{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BV5BZIMBL653X5EULHXY7RPC7D","short_pith_number":"pith:BV5BZIMB","canonical_record":{"source":{"id":"2407.19026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-26T18:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"8cb6d98df03dd5e86f5b3e8cfecc920f353b726372c30559a0198596adb622a5","abstract_canon_sha256":"44ad0148db01ce11116419faf020f6563aa041dd743714e20001a55a8b723064"},"schema_version":"1.0"},"canonical_sha256":"0d7a1ca1815fbbbbf49459ef8fc5e2f8caf8abe5b81cdb976006108a9ecb5054","source":{"kind":"arxiv","id":"2407.19026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.19026","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2407.19026v1","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19026","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"BV5BZIMBL653","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"BV5BZIMBL653X5EU","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"BV5BZIMB","created_at":"2026-07-05T08:49:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BV5BZIMBL653X5EULHXY7RPC7D","target":"record","payload":{"canonical_record":{"source":{"id":"2407.19026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-26T18:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"8cb6d98df03dd5e86f5b3e8cfecc920f353b726372c30559a0198596adb622a5","abstract_canon_sha256":"44ad0148db01ce11116419faf020f6563aa041dd743714e20001a55a8b723064"},"schema_version":"1.0"},"canonical_sha256":"0d7a1ca1815fbbbbf49459ef8fc5e2f8caf8abe5b81cdb976006108a9ecb5054","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:12.572118Z","signature_b64":"1xZ32SvntHd8XXPeCZh0do6WRQqEJC4HvMys+aVx2w4F9hy1YU+hnJUDad62+Dzw37S3cGvg/IZrntd7v1ZZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d7a1ca1815fbbbbf49459ef8fc5e2f8caf8abe5b81cdb976006108a9ecb5054","last_reissued_at":"2026-07-05T08:49:12.571645Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:12.571645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.19026","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":"2026-07-05T08:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/293xc/V/koV7kejL/TEL/Y1DTkfWQIzbYNYj8WoCByttflBsZokgbZODncRAKOCe/m+lCgs6PdS0aJl1T2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:50:59.318916Z"},"content_sha256":"ff630a74b80b9416762fece818b9a5988a3e0bd8b6d07ac08d3defc98fbc6ea7","schema_version":"1.0","event_id":"sha256:ff630a74b80b9416762fece818b9a5988a3e0bd8b6d07ac08d3defc98fbc6ea7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BV5BZIMBL653X5EULHXY7RPC7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimizing the CGMS upper bound on Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis Wei, Ndiame Ndiaye, Parth Gupta, Sergey Norin","submitted_at":"2024-07-26T18:08:35Z","abstract_excerpt":"In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the diagonal Ramsey numbers since 1935. We shorten their proof, replacing the underlying book algorithm with a simple inductive statement. This modification allows us\n  - to give a very short proof of an improved upper bound on the off-diagonal Ramsey numbers, which extends to the multicolor setting, and\n  - to clarify the dependence of the bounds on underlying parameters and optimize these parameters, obtaining, in particular, an upper bound $$R(k,k) \\leq (3.8)^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19026","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.19026/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":"2026-07-05T08:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmL2DGBgg0YhBuj9VJ9VMu5DtycNTl416D82A0R2jzGnnzTQQqFClY9rrBjkeSegnht11SblUDk22d5+ZmSDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:50:59.319436Z"},"content_sha256":"b83acb869ce37ac8fc2a575f3b5b50cb56c27b7bbd7a56ec256340bba0e5a8ec","schema_version":"1.0","event_id":"sha256:b83acb869ce37ac8fc2a575f3b5b50cb56c27b7bbd7a56ec256340bba0e5a8ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BV5BZIMBL653X5EULHXY7RPC7D/bundle.json","state_url":"https://pith.science/pith/BV5BZIMBL653X5EULHXY7RPC7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BV5BZIMBL653X5EULHXY7RPC7D/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":"2026-08-04T16:50:59Z","links":{"resolver":"https://pith.science/pith/BV5BZIMBL653X5EULHXY7RPC7D","bundle":"https://pith.science/pith/BV5BZIMBL653X5EULHXY7RPC7D/bundle.json","state":"https://pith.science/pith/BV5BZIMBL653X5EULHXY7RPC7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BV5BZIMBL653X5EULHXY7RPC7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BV5BZIMBL653X5EULHXY7RPC7D","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":"44ad0148db01ce11116419faf020f6563aa041dd743714e20001a55a8b723064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-26T18:08:35Z","title_canon_sha256":"8cb6d98df03dd5e86f5b3e8cfecc920f353b726372c30559a0198596adb622a5"},"schema_version":"1.0","source":{"id":"2407.19026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.19026","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2407.19026v1","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19026","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"BV5BZIMBL653","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"BV5BZIMBL653X5EU","created_at":"2026-07-05T08:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"BV5BZIMB","created_at":"2026-07-05T08:49:12Z"}],"graph_snapshots":[{"event_id":"sha256:b83acb869ce37ac8fc2a575f3b5b50cb56c27b7bbd7a56ec256340bba0e5a8ec","target":"graph","created_at":"2026-07-05T08:49:12Z","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/2407.19026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the diagonal Ramsey numbers since 1935. We shorten their proof, replacing the underlying book algorithm with a simple inductive statement. This modification allows us\n  - to give a very short proof of an improved upper bound on the off-diagonal Ramsey numbers, which extends to the multicolor setting, and\n  - to clarify the dependence of the bounds on underlying parameters and optimize these parameters, obtaining, in particular, an upper bound $$R(k,k) \\leq (3.8)^","authors_text":"Louis Wei, Ndiame Ndiaye, Parth Gupta, Sergey Norin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-26T18:08:35Z","title":"Optimizing the CGMS upper bound on Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19026","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:ff630a74b80b9416762fece818b9a5988a3e0bd8b6d07ac08d3defc98fbc6ea7","target":"record","created_at":"2026-07-05T08:49:12Z","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":"44ad0148db01ce11116419faf020f6563aa041dd743714e20001a55a8b723064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-26T18:08:35Z","title_canon_sha256":"8cb6d98df03dd5e86f5b3e8cfecc920f353b726372c30559a0198596adb622a5"},"schema_version":"1.0","source":{"id":"2407.19026","kind":"arxiv","version":1}},"canonical_sha256":"0d7a1ca1815fbbbbf49459ef8fc5e2f8caf8abe5b81cdb976006108a9ecb5054","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7a1ca1815fbbbbf49459ef8fc5e2f8caf8abe5b81cdb976006108a9ecb5054","first_computed_at":"2026-07-05T08:49:12.571645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:49:12.571645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1xZ32SvntHd8XXPeCZh0do6WRQqEJC4HvMys+aVx2w4F9hy1YU+hnJUDad62+Dzw37S3cGvg/IZrntd7v1ZZDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:49:12.572118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.19026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff630a74b80b9416762fece818b9a5988a3e0bd8b6d07ac08d3defc98fbc6ea7","sha256:b83acb869ce37ac8fc2a575f3b5b50cb56c27b7bbd7a56ec256340bba0e5a8ec"],"state_sha256":"b1a7cb96eb9f022ad51386a159c0b75efcb4cc1147931619f7611182941240a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/qEzaEcaBnZwwtw8f2Vsnuxn8l6MzdK1kTtnC3cUfpDSu9kPzbBJvm8KFvLp+4uPPAMN4Tvv74b2mnFe3HB9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:50:59.328191Z","bundle_sha256":"1d35be3beb4ae6364c539e0b5f65707120bc9afddf4a61682dfa2ac496c5c561"}}