{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RYMFQ6CP6ZMU3ZNYX4AILUJHVU","short_pith_number":"pith:RYMFQ6CP","canonical_record":{"source":{"id":"1604.06513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-21T23:53:58Z","cross_cats_sorted":[],"title_canon_sha256":"71bdb0318b74df4c250faa75aff93df3dce8ace83451106359632d26b327b184","abstract_canon_sha256":"b0220fc9048b74651ac4c8a057abffe0a294f43be15a76b9984f63d38275e967"},"schema_version":"1.0"},"canonical_sha256":"8e1858784ff6594de5b8bf0085d127ad0e2e4632f5044a33683b5d05555e928e","source":{"kind":"arxiv","id":"1604.06513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06513","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06513v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06513","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"RYMFQ6CP6ZMU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RYMFQ6CP6ZMU3ZNY","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RYMFQ6CP","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RYMFQ6CP6ZMU3ZNYX4AILUJHVU","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-21T23:53:58Z","cross_cats_sorted":[],"title_canon_sha256":"71bdb0318b74df4c250faa75aff93df3dce8ace83451106359632d26b327b184","abstract_canon_sha256":"b0220fc9048b74651ac4c8a057abffe0a294f43be15a76b9984f63d38275e967"},"schema_version":"1.0"},"canonical_sha256":"8e1858784ff6594de5b8bf0085d127ad0e2e4632f5044a33683b5d05555e928e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:28.871332Z","signature_b64":"a45JvaPw82O9yUEdiyZTZAdAbMHztxc+b7i6dF0COOyOvrfiqvCgrgsHZp/G6qFN8MB6CAzaB8tA6He6uW2bAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e1858784ff6594de5b8bf0085d127ad0e2e4632f5044a33683b5d05555e928e","last_reissued_at":"2026-05-18T01:16:28.870685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:28.870685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06513","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":"2026-05-18T01:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYJyIichKi/Mwh73Z4UXGjy8JE9Or/BwG2T2tSktpLFTg4g0QpEtl9HZkvR/1MgLWQo5OvCFI1GRjCTUzjSDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:47.053987Z"},"content_sha256":"68548c84746d98670c4e352d36975f84c4b2d9ed5b002dae5a92f20273d5d54c","schema_version":"1.0","event_id":"sha256:68548c84746d98670c4e352d36975f84c4b2d9ed5b002dae5a92f20273d5d54c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RYMFQ6CP6ZMU3ZNYX4AILUJHVU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Ramsey Numbers of Trees with Small Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Patrick Bahls, T. Scott Spencer","submitted_at":"2016-04-21T23:53:58Z","abstract_excerpt":"We estimate the Ramsey number r(T) = r(T,T) for various trees T, obtaining a precise value for r(T) for a large number of trees of diameter 3. Furthermore we prove that all trees of diameter 3 are Ramsey unsaturated as defined by Balister, Lehel, and Schelp in their article \"Ramsey unsaturated and saturated graphs.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06513","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":"2026-05-18T01:16:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XF82uFWf9UAyTO1RrGtXNThMuCzfYuwOKuGrI2vc75u4Ry0AgYXIy6NY+hRcgQSvkQuxrPQ7GlZ0c5INY87pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:47.054348Z"},"content_sha256":"4fd42b9128348c0cb3541cabe3003108bb88d64985f8794e75abd227fb999f85","schema_version":"1.0","event_id":"sha256:4fd42b9128348c0cb3541cabe3003108bb88d64985f8794e75abd227fb999f85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/bundle.json","state_url":"https://pith.science/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/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":"2026-06-23T16:25:47Z","links":{"resolver":"https://pith.science/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU","bundle":"https://pith.science/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/bundle.json","state":"https://pith.science/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RYMFQ6CP6ZMU3ZNYX4AILUJHVU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RYMFQ6CP6ZMU3ZNYX4AILUJHVU","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":"b0220fc9048b74651ac4c8a057abffe0a294f43be15a76b9984f63d38275e967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-21T23:53:58Z","title_canon_sha256":"71bdb0318b74df4c250faa75aff93df3dce8ace83451106359632d26b327b184"},"schema_version":"1.0","source":{"id":"1604.06513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06513","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06513v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06513","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"RYMFQ6CP6ZMU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RYMFQ6CP6ZMU3ZNY","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RYMFQ6CP","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:4fd42b9128348c0cb3541cabe3003108bb88d64985f8794e75abd227fb999f85","target":"graph","created_at":"2026-05-18T01:16:28Z","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":"We estimate the Ramsey number r(T) = r(T,T) for various trees T, obtaining a precise value for r(T) for a large number of trees of diameter 3. Furthermore we prove that all trees of diameter 3 are Ramsey unsaturated as defined by Balister, Lehel, and Schelp in their article \"Ramsey unsaturated and saturated graphs.\"","authors_text":"Patrick Bahls, T. Scott Spencer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-21T23:53:58Z","title":"On the Ramsey Numbers of Trees with Small Diameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06513","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":"sha256:68548c84746d98670c4e352d36975f84c4b2d9ed5b002dae5a92f20273d5d54c","target":"record","created_at":"2026-05-18T01:16:28Z","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":"b0220fc9048b74651ac4c8a057abffe0a294f43be15a76b9984f63d38275e967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-21T23:53:58Z","title_canon_sha256":"71bdb0318b74df4c250faa75aff93df3dce8ace83451106359632d26b327b184"},"schema_version":"1.0","source":{"id":"1604.06513","kind":"arxiv","version":1}},"canonical_sha256":"8e1858784ff6594de5b8bf0085d127ad0e2e4632f5044a33683b5d05555e928e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e1858784ff6594de5b8bf0085d127ad0e2e4632f5044a33683b5d05555e928e","first_computed_at":"2026-05-18T01:16:28.870685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:28.870685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a45JvaPw82O9yUEdiyZTZAdAbMHztxc+b7i6dF0COOyOvrfiqvCgrgsHZp/G6qFN8MB6CAzaB8tA6He6uW2bAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:28.871332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68548c84746d98670c4e352d36975f84c4b2d9ed5b002dae5a92f20273d5d54c","sha256:4fd42b9128348c0cb3541cabe3003108bb88d64985f8794e75abd227fb999f85"],"state_sha256":"5d470544b16e752bf210998663562c241d27ee4155ca0bb172b3aea929a74403"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPM7WvX8trFSn4wSWsNLveWeS7mEZrMGft+Rb2TKOZ8AnVGp8u9UcFJYvOJ2FPqCwItWptbtYzTTHNm4X9ouDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:25:47.056360Z","bundle_sha256":"e07d49db47f6e32548f994942530f76a743770c81573aaa74c1dfdf69c14678c"}}