{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DSVOEBTU4V7AWAWGZFZDC4FEVN","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":"88e14f3aae5af81d7fbc79be15f259963d9426c83e3141a1312c2d57661fd10c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-05T19:31:11Z","title_canon_sha256":"193f7a6a134d787b1ff2f9615739ab6b137b1aa76163bdc45338f85e930d0ba6"},"schema_version":"1.0","source":{"id":"2404.04369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04369","created_at":"2026-07-05T08:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04369v1","created_at":"2026-07-05T08:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04369","created_at":"2026-07-05T08:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"DSVOEBTU4V7A","created_at":"2026-07-05T08:05:15Z"},{"alias_kind":"pith_short_16","alias_value":"DSVOEBTU4V7AWAWG","created_at":"2026-07-05T08:05:15Z"},{"alias_kind":"pith_short_8","alias_value":"DSVOEBTU","created_at":"2026-07-05T08:05:15Z"}],"graph_snapshots":[{"event_id":"sha256:dc26dee3cb33cda599b23680d6c067f2d822e878b3b12bbe53184be05cb0c198","target":"graph","created_at":"2026-07-05T08:05:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.04369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In an $m$-edge host graph $G$, all triangles can be listed in time $O(m^{1.5})$ [Itai, Rodeh '78], and all $k$-cycles can be listed in time $O(m^{2-1/{\\lceil k/2 \\rceil}} + t)$ where $t$ is the output size [Alon, Yuster, Zwick '97]. These classic results also hold for the colored problem variant, where the nodes of the host graph $G$ are colored by nodes in the pattern graph $H$, and we are only interested in subgraphs of $G$ that are isomorphic to the pattern $H$ and respect the colors. We study the problem of listing all $H$-subgraphs in the colored setting, for fixed pattern graphs $H$.\n  A","authors_text":"Egor Gorbachev, Karl Bringmann","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-05T19:31:11Z","title":"A Fine-grained Classification of Subquadratic Patterns for Subgraph Listing and Friends"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04369","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:c7e65324cd160bd1c23389a6a445a01d8f35a1973178682c8fd8956e0cf65997","target":"record","created_at":"2026-07-05T08:05:15Z","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":"88e14f3aae5af81d7fbc79be15f259963d9426c83e3141a1312c2d57661fd10c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-05T19:31:11Z","title_canon_sha256":"193f7a6a134d787b1ff2f9615739ab6b137b1aa76163bdc45338f85e930d0ba6"},"schema_version":"1.0","source":{"id":"2404.04369","kind":"arxiv","version":1}},"canonical_sha256":"1caae20674e57e0b02c6c9723170a4ab717031db4aae1ebc773e49aafc1c5084","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1caae20674e57e0b02c6c9723170a4ab717031db4aae1ebc773e49aafc1c5084","first_computed_at":"2026-07-05T08:05:15.644088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:15.644088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2fZuELHpHuV9FMwgBR5QMCgDWiGhCzV6BQcShkdnnoIqklU6xjlpG+XTSb+0uT/08nFNNCtuDLhltShmttNUDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:15.644590Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.04369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7e65324cd160bd1c23389a6a445a01d8f35a1973178682c8fd8956e0cf65997","sha256:dc26dee3cb33cda599b23680d6c067f2d822e878b3b12bbe53184be05cb0c198"],"state_sha256":"b375a7858cb70535db5cdbdd790157d43ffc4c441b4b84413b0a152f55856524"}