{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:Y4GK3LNKETUKIH3NZS5FGQTNLC","short_pith_number":"pith:Y4GK3LNK","canonical_record":{"source":{"id":"2307.15032","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-07-27T17:39:14Z","cross_cats_sorted":[],"title_canon_sha256":"94883bd8967f220842c5567708d6e2651766fbd34a0adbb9cfe8faf21ba5ff4d","abstract_canon_sha256":"449dd739629f38018f63dcffbd5e38c3e147d2d01e35894f2a75af047c6a7a0a"},"schema_version":"1.0"},"canonical_sha256":"c70cadadaa24e8a41f6dccba53426d58a129070d1e92a55fa4ec22252fc29d6e","source":{"kind":"arxiv","id":"2307.15032","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.15032","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"2307.15032v2","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.15032","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y4GK3LNKETUK","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y4GK3LNKETUKIH3N","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y4GK3LNK","created_at":"2026-07-05T09:22:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:Y4GK3LNKETUKIH3NZS5FGQTNLC","target":"record","payload":{"canonical_record":{"source":{"id":"2307.15032","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-07-27T17:39:14Z","cross_cats_sorted":[],"title_canon_sha256":"94883bd8967f220842c5567708d6e2651766fbd34a0adbb9cfe8faf21ba5ff4d","abstract_canon_sha256":"449dd739629f38018f63dcffbd5e38c3e147d2d01e35894f2a75af047c6a7a0a"},"schema_version":"1.0"},"canonical_sha256":"c70cadadaa24e8a41f6dccba53426d58a129070d1e92a55fa4ec22252fc29d6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:22:59.888962Z","signature_b64":"jQME1/FywpYMLuRwAd9IdNflrrwmth2+zC07lZFnuaLUD4G11L2idNTat1SOlUgxjcgEnkxIe/EWPrs0DwQRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c70cadadaa24e8a41f6dccba53426d58a129070d1e92a55fa4ec22252fc29d6e","last_reissued_at":"2026-07-05T09:22:59.888550Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:22:59.888550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.15032","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":"2026-07-05T09:22:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RkMNYMPUgifl5D7ufldj5ShdGleI3pVUMSK3+gYVBg7kZnYiEXsu339UTsuad8XpgDcpmvGItAW7yZtlN/vvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T04:31:02.715954Z"},"content_sha256":"dfdee30f230d14b2fd551a379c8acd13d92a69c3cd7c08164af8b176c51b1820","schema_version":"1.0","event_id":"sha256:dfdee30f230d14b2fd551a379c8acd13d92a69c3cd7c08164af8b176c51b1820"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:Y4GK3LNKETUKIH3NZS5FGQTNLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Induced subgraph density. V. All paths approach Erdos-Hajnal","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Paul Seymour, Tung Nguyen","submitted_at":"2023-07-27T17:39:14Z","abstract_excerpt":"The Erd\\H{o}s-Hajnal conjecture says that, for every graph $H$, there exists $c>0$ such that every $H$-free graph on $n$ vertices has a clique or stable set of size at least $n^c$. In this paper we are concerned with the case when $H$ is a path. The conjecture has been proved for paths with at most five vertices, but not for longer paths. We prove that the conjecture is ``nearly'' true for all paths: for every path $H$, all $H$-free graphs with $n$ vertices have cliques or stable sets of size at least $2^{(\\log n)^{1-o(1)}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15032","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/2307.15032/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":"2026-07-05T09:22:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elQcpUCYStaTj4DvvigVgPuo+MgaaFET2fGLGkynvYGH4Cv3LA0M7J9pTv0bzxYtRfc9luUQDjY1otm9Yxg8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T04:31:02.716466Z"},"content_sha256":"902cd540e56f70248848a7ce2ea2b74b59c7929e4dc43dec371a5e1b0b66b8a9","schema_version":"1.0","event_id":"sha256:902cd540e56f70248848a7ce2ea2b74b59c7929e4dc43dec371a5e1b0b66b8a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/bundle.json","state_url":"https://pith.science/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/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":"2026-08-19T04:31:02Z","links":{"resolver":"https://pith.science/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC","bundle":"https://pith.science/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/bundle.json","state":"https://pith.science/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4GK3LNKETUKIH3NZS5FGQTNLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Y4GK3LNKETUKIH3NZS5FGQTNLC","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":"449dd739629f38018f63dcffbd5e38c3e147d2d01e35894f2a75af047c6a7a0a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-07-27T17:39:14Z","title_canon_sha256":"94883bd8967f220842c5567708d6e2651766fbd34a0adbb9cfe8faf21ba5ff4d"},"schema_version":"1.0","source":{"id":"2307.15032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.15032","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"2307.15032v2","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.15032","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y4GK3LNKETUK","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y4GK3LNKETUKIH3N","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y4GK3LNK","created_at":"2026-07-05T09:22:59Z"}],"graph_snapshots":[{"event_id":"sha256:902cd540e56f70248848a7ce2ea2b74b59c7929e4dc43dec371a5e1b0b66b8a9","target":"graph","created_at":"2026-07-05T09:22:59Z","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/2307.15032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Erd\\H{o}s-Hajnal conjecture says that, for every graph $H$, there exists $c>0$ such that every $H$-free graph on $n$ vertices has a clique or stable set of size at least $n^c$. In this paper we are concerned with the case when $H$ is a path. The conjecture has been proved for paths with at most five vertices, but not for longer paths. We prove that the conjecture is ``nearly'' true for all paths: for every path $H$, all $H$-free graphs with $n$ vertices have cliques or stable sets of size at least $2^{(\\log n)^{1-o(1)}}$.","authors_text":"Alex Scott, Paul Seymour, Tung Nguyen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-07-27T17:39:14Z","title":"Induced subgraph density. V. All paths approach Erdos-Hajnal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15032","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:dfdee30f230d14b2fd551a379c8acd13d92a69c3cd7c08164af8b176c51b1820","target":"record","created_at":"2026-07-05T09:22:59Z","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":"449dd739629f38018f63dcffbd5e38c3e147d2d01e35894f2a75af047c6a7a0a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-07-27T17:39:14Z","title_canon_sha256":"94883bd8967f220842c5567708d6e2651766fbd34a0adbb9cfe8faf21ba5ff4d"},"schema_version":"1.0","source":{"id":"2307.15032","kind":"arxiv","version":2}},"canonical_sha256":"c70cadadaa24e8a41f6dccba53426d58a129070d1e92a55fa4ec22252fc29d6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c70cadadaa24e8a41f6dccba53426d58a129070d1e92a55fa4ec22252fc29d6e","first_computed_at":"2026-07-05T09:22:59.888550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:22:59.888550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQME1/FywpYMLuRwAd9IdNflrrwmth2+zC07lZFnuaLUD4G11L2idNTat1SOlUgxjcgEnkxIe/EWPrs0DwQRAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:22:59.888962Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.15032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfdee30f230d14b2fd551a379c8acd13d92a69c3cd7c08164af8b176c51b1820","sha256:902cd540e56f70248848a7ce2ea2b74b59c7929e4dc43dec371a5e1b0b66b8a9"],"state_sha256":"0af622eb1dc316b2710af031d2a04922ade787d05da9fb74f100ff90abdab3ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3bHU9QJh+CwiB4YRnlFZarjobLfzfc6eUY01EqsM8NBsCrm3QZC5vN35ZjcbpPpACAwDZg21nHhV2qy4PWkAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T04:31:02.722499Z","bundle_sha256":"edf4c0097a6bd06e56ee3cc20fb82f7c74b7d636c280e11310660974626c8df7"}}