{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TQJEYVXFJN7ZZRQBWFEOXJOM3B","short_pith_number":"pith:TQJEYVXF","canonical_record":{"source":{"id":"1405.6587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-26T14:26:04Z","cross_cats_sorted":[],"title_canon_sha256":"e5f0823f3e0566cb9110e4a5f6d898fa7fd8848a9257fca21954455f002ef213","abstract_canon_sha256":"82674b70979b8e45729651df746034c3eeb4dab82d54d5370e7c47e545cea39b"},"schema_version":"1.0"},"canonical_sha256":"9c124c56e54b7f9cc601b148eba5ccd866f26b29a37f8f222fcfb1767ae85022","source":{"kind":"arxiv","id":"1405.6587","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6587","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6587v2","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6587","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"TQJEYVXFJN7Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TQJEYVXFJN7ZZRQB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TQJEYVXF","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TQJEYVXFJN7ZZRQBWFEOXJOM3B","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-26T14:26:04Z","cross_cats_sorted":[],"title_canon_sha256":"e5f0823f3e0566cb9110e4a5f6d898fa7fd8848a9257fca21954455f002ef213","abstract_canon_sha256":"82674b70979b8e45729651df746034c3eeb4dab82d54d5370e7c47e545cea39b"},"schema_version":"1.0"},"canonical_sha256":"9c124c56e54b7f9cc601b148eba5ccd866f26b29a37f8f222fcfb1767ae85022","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:14.418781Z","signature_b64":"Z8U8iqf/uw8BRkPelE7DKQoKG6YpSuWF850O3OEq8yHbwm/hAE7LMC/VmioqALPs1Iv2633Wbk8hy60a0XVeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c124c56e54b7f9cc601b148eba5ccd866f26b29a37f8f222fcfb1767ae85022","last_reissued_at":"2026-05-18T02:42:14.418393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:14.418393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6587","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":"2026-05-18T02:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIvA7xA2a80wMQ1Gavu/dgzGw0mMeelj5dwBn5nHHpdmRItEK0h9Uh5K8r8KuxyNtwi0F7/JKcWOffoIXinzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:15:06.662088Z"},"content_sha256":"5f7cfa9a0ff88357c700fd38a7e18796538019594614ee4e5fca7671dec65cd2","schema_version":"1.0","event_id":"sha256:5f7cfa9a0ff88357c700fd38a7e18796538019594614ee4e5fca7671dec65cd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TQJEYVXFJN7ZZRQBWFEOXJOM3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the grid Ramsey problem and related questions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, David Conlon, Jacob Fox","submitted_at":"2014-05-26T14:26:04Z","abstract_excerpt":"The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product $K_n \\times K_n$ in $r$ colors then, for $n$ sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah's proof shows that $n = r^{\\binom{r+1}{2}} + 1$ suffices. More than tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6587","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":"2026-05-18T02:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsL1ea6KBUhQ94KuxCVVeTMl+SKUFHs2vPkGnoH+kYKgNfwdmoPatoEzQTfp0QAflwceGBEo9W0NZeznrKL7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:15:06.662444Z"},"content_sha256":"7d60ebdc31c2280e0f12de117f4c78409eb6134621390ea669ad10ff7c5238c9","schema_version":"1.0","event_id":"sha256:7d60ebdc31c2280e0f12de117f4c78409eb6134621390ea669ad10ff7c5238c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/bundle.json","state_url":"https://pith.science/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/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":"2026-05-30T04:15:06Z","links":{"resolver":"https://pith.science/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B","bundle":"https://pith.science/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/bundle.json","state":"https://pith.science/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQJEYVXFJN7ZZRQBWFEOXJOM3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TQJEYVXFJN7ZZRQBWFEOXJOM3B","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":"82674b70979b8e45729651df746034c3eeb4dab82d54d5370e7c47e545cea39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-26T14:26:04Z","title_canon_sha256":"e5f0823f3e0566cb9110e4a5f6d898fa7fd8848a9257fca21954455f002ef213"},"schema_version":"1.0","source":{"id":"1405.6587","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6587","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6587v2","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6587","created_at":"2026-05-18T02:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"TQJEYVXFJN7Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TQJEYVXFJN7ZZRQB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TQJEYVXF","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:7d60ebdc31c2280e0f12de117f4c78409eb6134621390ea669ad10ff7c5238c9","target":"graph","created_at":"2026-05-18T02:42:14Z","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 Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product $K_n \\times K_n$ in $r$ colors then, for $n$ sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah's proof shows that $n = r^{\\binom{r+1}{2}} + 1$ suffices. More than tw","authors_text":"Benny Sudakov, Choongbum Lee, David Conlon, Jacob Fox","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-26T14:26:04Z","title":"On the grid Ramsey problem and related questions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6587","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":"sha256:5f7cfa9a0ff88357c700fd38a7e18796538019594614ee4e5fca7671dec65cd2","target":"record","created_at":"2026-05-18T02:42:14Z","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":"82674b70979b8e45729651df746034c3eeb4dab82d54d5370e7c47e545cea39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-26T14:26:04Z","title_canon_sha256":"e5f0823f3e0566cb9110e4a5f6d898fa7fd8848a9257fca21954455f002ef213"},"schema_version":"1.0","source":{"id":"1405.6587","kind":"arxiv","version":2}},"canonical_sha256":"9c124c56e54b7f9cc601b148eba5ccd866f26b29a37f8f222fcfb1767ae85022","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c124c56e54b7f9cc601b148eba5ccd866f26b29a37f8f222fcfb1767ae85022","first_computed_at":"2026-05-18T02:42:14.418393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:14.418393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z8U8iqf/uw8BRkPelE7DKQoKG6YpSuWF850O3OEq8yHbwm/hAE7LMC/VmioqALPs1Iv2633Wbk8hy60a0XVeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:14.418781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6587","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f7cfa9a0ff88357c700fd38a7e18796538019594614ee4e5fca7671dec65cd2","sha256:7d60ebdc31c2280e0f12de117f4c78409eb6134621390ea669ad10ff7c5238c9"],"state_sha256":"260d82ff954f53bdff18f8788d2df63ba063560072e787aab55f51de6c25ae2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATYjonrR9lxRGPwnUTYgE49HhlNeVM932AGq2GgSsGzbhZreEToLABmqOsc2HObFasvvfcJtojfTSNA7d8szDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:15:06.664640Z","bundle_sha256":"4dac3333bca20bd55d17ee95287ed7f62770ff54158914882d558d31c079af4b"}}