_canon_sha256":"cae1ad2addf7cb8fa920ac325eff44a8ad38dba80de1c204d2a14f5369b5cc0a"},"schema_version":"1.0","source":{"id":"1212.4129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4129","created_at":"2026-05-18T02:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4129v2","created_at":"2026-05-18T02:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4129","created_at":"2026-05-18T02:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"KPY5SZ2SPGEI","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KPY5SZ2SPGEIRF7I","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KPY5SZ2S","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:7513787d96081acfef4ad059e20795a4ab04e70e8db040ca82535b3d3802c962","target":"graph","created_at":"2026-05-18T02:39:54Z","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":"Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form $f(G*H)$ where $G$ and $H$ are graphs, * is a graph product and $f$ is a graph property. For example, if $f$ is the independence number and * is the disjunctive product, then the product is known to be multiplicative: $f(G*H)=f(G)f(H)$.\n  In this paper, we study graph products in the following non-standard form: $f((G\\oplus H)*J)$ where $G$, $H$ and $J$ are graphs, $\\oplus$ and * are two different graph products and $f$ is a graph property. We show","authors_text":"Bundit Laekhanukit, Danupon Nanongkai, Parinya Chalermsook","cross_cats":["cs.CC","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-17T20:38:28Z","title":"Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4129","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":"sha256:459b6e852b0781188d96d6356f5b764dd1ede8210fc632bb45a2b155ec3b4909","target":"record","created_at":"2026-05-18T02:39:54Z","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":"71360493a0d73da49acb9c3b951dc08b5d952bd663599dc0b987d000e3dc107b","cross_cats_sorted":["cs.CC","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-17T20:38:28Z","title_canon_sha256":"cae1ad2addf7cb8fa920ac325eff44a8ad38dba80de1c204d2a14f5369b5cc0a"},"schema_version":"1.0","source":{"id":"1212.4129","kind":"arxiv","version":2}},"canonical_sha256":"53f1d9675279888897e8b502ca564b19219c70efa317240fd857513da8db0c06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53f1d9675279888897e8b502ca564b19219c70efa317240fd857513da8db0c06","first_computed_at":"2026-05-18T02:39:54.371705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:54.371705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AFTv+vGrZK2tsg/IUpCa09kmAp9qiiAYgroVBrVGPRkl96nOuvcbtASWUaTsyblc12u1y0HJYDPtX17fidwxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:54.372126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:459b6e852b0781188d96d6356f5b764dd1ede8210fc632bb45a2b155ec3b4909","sha256:7513787d96081acfef4ad059e20795a4ab04e70e8db040ca82535b3d3802c962"],"state_sha256":"6b2236c3ed0f4b90b0c1142bb951aded6161345b7f633ace4001b88f59ff7542"}