{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6VGNULUPCVJ3EBZ5AB4YXAOTQT","short_pith_number":"pith:6VGNULUP","canonical_record":{"source":{"id":"1608.08990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T18:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"1005e03182d20a5e42b1694ff686b99daed53159ac12a1ea65947a435f301f40","abstract_canon_sha256":"76a60fbd2090d169b14a8d8da629ccde46e0e7e371912647a7debec8925f151e"},"schema_version":"1.0"},"canonical_sha256":"f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f","source":{"kind":"arxiv","id":"1608.08990","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08990","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08990v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08990","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"6VGNULUPCVJ3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VGNULUPCVJ3EBZ5","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VGNULUP","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6VGNULUPCVJ3EBZ5AB4YXAOTQT","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T18:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"1005e03182d20a5e42b1694ff686b99daed53159ac12a1ea65947a435f301f40","abstract_canon_sha256":"76a60fbd2090d169b14a8d8da629ccde46e0e7e371912647a7debec8925f151e"},"schema_version":"1.0"},"canonical_sha256":"f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:39.507500Z","signature_b64":"Wi2etQqTs+bzL3NNN5rs8WYjlSxx8Q76OW2Hknv0E3A9GcRFwhrclEEIHz1nTJh8dRQQxNyBzEnwOO0hyWF0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f","last_reissued_at":"2026-05-18T01:06:39.506727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:39.506727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08990","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":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MC1Gg6CMn2o8CwViY2Hix8jKqigC5uCHLNwJDdlQHVNvRE7gJnsopj3Q6WSSnk7ANTUIiIA12nrmv9Qhw1SAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:55:58.386991Z"},"content_sha256":"2bc9fa864c9ca81fc5f02c38cb4184a588fc764d433663b9907041fdad29f957","schema_version":"1.0","event_id":"sha256:2bc9fa864c9ca81fc5f02c38cb4184a588fc764d433663b9907041fdad29f957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6VGNULUPCVJ3EBZ5AB4YXAOTQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The structure of typical eye-free graphs and a Turan-type result for two weighted colours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Keevash, William Lochet","submitted_at":"2016-08-31T18:46:34Z","abstract_excerpt":"The $(a,b)$-eye is the graph $I_{a,b} = K_{a+b}-K_b$ obtained by deleting the edges of a clique of size $b$ from a clique of size $a+b$. We show that for any $a,b \\ge 2$ and $p \\in (0,1)$, if we condition the random graph $G \\sim G(n,p)$ on having no induced copy of $I_{a,b}$, then with high probability $G$ is close to an $a$-partite graph or the complement of a $(b-1)$-partite graph. Our proof uses the recently developed theory of hypergraph containers, and a stability result for an extremal problem with two weighted colours. We also apply the stability method to obtain an exact Tur\\'an-type "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08990","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":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBZdpabCqtIq5cgoUiywj8uwkB0fcvpMVfFkEf8i9Cg1Zj+f+4KROSbnuVm6p/l8ACIdDvJVy7Xgcoyos3CnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:55:58.387632Z"},"content_sha256":"266ae1b930a2ee68e0c163c65a1b4ecf2e6b508310588a12921dcc93dd1e912a","schema_version":"1.0","event_id":"sha256:266ae1b930a2ee68e0c163c65a1b4ecf2e6b508310588a12921dcc93dd1e912a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/bundle.json","state_url":"https://pith.science/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/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":"2026-05-27T03:55:58Z","links":{"resolver":"https://pith.science/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT","bundle":"https://pith.science/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/bundle.json","state":"https://pith.science/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VGNULUPCVJ3EBZ5AB4YXAOTQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6VGNULUPCVJ3EBZ5AB4YXAOTQT","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":"76a60fbd2090d169b14a8d8da629ccde46e0e7e371912647a7debec8925f151e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T18:46:34Z","title_canon_sha256":"1005e03182d20a5e42b1694ff686b99daed53159ac12a1ea65947a435f301f40"},"schema_version":"1.0","source":{"id":"1608.08990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08990","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08990v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08990","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"6VGNULUPCVJ3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VGNULUPCVJ3EBZ5","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VGNULUP","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:266ae1b930a2ee68e0c163c65a1b4ecf2e6b508310588a12921dcc93dd1e912a","target":"graph","created_at":"2026-05-18T01:06:39Z","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 $(a,b)$-eye is the graph $I_{a,b} = K_{a+b}-K_b$ obtained by deleting the edges of a clique of size $b$ from a clique of size $a+b$. We show that for any $a,b \\ge 2$ and $p \\in (0,1)$, if we condition the random graph $G \\sim G(n,p)$ on having no induced copy of $I_{a,b}$, then with high probability $G$ is close to an $a$-partite graph or the complement of a $(b-1)$-partite graph. Our proof uses the recently developed theory of hypergraph containers, and a stability result for an extremal problem with two weighted colours. We also apply the stability method to obtain an exact Tur\\'an-type ","authors_text":"Peter Keevash, William Lochet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T18:46:34Z","title":"The structure of typical eye-free graphs and a Turan-type result for two weighted colours"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08990","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":"sha256:2bc9fa864c9ca81fc5f02c38cb4184a588fc764d433663b9907041fdad29f957","target":"record","created_at":"2026-05-18T01:06:39Z","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":"76a60fbd2090d169b14a8d8da629ccde46e0e7e371912647a7debec8925f151e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-31T18:46:34Z","title_canon_sha256":"1005e03182d20a5e42b1694ff686b99daed53159ac12a1ea65947a435f301f40"},"schema_version":"1.0","source":{"id":"1608.08990","kind":"arxiv","version":1}},"canonical_sha256":"f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f","first_computed_at":"2026-05-18T01:06:39.506727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:39.506727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wi2etQqTs+bzL3NNN5rs8WYjlSxx8Q76OW2Hknv0E3A9GcRFwhrclEEIHz1nTJh8dRQQxNyBzEnwOO0hyWF0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:39.507500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bc9fa864c9ca81fc5f02c38cb4184a588fc764d433663b9907041fdad29f957","sha256:266ae1b930a2ee68e0c163c65a1b4ecf2e6b508310588a12921dcc93dd1e912a"],"state_sha256":"373c6e47b5c56ac4256a6169daf0fafb5a5f6090769fce0b83c54eeca3626ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5Lhcc9Hnt25kSS94i8WZ/SYvaLQFiYQtOipVN9Jj4MZsjONpJBaem9pdEodup1dN/2+RLvYZt4MDpqQliwvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:55:58.390664Z","bundle_sha256":"006cd6627bbab33f81008dfd862e6f57b86dd41dadf29edf5ac51f7fd5238379"}}