{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:47VSVEO2SIN45BPZO7MBNB75XG","short_pith_number":"pith:47VSVEO2","canonical_record":{"source":{"id":"2407.17947","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-07-25T11:07:28Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"1a5ca05657cae0d942cdb6a2a15aed74f784b27461420ce510701f8ea9120a62","abstract_canon_sha256":"df16713817c2bdeeada39b06de2dca8f7e7bcee809bd482001b1aa8c18f69e3c"},"schema_version":"1.0"},"canonical_sha256":"e7eb2a91da921bce85f977d81687fdb981c309cd165404ab92abda000d9c3123","source":{"kind":"arxiv","id":"2407.17947","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17947","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17947v2","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17947","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"47VSVEO2SIN4","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_16","alias_value":"47VSVEO2SIN45BPZ","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_8","alias_value":"47VSVEO2","created_at":"2026-07-05T11:34:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:47VSVEO2SIN45BPZO7MBNB75XG","target":"record","payload":{"canonical_record":{"source":{"id":"2407.17947","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-07-25T11:07:28Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"1a5ca05657cae0d942cdb6a2a15aed74f784b27461420ce510701f8ea9120a62","abstract_canon_sha256":"df16713817c2bdeeada39b06de2dca8f7e7bcee809bd482001b1aa8c18f69e3c"},"schema_version":"1.0"},"canonical_sha256":"e7eb2a91da921bce85f977d81687fdb981c309cd165404ab92abda000d9c3123","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:42.689185Z","signature_b64":"o4sQmulyKqn3gWi9U+/ar5MBClJntzUYoxEfo3k6qKu9vLNSWKgXblQ2F6Q52zR0UHgmLu9gOau0xNin/KXNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7eb2a91da921bce85f977d81687fdb981c309cd165404ab92abda000d9c3123","last_reissued_at":"2026-07-05T11:34:42.688561Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:42.688561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.17947","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9c2RJ1dit8LNAbbdRGgPHYFSxX96TEESWlJKJP771fddqG2QFcHNng6+c5WYzAYKuKTQZ8RM2l8ORHgtcqQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:27:31.915089Z"},"content_sha256":"0ee62ee800b13c67711b022099a0e8b58018e4d2047725e4413e61e842b474af","schema_version":"1.0","event_id":"sha256:0ee62ee800b13c67711b022099a0e8b58018e4d2047725e4413e61e842b474af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:47VSVEO2SIN45BPZO7MBNB75XG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"Christoph Berkholz, Harry Vinall-Smeeth, Moritz Lichter","submitted_at":"2024-07-25T11:07:28Z","abstract_excerpt":"We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Tor\\'an and W\\\"orz (TOCL 2023) showed that there is a resolution refutation of narrow width $k$ for two graphs if and only if they can be distinguished in ($k+1$)-variable first-order logic (FO$^{k+1}$) and hence by a count-free variant of the $k$-dimensional Weisfeiler-Leman algorithm. While DAG-like narrow width $k$ resolution refutations have size at most $n^k$, tree-like refutations may be much larger. We show that there are graphs of order n, whose isomorphism can be refuted in narrow width $k$ b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17947","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17947/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oRc5VqTCefVUbOsbBLIeN+GrS/KKBNoQI70siN5bsOc6ZSbEwFHYBhPyrpOzF3G2i5IHQ1TE1zZ3DZ+7iLPRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:27:31.915976Z"},"content_sha256":"a7910e192f443cabd8c0c17a8f0e8312a405ff540322c3afe84963dd1a93b43f","schema_version":"1.0","event_id":"sha256:a7910e192f443cabd8c0c17a8f0e8312a405ff540322c3afe84963dd1a93b43f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47VSVEO2SIN45BPZO7MBNB75XG/bundle.json","state_url":"https://pith.science/pith/47VSVEO2SIN45BPZO7MBNB75XG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