{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2IVCYOOHO3O66JQBLCJNASKGU7","short_pith_number":"pith:2IVCYOOH","canonical_record":{"source":{"id":"1103.2601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-14T08:20:40Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"e1681a47be9b1664f417ae14766728cf130de9d6aa0c4302f424d5dd3408900b","abstract_canon_sha256":"ffaa00dc0e569c2470ca6c7cc81c1dcaaf4730d494890ec338044d0388507c9a"},"schema_version":"1.0"},"canonical_sha256":"d22a2c39c776ddef26015892d04946a7eb3cab6f9493ec0d6a8e6e82b8172f11","source":{"kind":"arxiv","id":"1103.2601","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2601","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2601v1","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2601","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"pith_short_12","alias_value":"2IVCYOOHO3O6","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2IVCYOOHO3O66JQB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2IVCYOOH","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2IVCYOOHO3O66JQBLCJNASKGU7","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-14T08:20:40Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"e1681a47be9b1664f417ae14766728cf130de9d6aa0c4302f424d5dd3408900b","abstract_canon_sha256":"ffaa00dc0e569c2470ca6c7cc81c1dcaaf4730d494890ec338044d0388507c9a"},"schema_version":"1.0"},"canonical_sha256":"d22a2c39c776ddef26015892d04946a7eb3cab6f9493ec0d6a8e6e82b8172f11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:55.026203Z","signature_b64":"ltb7XJbf0MctwG0Q6kEiM19FbfCJmr9wWug7xckySzk45cP/KEiHKQOIUjVnqjUpgtKJKWG43Kcgkc+6mA2aCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d22a2c39c776ddef26015892d04946a7eb3cab6f9493ec0d6a8e6e82b8172f11","last_reissued_at":"2026-05-18T04:26:55.025491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:55.025491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2601","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":"2026-05-18T04:26:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIytGw5K7mngx3mz/04bEl9FtzB48eOa1DrLGqV/c5mf/s5nvVdarEOJBzXRQvOYij9LMY5LJ/TGxbGlUnR/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:06:06.709310Z"},"content_sha256":"bba8f389e3a0fa2936d84c409eea13d5c95683ae8530db934b1b180d3959b65b","schema_version":"1.0","event_id":"sha256:bba8f389e3a0fa2936d84c409eea13d5c95683ae8530db934b1b180d3959b65b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2IVCYOOHO3O66JQBLCJNASKGU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fast algorithm to remove proper and homogenous pairs of cliques (while preserving some graph invariants)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.OC","authors_text":"Claudia Snels, Gianpaolo Oriolo, Yuri Faenza","submitted_at":"2011-03-14T08:20:40Z","abstract_excerpt":"We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be embedded in a simple algorithm that in at most |E(G)| steps builds a new graph G' without proper and homogeneous pairs of cliques, and such that G and G' agree on the value of some relevant invariant (or property)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2601","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":"2026-05-18T04:26:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8s3dhypISwZVwLr41RgYdA2NjZE0g0s5nJS8MfeWHRzJxlbhirqWgfd+ltW+o2VaQgc3Ht5GZjmDMbwKQ8wfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:06:06.710072Z"},"content_sha256":"3c25904fde412645cb2694fe3db35fb584e59bac8a6cba3ac8fccd400912bc82","schema_version":"1.0","event_id":"sha256:3c25904fde412645cb2694fe3db35fb584e59bac8a6cba3ac8fccd400912bc82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IVCYOOHO3O66JQBLCJNASKGU7/bundle.json","state_url":"https://pith.science/pith/2IVCYOOHO3O66JQBLCJNASKGU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IVCYOOHO3O66JQBLCJNASKGU7/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":"2026-05-31T16:06:06Z","links":{"resolver":"https://pith.science/pith/2IVCYOOHO3O66JQBLCJNASKGU7","bundle":"https://pith.science/pith/2IVCYOOHO3O66JQBLCJNASKGU7/bundle.json","state":"https://pith.science/pith/2IVCYOOHO3O66JQBLCJNASKGU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IVCYOOHO3O66JQBLCJNASKGU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2IVCYOOHO3O66JQBLCJNASKGU7","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":"ffaa00dc0e569c2470ca6c7cc81c1dcaaf4730d494890ec338044d0388507c9a","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-14T08:20:40Z","title_canon_sha256":"e1681a47be9b1664f417ae14766728cf130de9d6aa0c4302f424d5dd3408900b"},"schema_version":"1.0","source":{"id":"1103.2601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2601","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2601v1","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2601","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"pith_short_12","alias_value":"2IVCYOOHO3O6","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2IVCYOOHO3O66JQB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2IVCYOOH","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:3c25904fde412645cb2694fe3db35fb584e59bac8a6cba3ac8fccd400912bc82","target":"graph","created_at":"2026-05-18T04:26:55Z","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":"We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be embedded in a simple algorithm that in at most |E(G)| steps builds a new graph G' without proper and homogeneous pairs of cliques, and such that G and G' agree on the value of some relevant invariant (or property).","authors_text":"Claudia Snels, Gianpaolo Oriolo, Yuri Faenza","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-14T08:20:40Z","title":"A fast algorithm to remove proper and homogenous pairs of cliques (while preserving some graph invariants)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2601","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:bba8f389e3a0fa2936d84c409eea13d5c95683ae8530db934b1b180d3959b65b","target":"record","created_at":"2026-05-18T04:26:55Z","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":"ffaa00dc0e569c2470ca6c7cc81c1dcaaf4730d494890ec338044d0388507c9a","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-14T08:20:40Z","title_canon_sha256":"e1681a47be9b1664f417ae14766728cf130de9d6aa0c4302f424d5dd3408900b"},"schema_version":"1.0","source":{"id":"1103.2601","kind":"arxiv","version":1}},"canonical_sha256":"d22a2c39c776ddef26015892d04946a7eb3cab6f9493ec0d6a8e6e82b8172f11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d22a2c39c776ddef26015892d04946a7eb3cab6f9493ec0d6a8e6e82b8172f11","first_computed_at":"2026-05-18T04:26:55.025491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:55.025491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ltb7XJbf0MctwG0Q6kEiM19FbfCJmr9wWug7xckySzk45cP/KEiHKQOIUjVnqjUpgtKJKWG43Kcgkc+6mA2aCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:55.026203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bba8f389e3a0fa2936d84c409eea13d5c95683ae8530db934b1b180d3959b65b","sha256:3c25904fde412645cb2694fe3db35fb584e59bac8a6cba3ac8fccd400912bc82"],"state_sha256":"7b683e5bf3536f4d36f2b224741661f941cfee03e9d8350097dea54ac684b8fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"plP2sOm9+Ar4dVnLRN9m9P+rHL/rfg8gqPz/HqdDnhXUt7Mp8sWrLG7hsuDTJ6Gp6K1FnCODj6Um5dQpAQ+zDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:06:06.714374Z","bundle_sha256":"b7b408133bfa07a70e680929f1ff0972598eaceed72cf89b89dd16ee8425647b"}}