{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OG4TIFJ4QHWPR6C6EUZE34QHHO","short_pith_number":"pith:OG4TIFJ4","canonical_record":{"source":{"id":"1801.00474","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T16:55:10Z","cross_cats_sorted":[],"title_canon_sha256":"1a4fe05c80447963dc589011f76f5e9369c664c92c8cc1b0d546be765e20bd69","abstract_canon_sha256":"94f3fdff2c0642b3836f64983872d8295e5cea1a1f3936aab8287bb74919e1e2"},"schema_version":"1.0"},"canonical_sha256":"71b934153c81ecf8f85e25324df2073b9c3b011767afff928d6d8e61ab3b38f9","source":{"kind":"arxiv","id":"1801.00474","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00474","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00474v2","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00474","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"OG4TIFJ4QHWP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OG4TIFJ4QHWPR6C6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OG4TIFJ4","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OG4TIFJ4QHWPR6C6EUZE34QHHO","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00474","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T16:55:10Z","cross_cats_sorted":[],"title_canon_sha256":"1a4fe05c80447963dc589011f76f5e9369c664c92c8cc1b0d546be765e20bd69","abstract_canon_sha256":"94f3fdff2c0642b3836f64983872d8295e5cea1a1f3936aab8287bb74919e1e2"},"schema_version":"1.0"},"canonical_sha256":"71b934153c81ecf8f85e25324df2073b9c3b011767afff928d6d8e61ab3b38f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:56.545441Z","signature_b64":"aKAxEcGifbVB3BRtdHMiamYVW0FvR+F7/iJOHFAaJFprqv5KXf9dZpo8mPpky9to/5PR7r5rwFcH+31GQ5y+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71b934153c81ecf8f85e25324df2073b9c3b011767afff928d6d8e61ab3b38f9","last_reissued_at":"2026-05-18T00:19:56.544681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:56.544681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00474","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":"2026-05-18T00:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5Coit8dGYRN46faTaIk9D7BUskLtqlUcNh9k0Elbu4k6vSAQaNi+9Y9FgNpZKFICQiC7i2S5+bf614f639rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:55:29.451131Z"},"content_sha256":"7e7db0b22d9f64f38f1da8b5f12b671355130c585d96940af0716b65028207c6","schema_version":"1.0","event_id":"sha256:7e7db0b22d9f64f38f1da8b5f12b671355130c585d96940af0716b65028207c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OG4TIFJ4QHWPR6C6EUZE34QHHO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anti-Ramsey Multiplicities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jessica De Silva, Michael Tait, Michael Young, Ruifan Yang, Xiang Si, Yunus Tun\\c{c}bilek","submitted_at":"2018-01-01T16:55:10Z","abstract_excerpt":"The Ramsey multiplicity constant of a graph $H$ is the minimum proportion of copies of $H$ in the complete graph which are monochromatic under an edge-coloring of $K_n$ as $n$ goes to infinity. Graphs for which this minimum is asymptotically achieved by taking a random coloring are called {\\em common}, and common graphs have been studied extensively, leading to the Burr-Rosta conjecture and Sidorenko's conjecture. Erd\\H{o}s and S\\'os asked what the maximum number of rainbow triangles is in a $3$-coloring of the edge set of $K_n$, a rainbow version of the Ramsey multiplicity question. A graph $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00474","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":""},"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":"2026-05-18T00:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9v1mQcRbrKM9+mfH/2He+yxpr9H+STQBtNv27P54ykuw3qvV8MR5e6DQcK9ZlqCA+uaFCykC+5wxS3+32GzxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:55:29.451495Z"},"content_sha256":"9e1e5d73eea50ed899cdea79b212883dfc489c37263074899fbf42fbed52531f","schema_version":"1.0","event_id":"sha256:9e1e5d73eea50ed899cdea79b212883dfc489c37263074899fbf42fbed52531f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/bundle.json","state_url":"https://pith.science/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/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":"2026-06-04T06:55:29Z","links":{"resolver":"https://pith.science/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO","bundle":"https://pith.science/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/bundle.json","state":"https://pith.science/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OG4TIFJ4QHWPR6C6EUZE34QHHO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OG4TIFJ4QHWPR6C6EUZE34QHHO","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":"94f3fdff2c0642b3836f64983872d8295e5cea1a1f3936aab8287bb74919e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T16:55:10Z","title_canon_sha256":"1a4fe05c80447963dc589011f76f5e9369c664c92c8cc1b0d546be765e20bd69"},"schema_version":"1.0","source":{"id":"1801.00474","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00474","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00474v2","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00474","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"OG4TIFJ4QHWP","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OG4TIFJ4QHWPR6C6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OG4TIFJ4","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:9e1e5d73eea50ed899cdea79b212883dfc489c37263074899fbf42fbed52531f","target":"graph","created_at":"2026-05-18T00:19:56Z","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 Ramsey multiplicity constant of a graph $H$ is the minimum proportion of copies of $H$ in the complete graph which are monochromatic under an edge-coloring of $K_n$ as $n$ goes to infinity. Graphs for which this minimum is asymptotically achieved by taking a random coloring are called {\\em common}, and common graphs have been studied extensively, leading to the Burr-Rosta conjecture and Sidorenko's conjecture. Erd\\H{o}s and S\\'os asked what the maximum number of rainbow triangles is in a $3$-coloring of the edge set of $K_n$, a rainbow version of the Ramsey multiplicity question. A graph $","authors_text":"Jessica De Silva, Michael Tait, Michael Young, Ruifan Yang, Xiang Si, Yunus Tun\\c{c}bilek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T16:55:10Z","title":"Anti-Ramsey Multiplicities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00474","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":"sha256:7e7db0b22d9f64f38f1da8b5f12b671355130c585d96940af0716b65028207c6","target":"record","created_at":"2026-05-18T00:19:56Z","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":"94f3fdff2c0642b3836f64983872d8295e5cea1a1f3936aab8287bb74919e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-01T16:55:10Z","title_canon_sha256":"1a4fe05c80447963dc589011f76f5e9369c664c92c8cc1b0d546be765e20bd69"},"schema_version":"1.0","source":{"id":"1801.00474","kind":"arxiv","version":2}},"canonical_sha256":"71b934153c81ecf8f85e25324df2073b9c3b011767afff928d6d8e61ab3b38f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71b934153c81ecf8f85e25324df2073b9c3b011767afff928d6d8e61ab3b38f9","first_computed_at":"2026-05-18T00:19:56.544681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:56.544681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKAxEcGifbVB3BRtdHMiamYVW0FvR+F7/iJOHFAaJFprqv5KXf9dZpo8mPpky9to/5PR7r5rwFcH+31GQ5y+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:56.545441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00474","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e7db0b22d9f64f38f1da8b5f12b671355130c585d96940af0716b65028207c6","sha256:9e1e5d73eea50ed899cdea79b212883dfc489c37263074899fbf42fbed52531f"],"state_sha256":"3bc545043678348da13bc9a4770285f659669f15ee45dd9a34a438d08d28b474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KjAyRE3kSj3WjyvqcFYVfKZ5lM003IjIIoiQqtSKkkJvry+SgZtfdXBugRZ8J9A2T7RC3Hq6yOIdszxpkweDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:55:29.453555Z","bundle_sha256":"54e895aa32f4c822c2580a1357806e8c4e42f05c8414bd9cd0c8275b31ff73b7"}}