{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5QO462NKAPGOSZWNSLRKX7A7TY","short_pith_number":"pith:5QO462NK","canonical_record":{"source":{"id":"1709.04719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-14T11:59:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"108012c53b32d9cd7f0dba2e1220d0bfebaf0af14d3b33d28fb9041f2a7c4794","abstract_canon_sha256":"6a6a5b6afc4d7c7909093aedf5239f8bc0289a4f305de169ebc4836c587afbc9"},"schema_version":"1.0"},"canonical_sha256":"ec1dcf69aa03cce966cd92e2abfc1f9e140e18503a187e31727d7766458a3d7d","source":{"kind":"arxiv","id":"1709.04719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04719","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04719v1","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04719","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"5QO462NKAPGO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5QO462NKAPGOSZWN","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5QO462NK","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5QO462NKAPGOSZWNSLRKX7A7TY","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-14T11:59:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"108012c53b32d9cd7f0dba2e1220d0bfebaf0af14d3b33d28fb9041f2a7c4794","abstract_canon_sha256":"6a6a5b6afc4d7c7909093aedf5239f8bc0289a4f305de169ebc4836c587afbc9"},"schema_version":"1.0"},"canonical_sha256":"ec1dcf69aa03cce966cd92e2abfc1f9e140e18503a187e31727d7766458a3d7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:28.651281Z","signature_b64":"al09MoVBsevUAOnJt3uICIRcigTv78/1gcxjX1Zh06zAZHGfLtxRd5U9plQ2sxZxpmoUzt/qKS1jCLoNYeKmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec1dcf69aa03cce966cd92e2abfc1f9e140e18503a187e31727d7766458a3d7d","last_reissued_at":"2026-05-17T23:43:28.650745Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:28.650745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04719","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":"2026-05-17T23:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMXRJXBRlviGp0gdqI/umu0NKA20Z4t5ooABAZWpCyloDE2QD4czMTNOzDlcxDArWbA6Bw6MrhYibWY3zlpQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:15:42.098632Z"},"content_sha256":"a1d6660b105368cb3877f9fb55bb1d7f591606f3519eddcc98bfecc7333e6958","schema_version":"1.0","event_id":"sha256:a1d6660b105368cb3877f9fb55bb1d7f591606f3519eddcc98bfecc7333e6958"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5QO462NKAPGOSZWNSLRKX7A7TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Szemer\\'edi's theorem in the primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Julia Wolf, Luka Rimanic","submitted_at":"2017-09-14T11:59:35Z","abstract_excerpt":"Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to zero sufficiently slowly contains a 3-term term progression. This was followed by work of Helfgott and de Roton, and Naslund, who improved the bounds on the relative density in the case of 3-term progressions. The aim of this note is to present an analogous result for longer progressions by combining a quantified version of the relative Szemer\\'edi theorem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04719","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":"2026-05-17T23:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8po7+D2zc0A4TcegNQrEKpMhv3NogKvg9kGf+ja9ST36nGniOF9JMphCVzKPNHlXZ+WN9oC6A6iDgeEqR78LDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:15:42.099254Z"},"content_sha256":"02722beb8f1c9e1a300e2ee98b3c2296ca611a173be55deaa433e37b2acfa3b9","schema_version":"1.0","event_id":"sha256:02722beb8f1c9e1a300e2ee98b3c2296ca611a173be55deaa433e37b2acfa3b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QO462NKAPGOSZWNSLRKX7A7TY/bundle.json","state_url":"https://pith.science/pith/5QO462NKAPGOSZWNSLRKX7A7TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QO462NKAPGOSZWNSLRKX7A7TY/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":"2026-06-11T06:15:42Z","links":{"resolver":"https://pith.science/pith/5QO462NKAPGOSZWNSLRKX7A7TY","bundle":"https://pith.science/pith/5QO462NKAPGOSZWNSLRKX7A7TY/bundle.json","state":"https://pith.science/pith/5QO462NKAPGOSZWNSLRKX7A7TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QO462NKAPGOSZWNSLRKX7A7TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5QO462NKAPGOSZWNSLRKX7A7TY","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":"6a6a5b6afc4d7c7909093aedf5239f8bc0289a4f305de169ebc4836c587afbc9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-14T11:59:35Z","title_canon_sha256":"108012c53b32d9cd7f0dba2e1220d0bfebaf0af14d3b33d28fb9041f2a7c4794"},"schema_version":"1.0","source":{"id":"1709.04719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04719","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04719v1","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04719","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"5QO462NKAPGO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5QO462NKAPGOSZWN","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5QO462NK","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:02722beb8f1c9e1a300e2ee98b3c2296ca611a173be55deaa433e37b2acfa3b9","target":"graph","created_at":"2026-05-17T23:43:28Z","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":"Green and Tao famously proved in 2005 that any subset of the primes of fixed positive density contains arbitrarily long arithmetic progressions. Green had previously shown that in fact any subset of the primes of relative density tending to zero sufficiently slowly contains a 3-term term progression. This was followed by work of Helfgott and de Roton, and Naslund, who improved the bounds on the relative density in the case of 3-term progressions. The aim of this note is to present an analogous result for longer progressions by combining a quantified version of the relative Szemer\\'edi theorem ","authors_text":"Julia Wolf, Luka Rimanic","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-14T11:59:35Z","title":"Szemer\\'edi's theorem in the primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04719","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:a1d6660b105368cb3877f9fb55bb1d7f591606f3519eddcc98bfecc7333e6958","target":"record","created_at":"2026-05-17T23:43:28Z","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":"6a6a5b6afc4d7c7909093aedf5239f8bc0289a4f305de169ebc4836c587afbc9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-14T11:59:35Z","title_canon_sha256":"108012c53b32d9cd7f0dba2e1220d0bfebaf0af14d3b33d28fb9041f2a7c4794"},"schema_version":"1.0","source":{"id":"1709.04719","kind":"arxiv","version":1}},"canonical_sha256":"ec1dcf69aa03cce966cd92e2abfc1f9e140e18503a187e31727d7766458a3d7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec1dcf69aa03cce966cd92e2abfc1f9e140e18503a187e31727d7766458a3d7d","first_computed_at":"2026-05-17T23:43:28.650745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:28.650745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"al09MoVBsevUAOnJt3uICIRcigTv78/1gcxjX1Zh06zAZHGfLtxRd5U9plQ2sxZxpmoUzt/qKS1jCLoNYeKmAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:28.651281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1d6660b105368cb3877f9fb55bb1d7f591606f3519eddcc98bfecc7333e6958","sha256:02722beb8f1c9e1a300e2ee98b3c2296ca611a173be55deaa433e37b2acfa3b9"],"state_sha256":"ee24ad5771f83e8e81765d6fefa61f6532a37aba65ca2037f020eb2645ecb61d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYqfhHQDPZUt3OS7BRzWBBoIKf4WMdd8fwJ7xOlgtiPWC7M0EwV5aVW7AMCxdQgjfB++YgiVfs6U3PqzTnsqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:15:42.102896Z","bundle_sha256":"087255c2bfd817d76a2e1fd2dad70af74a49bc6d49b7bb215beab80ba0cc5907"}}