{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:UDSC2IXWKKPD6NXQ3SZVEV46NV","short_pith_number":"pith:UDSC2IXW","canonical_record":{"source":{"id":"2203.03375","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-07T13:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"85d3a3fbf9a3c3430fdc9fbb26072ae3b315cc9344043f0979b85168b247ab7a","abstract_canon_sha256":"c1dad5bd050cc60eb284f1e7de4e79b88f66e80411da8410747c3d22076d6c0c"},"schema_version":"1.0"},"canonical_sha256":"a0e42d22f6529e3f36f0dcb352579e6d55d0bf02cde726e6b39c07875cffde17","source":{"kind":"arxiv","id":"2203.03375","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03375","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03375v2","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03375","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"UDSC2IXWKKPD","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_16","alias_value":"UDSC2IXWKKPD6NXQ","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_8","alias_value":"UDSC2IXW","created_at":"2026-07-05T05:27:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:UDSC2IXWKKPD6NXQ3SZVEV46NV","target":"record","payload":{"canonical_record":{"source":{"id":"2203.03375","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-07T13:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"85d3a3fbf9a3c3430fdc9fbb26072ae3b315cc9344043f0979b85168b247ab7a","abstract_canon_sha256":"c1dad5bd050cc60eb284f1e7de4e79b88f66e80411da8410747c3d22076d6c0c"},"schema_version":"1.0"},"canonical_sha256":"a0e42d22f6529e3f36f0dcb352579e6d55d0bf02cde726e6b39c07875cffde17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:27:47.251564Z","signature_b64":"pmFNPqTBsTMgLq5fOK3gCemmeoZ1D2zDU189N44zJOW40ccAYJ8mUPp0NT1oQyboMMb65K5xeB3ihnXjN17qDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0e42d22f6529e3f36f0dcb352579e6d55d0bf02cde726e6b39c07875cffde17","last_reissued_at":"2026-07-05T05:27:47.251057Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:27:47.251057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.03375","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":"2026-07-05T05:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDd2KI9FL3VMgJpQn9PH4FpnEyJqky68Gxyv3Ye94IXwtwFzFQv01KUoP2O/WESd4X2y0iZ3N0A6rVcuscHBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:03:56.922262Z"},"content_sha256":"e2c150ee6a24437bd8d39665f9d60f5e53632b3bd593363ae9b590e656520876","schema_version":"1.0","event_id":"sha256:e2c150ee6a24437bd8d39665f9d60f5e53632b3bd593363ae9b590e656520876"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:UDSC2IXWKKPD6NXQ3SZVEV46NV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational exponents near two","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Conlon, Oliver Janzer","submitted_at":"2022-03-07T13:32:50Z","abstract_excerpt":"A longstanding conjecture of Erd\\H{o}s and Simonovits states that for every rational $r$ between $1$ and $2$ there is a graph $H$ such that the largest number of edges in an $H$-free graph on $n$ vertices is $\\Theta(n^r)$. Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form $2 - a/b$ with $b$ sufficiently large in terms of $a$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03375","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/2203.03375/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":"2026-07-05T05:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gyC4V8qEyyRyxeWQD1nptCMkR2IKngwhQdZdMekoFcvuPMG/8rUctAZvBkku+TqNLjVwI2iPvZMnW3jqkPYtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:03:56.923137Z"},"content_sha256":"f82aee37412b0c1fa0ccec394cfec065d717dbdea57f6f3e01a55ff7fa3a02ce","schema_version":"1.0","event_id":"sha256:f82aee37412b0c1fa0ccec394cfec065d717dbdea57f6f3e01a55ff7fa3a02ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/bundle.json","state_url":"https://pith.science/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/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":"2026-08-04T23:03:56Z","links":{"resolver":"https://pith.science/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV","bundle":"https://pith.science/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/bundle.json","state":"https://pith.science/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDSC2IXWKKPD6NXQ3SZVEV46NV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UDSC2IXWKKPD6NXQ3SZVEV46NV","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":"c1dad5bd050cc60eb284f1e7de4e79b88f66e80411da8410747c3d22076d6c0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-07T13:32:50Z","title_canon_sha256":"85d3a3fbf9a3c3430fdc9fbb26072ae3b315cc9344043f0979b85168b247ab7a"},"schema_version":"1.0","source":{"id":"2203.03375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03375","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03375v2","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03375","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"UDSC2IXWKKPD","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_16","alias_value":"UDSC2IXWKKPD6NXQ","created_at":"2026-07-05T05:27:47Z"},{"alias_kind":"pith_short_8","alias_value":"UDSC2IXW","created_at":"2026-07-05T05:27:47Z"}],"graph_snapshots":[{"event_id":"sha256:f82aee37412b0c1fa0ccec394cfec065d717dbdea57f6f3e01a55ff7fa3a02ce","target":"graph","created_at":"2026-07-05T05:27:47Z","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/2203.03375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A longstanding conjecture of Erd\\H{o}s and Simonovits states that for every rational $r$ between $1$ and $2$ there is a graph $H$ such that the largest number of edges in an $H$-free graph on $n$ vertices is $\\Theta(n^r)$. Answering a question raised by Jiang, Jiang and Ma, we show that the conjecture holds for all rationals of the form $2 - a/b$ with $b$ sufficiently large in terms of $a$.","authors_text":"David Conlon, Oliver Janzer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-07T13:32:50Z","title":"Rational exponents near two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03375","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:e2c150ee6a24437bd8d39665f9d60f5e53632b3bd593363ae9b590e656520876","target":"record","created_at":"2026-07-05T05:27:47Z","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":"c1dad5bd050cc60eb284f1e7de4e79b88f66e80411da8410747c3d22076d6c0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-03-07T13:32:50Z","title_canon_sha256":"85d3a3fbf9a3c3430fdc9fbb26072ae3b315cc9344043f0979b85168b247ab7a"},"schema_version":"1.0","source":{"id":"2203.03375","kind":"arxiv","version":2}},"canonical_sha256":"a0e42d22f6529e3f36f0dcb352579e6d55d0bf02cde726e6b39c07875cffde17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0e42d22f6529e3f36f0dcb352579e6d55d0bf02cde726e6b39c07875cffde17","first_computed_at":"2026-07-05T05:27:47.251057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:27:47.251057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pmFNPqTBsTMgLq5fOK3gCemmeoZ1D2zDU189N44zJOW40ccAYJ8mUPp0NT1oQyboMMb65K5xeB3ihnXjN17qDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:27:47.251564Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.03375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2c150ee6a24437bd8d39665f9d60f5e53632b3bd593363ae9b590e656520876","sha256:f82aee37412b0c1fa0ccec394cfec065d717dbdea57f6f3e01a55ff7fa3a02ce"],"state_sha256":"d6907057ee63653db097e344d5231a56c986bf65cec798ae214882d73f9599a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b3kRmySpCEhI9HmfoJBNt/A8cM4jTUsGkhiXZGxc7XsncTv/h/tGOgfW0FjqeyPQSvZAudMDAiO0xBeLAK4rBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T23:03:56.930391Z","bundle_sha256":"769a1013c19995fe86417e1c7be14594da79a65e82280f678aaa4ea554d8e989"}}