47VSVEO2SIN45BPZO7MBNB75XG/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":"2026-08-13T00:27:31Z","links":{"resolver":"https://pith.science/pith/47VSVEO2SIN45BPZO7MBNB75XG","bundle":"https://pith.science/pith/47VSVEO2SIN45BPZO7MBNB75XG/bundle.json","state":"https://pith.science/pith/47VSVEO2SIN45BPZO7MBNB75XG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47VSVEO2SIN45BPZO7MBNB75XG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:47VSVEO2SIN45BPZO7MBNB75XG","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":"df16713817c2bdeeada39b06de2dca8f7e7bcee809bd482001b1aa8c18f69e3c","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-07-25T11:07:28Z","title_canon_sha256":"1a5ca05657cae0d942cdb6a2a15aed74f784b27461420ce510701f8ea9120a62"},"schema_version":"1.0","source":{"id":"2407.17947","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17947","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17947v2","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17947","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"47VSVEO2SIN4","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_16","alias_value":"47VSVEO2SIN45BPZ","created_at":"2026-07-05T11:34:42Z"},{"alias_kind":"pith_short_8","alias_value":"47VSVEO2","created_at":"2026-07-05T11:34:42Z"}],"graph_snapshots":[{"event_id":"sha256:a7910e192f443cabd8c0c17a8f0e8312a405ff540322c3afe84963dd1a93b43f","target":"graph","created_at":"2026-07-05T11:34:42Z","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/2407.17947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Tor\\'an and W\\\"orz (TOCL 2023) showed that there is a resolution refutation of narrow width $k$ for two graphs if and only if they can be distinguished in ($k+1$)-variable first-order logic (FO$^{k+1}$) and hence by a count-free variant of the $k$-dimensional Weisfeiler-Leman algorithm. While DAG-like narrow width $k$ resolution refutations have size at most $n^k$, tree-like refutations may be much larger. We show that there are graphs of order n, whose isomorphism can be refuted in narrow width $k$ b","authors_text":"Christoph Berkholz, Harry Vinall-Smeeth, Moritz Lichter","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-07-25T11:07:28Z","title":"Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17947","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":"sha256:0ee62ee800b13c67711b022099a0e8b58018e4d2047725e4413e61e842b474af","target":"record","created_at":"2026-07-05T11:34:42Z","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":"df16713817c2bdeeada39b06de2dca8f7e7bcee809bd482001b1aa8c18f69e3c","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-07-25T11:07:28Z","title_canon_sha256":"1a5ca05657cae0d942cdb6a2a15aed74f784b27461420ce510701f8ea9120a62"},"schema_version":"1.0","source":{"id":"2407.17947","kind":"arxiv","version":2}},"canonical_sha256":"e7eb2a91da921bce85f977d81687fdb981c309cd165404ab92abda000d9c3123","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7eb2a91da921bce85f977d81687fdb981c309cd165404ab92abda000d9c3123","first_computed_at":"2026-07-05T11:34:42.688561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:42.688561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o4sQmulyKqn3gWi9U+/ar5MBClJntzUYoxEfo3k6qKu9vLNSWKgXblQ2F6Q52zR0UHgmLu9gOau0xNin/KXNBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:42.689185Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.17947","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ee62ee800b13c67711b022099a0e8b58018e4d2047725e4413e61e842b474af","sha256:a7910e192f443cabd8c0c17a8f0e8312a405ff540322c3afe84963dd1a93b43f"],"state_sha256":"6b1fc07285c4bdd95b95ed71f3ec0d57b59b6909631b90b15522b56db1bd44ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lg8f00b6bRSepYjIOXjmnLFs0nV/t7afdudQDpVJx/QyrbiJm5Rm8PHoXcTkLaq6TziKHx9R5hmb75jy11IsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:27:31.923389Z","bundle_sha256":"4f763418dfd5f260e17211eb3a456667cd1b4de09eb307f3b7fc261414c23cfc"}}