{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RDJ2K6TWWNNRV26SHMUC2Q5U6R","short_pith_number":"pith:RDJ2K6TW","canonical_record":{"source":{"id":"1605.00663","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-02T20:03:12Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4ccc454a927239212908dd71dd6da0a7ff55613920ce28969d46724db610b634","abstract_canon_sha256":"f7d3eac2edff2c69a9de8a284e471baa05556723eafea6f23a48890f10cdf93f"},"schema_version":"1.0"},"canonical_sha256":"88d3a57a76b35b1aebd23b282d43b4f46f29ad029b707839fbf50ff422a59bf7","source":{"kind":"arxiv","id":"1605.00663","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00663","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00663v2","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00663","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"RDJ2K6TWWNNR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDJ2K6TWWNNRV26S","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDJ2K6TW","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RDJ2K6TWWNNRV26SHMUC2Q5U6R","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00663","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-02T20:03:12Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4ccc454a927239212908dd71dd6da0a7ff55613920ce28969d46724db610b634","abstract_canon_sha256":"f7d3eac2edff2c69a9de8a284e471baa05556723eafea6f23a48890f10cdf93f"},"schema_version":"1.0"},"canonical_sha256":"88d3a57a76b35b1aebd23b282d43b4f46f29ad029b707839fbf50ff422a59bf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:25.374370Z","signature_b64":"cmWfoBVc7dwggx7VMlpKvSuqTinKPSJx6EgKs7+20bD44D5AqsIOUC+pCmsY1iLojNGmS4XO/byXZK2pAS26Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88d3a57a76b35b1aebd23b282d43b4f46f29ad029b707839fbf50ff422a59bf7","last_reissued_at":"2026-05-18T00:59:25.373709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:25.373709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00663","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":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1N7P9UvMaGYeTTyicSBfy6ZqrPQzWUTuOCA2DsWRO5oAiP+v588uHHf2519p7xtg3I2NGnNtKwcYMVMTbU0mBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:10:00.994502Z"},"content_sha256":"69c315b84ed31d56a0b451df1956f8d5eeb98148841d3b6e612c372ee377c71b","schema_version":"1.0","event_id":"sha256:69c315b84ed31d56a0b451df1956f8d5eeb98148841d3b6e612c372ee377c71b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RDJ2K6TWWNNRV26SHMUC2Q5U6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The van der Waerden complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Likith Govindaiah, Margaret Readdy, Peter S. Park, Richard Ehrenborg","submitted_at":"2016-05-02T20:03:12Z","abstract_excerpt":"We introduce the van der Waerden complex ${\\rm vdW}(n,k)$ defined as the simplicial complex whose facets correspond to arithmetic progressions of length $k$ in the vertex set $\\{1, 2, \\ldots, n\\}$. We show the van der Waerden complex ${\\rm vdW}(n,k)$ is homotopy equivalent to a $CW$-complex whose cells asymptotically have dimension at most $\\log k / \\log \\log k$. Furthermore, we give bounds on $n$ and $k$ which imply that the van der Waerden complex is contractible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00663","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":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4OBna44PeiR7Iknyc2ZK5MSe3I2VJ2f76QZxV/olRkYuLaEVRNOdYrLeEXiE0A1NLvrF6f7ARvgIGUTvRbTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:10:00.994848Z"},"content_sha256":"ea7d146f7f91859e16c2f97dafd665c155932e713ce452bd53792b42e66ac0a2","schema_version":"1.0","event_id":"sha256:ea7d146f7f91859e16c2f97dafd665c155932e713ce452bd53792b42e66ac0a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/bundle.json","state_url":"https://pith.science/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/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":"2026-06-27T14:10:00Z","links":{"resolver":"https://pith.science/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R","bundle":"https://pith.science/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/bundle.json","state":"https://pith.science/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDJ2K6TWWNNRV26SHMUC2Q5U6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RDJ2K6TWWNNRV26SHMUC2Q5U6R","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":"f7d3eac2edff2c69a9de8a284e471baa05556723eafea6f23a48890f10cdf93f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-02T20:03:12Z","title_canon_sha256":"4ccc454a927239212908dd71dd6da0a7ff55613920ce28969d46724db610b634"},"schema_version":"1.0","source":{"id":"1605.00663","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00663","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00663v2","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00663","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"RDJ2K6TWWNNR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDJ2K6TWWNNRV26S","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDJ2K6TW","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:ea7d146f7f91859e16c2f97dafd665c155932e713ce452bd53792b42e66ac0a2","target":"graph","created_at":"2026-05-18T00:59:25Z","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 introduce the van der Waerden complex ${\\rm vdW}(n,k)$ defined as the simplicial complex whose facets correspond to arithmetic progressions of length $k$ in the vertex set $\\{1, 2, \\ldots, n\\}$. We show the van der Waerden complex ${\\rm vdW}(n,k)$ is homotopy equivalent to a $CW$-complex whose cells asymptotically have dimension at most $\\log k / \\log \\log k$. Furthermore, we give bounds on $n$ and $k$ which imply that the van der Waerden complex is contractible.","authors_text":"Likith Govindaiah, Margaret Readdy, Peter S. Park, Richard Ehrenborg","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-02T20:03:12Z","title":"The van der Waerden complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00663","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":"sha256:69c315b84ed31d56a0b451df1956f8d5eeb98148841d3b6e612c372ee377c71b","target":"record","created_at":"2026-05-18T00:59:25Z","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":"f7d3eac2edff2c69a9de8a284e471baa05556723eafea6f23a48890f10cdf93f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-02T20:03:12Z","title_canon_sha256":"4ccc454a927239212908dd71dd6da0a7ff55613920ce28969d46724db610b634"},"schema_version":"1.0","source":{"id":"1605.00663","kind":"arxiv","version":2}},"canonical_sha256":"88d3a57a76b35b1aebd23b282d43b4f46f29ad029b707839fbf50ff422a59bf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88d3a57a76b35b1aebd23b282d43b4f46f29ad029b707839fbf50ff422a59bf7","first_computed_at":"2026-05-18T00:59:25.373709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:25.373709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmWfoBVc7dwggx7VMlpKvSuqTinKPSJx6EgKs7+20bD44D5AqsIOUC+pCmsY1iLojNGmS4XO/byXZK2pAS26Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:25.374370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00663","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69c315b84ed31d56a0b451df1956f8d5eeb98148841d3b6e612c372ee377c71b","sha256:ea7d146f7f91859e16c2f97dafd665c155932e713ce452bd53792b42e66ac0a2"],"state_sha256":"34d44b652dd206960e28cd7c4e0ec3ff93497496ec08217088b1b87c787325a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NL+KBHCue6+wuUDKA4stjfTFTttWcPYcP+m+xrMYabzC1R+vac3r2peneArpDxhl2ikWTbhDXHVrLQLF5jIeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:10:00.999467Z","bundle_sha256":"1e9101dfd110aad7443d50fa8e9bc28689282d87b0442ef14508897747395dd7"}}