{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OTWOB7MHAQNE3SCPWRKPADZPDZ","short_pith_number":"pith:OTWOB7MH","canonical_record":{"source":{"id":"1603.06695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T07:48:00Z","cross_cats_sorted":[],"title_canon_sha256":"7e1e55505a2e3ca69291e6ae067e39bea27b0f5903761a86d41f22aa6a87a648","abstract_canon_sha256":"583ca82f96956332e0095598190f55c907d5edd35b875dacbfe2e026000fbf13"},"schema_version":"1.0"},"canonical_sha256":"74ece0fd87041a4dc84fb454f00f2f1e6fb0305e9e5095d1911d309ed62bbe01","source":{"kind":"arxiv","id":"1603.06695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06695","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06695v1","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06695","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"OTWOB7MHAQNE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OTWOB7MHAQNE3SCP","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OTWOB7MH","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OTWOB7MHAQNE3SCPWRKPADZPDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T07:48:00Z","cross_cats_sorted":[],"title_canon_sha256":"7e1e55505a2e3ca69291e6ae067e39bea27b0f5903761a86d41f22aa6a87a648","abstract_canon_sha256":"583ca82f96956332e0095598190f55c907d5edd35b875dacbfe2e026000fbf13"},"schema_version":"1.0"},"canonical_sha256":"74ece0fd87041a4dc84fb454f00f2f1e6fb0305e9e5095d1911d309ed62bbe01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:48.681869Z","signature_b64":"tghsnIlFEioSGPFB3SeqXL97AvnDT0t7RgpN9b9kfKZzHMOXGC2rflB5qEObFDzL3kaSSN5BJvM31h+DUO7XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74ece0fd87041a4dc84fb454f00f2f1e6fb0305e9e5095d1911d309ed62bbe01","last_reissued_at":"2026-05-18T01:12:48.681549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:48.681549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06695","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":"2026-05-18T01:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBVg70Dw+n8X+5tBwlkQ75mrQZtKNAYHoNwvkEEMn7EUrRPfB4ffcxeFuLxBg0QJKPFxnbYwjTKInATFMWurDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:21:20.805108Z"},"content_sha256":"6d7daff484ae5b00782b48de5f28e182d3aa4a924c4c8c95d66238bfc332366d","schema_version":"1.0","event_id":"sha256:6d7daff484ae5b00782b48de5f28e182d3aa4a924c4c8c95d66238bfc332366d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OTWOB7MHAQNE3SCPWRKPADZPDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transition results for three Ramsey-like theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy","submitted_at":"2016-03-22T07:48:00Z","abstract_excerpt":"We classify a sharp phase transition threshold for Friedman's finite adjacent Ramsey theorem. We extend the method for showing this result to two previously known classifications involving Ramsey theorem variants: the Paris--Harrington theorem and the Kanamori--McAloon theorem. We also provide tools to remove ad-hoc arguments from the proofs of phase transition results as much as currently possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06695","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":"2026-05-18T01:12:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXA7lkFgwwAmkTinODdAQ+yj+v46jq7bI/caQcXTYm0b+GHRStSDCdfK+GzyUwrdvPfFlxB/A/VuIGWl5C/tDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:21:20.805750Z"},"content_sha256":"abba1a602333f103a1d9f211bb7bbeba8739cf5e7d166a69d1e886bd59d8f7ad","schema_version":"1.0","event_id":"sha256:abba1a602333f103a1d9f211bb7bbeba8739cf5e7d166a69d1e886bd59d8f7ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/bundle.json","state_url":"https://pith.science/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/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":"2026-05-26T07:21:20Z","links":{"resolver":"https://pith.science/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ","bundle":"https://pith.science/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/bundle.json","state":"https://pith.science/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTWOB7MHAQNE3SCPWRKPADZPDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OTWOB7MHAQNE3SCPWRKPADZPDZ","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":"583ca82f96956332e0095598190f55c907d5edd35b875dacbfe2e026000fbf13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T07:48:00Z","title_canon_sha256":"7e1e55505a2e3ca69291e6ae067e39bea27b0f5903761a86d41f22aa6a87a648"},"schema_version":"1.0","source":{"id":"1603.06695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06695","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06695v1","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06695","created_at":"2026-05-18T01:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"OTWOB7MHAQNE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OTWOB7MHAQNE3SCP","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OTWOB7MH","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:abba1a602333f103a1d9f211bb7bbeba8739cf5e7d166a69d1e886bd59d8f7ad","target":"graph","created_at":"2026-05-18T01:12:48Z","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 classify a sharp phase transition threshold for Friedman's finite adjacent Ramsey theorem. We extend the method for showing this result to two previously known classifications involving Ramsey theorem variants: the Paris--Harrington theorem and the Kanamori--McAloon theorem. We also provide tools to remove ad-hoc arguments from the proofs of phase transition results as much as currently possible.","authors_text":"Florian Pelupessy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T07:48:00Z","title":"Phase transition results for three Ramsey-like theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06695","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":"sha256:6d7daff484ae5b00782b48de5f28e182d3aa4a924c4c8c95d66238bfc332366d","target":"record","created_at":"2026-05-18T01:12:48Z","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":"583ca82f96956332e0095598190f55c907d5edd35b875dacbfe2e026000fbf13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-22T07:48:00Z","title_canon_sha256":"7e1e55505a2e3ca69291e6ae067e39bea27b0f5903761a86d41f22aa6a87a648"},"schema_version":"1.0","source":{"id":"1603.06695","kind":"arxiv","version":1}},"canonical_sha256":"74ece0fd87041a4dc84fb454f00f2f1e6fb0305e9e5095d1911d309ed62bbe01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74ece0fd87041a4dc84fb454f00f2f1e6fb0305e9e5095d1911d309ed62bbe01","first_computed_at":"2026-05-18T01:12:48.681549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:48.681549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tghsnIlFEioSGPFB3SeqXL97AvnDT0t7RgpN9b9kfKZzHMOXGC2rflB5qEObFDzL3kaSSN5BJvM31h+DUO7XBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:48.681869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d7daff484ae5b00782b48de5f28e182d3aa4a924c4c8c95d66238bfc332366d","sha256:abba1a602333f103a1d9f211bb7bbeba8739cf5e7d166a69d1e886bd59d8f7ad"],"state_sha256":"001aab302ff8b58a2b45a6f3e5860eda920462ac710ba5e05c8321df87f6a664"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+LbP8m2Kw45ErEBG30dCXRmTFESeT0Mrd/VP0lI6/iIRhAMmRQe0T+497D6OyFW9b+s/MLUt4lc1t/P1w5+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:21:20.808718Z","bundle_sha256":"344c541266db532d6709f045b4b97ef9534c69adeca883d8371e4853f3bbfb8a"}}