{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YX6PVKXN3KSP5CZ65O6RC3EWFJ","short_pith_number":"pith:YX6PVKXN","canonical_record":{"source":{"id":"1404.1557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-06T08:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"3a0c842366e580d6b259b11e73747e4b3de5dca6e44b505d84e197d3a61bff00","abstract_canon_sha256":"330b88ca5cc89ef22d6b803a3adb4f65818217ee82d0f581f46442adb5a98a48"},"schema_version":"1.0"},"canonical_sha256":"c5fcfaaaeddaa4fe8b3eebbd116c962a79c00bc50e619d16d2fd4671e6cd73a8","source":{"kind":"arxiv","id":"1404.1557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1557","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1557v1","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1557","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"YX6PVKXN3KSP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YX6PVKXN3KSP5CZ6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YX6PVKXN","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YX6PVKXN3KSP5CZ65O6RC3EWFJ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-06T08:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"3a0c842366e580d6b259b11e73747e4b3de5dca6e44b505d84e197d3a61bff00","abstract_canon_sha256":"330b88ca5cc89ef22d6b803a3adb4f65818217ee82d0f581f46442adb5a98a48"},"schema_version":"1.0"},"canonical_sha256":"c5fcfaaaeddaa4fe8b3eebbd116c962a79c00bc50e619d16d2fd4671e6cd73a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.021291Z","signature_b64":"C0dQ1r2mjkxKIiOd9880mlLBU2VwcBetr6O4mnLKl9DKsim36ac8qoUXYmELMsQaGOIr9eXJAPwzs0n/t1puAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5fcfaaaeddaa4fe8b3eebbd116c962a79c00bc50e619d16d2fd4671e6cd73a8","last_reissued_at":"2026-05-18T02:54:46.020865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.020865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1557","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":"2026-05-18T02:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfKFQNSTT7XvaAt9wsaZMX2KUidoSxWPYJQJglE0yA5j3/mb5f65ToF1Z3Gc8El6xATAXl1CZ3+fwc4w1QxHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:18:46.160747Z"},"content_sha256":"2674a666bcd4b053e56b323ddaaba11acdcc0201ba9f84b8595ebe7ae3bdfe99","schema_version":"1.0","event_id":"sha256:2674a666bcd4b053e56b323ddaaba11acdcc0201ba9f84b8595ebe7ae3bdfe99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YX6PVKXN3KSP5CZ65O6RC3EWFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gabor Korvin","submitted_at":"2014-04-06T08:57:11Z","abstract_excerpt":"I show that a trivial modification of a standard proof of the Roth's Theorem on triples in arithmetic progression would lead to the following Theorem: If A is a \"large set\" that is its elements are monotone increasing integers and the sum of reciprocals of its elements diverges then the sequence contains an arithmetic progression of length three."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1557","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":"2026-05-18T02:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9lTTQ+sv0FqiRQPKpJcNty1yA5Lq//Quo5NEcYixayizUbsyWk1wTpqPc5dvnNgOozn/7qNcWfDctgmTF6oVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:18:46.161077Z"},"content_sha256":"81b9d48a2357105aa7356c33d8c31726a3161c1b34a46467be2e06f186deea44","schema_version":"1.0","event_id":"sha256:81b9d48a2357105aa7356c33d8c31726a3161c1b34a46467be2e06f186deea44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/bundle.json","state_url":"https://pith.science/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/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":"2026-06-24T23:18:46Z","links":{"resolver":"https://pith.science/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ","bundle":"https://pith.science/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/bundle.json","state":"https://pith.science/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YX6PVKXN3KSP5CZ65O6RC3EWFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YX6PVKXN3KSP5CZ65O6RC3EWFJ","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":"330b88ca5cc89ef22d6b803a3adb4f65818217ee82d0f581f46442adb5a98a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-06T08:57:11Z","title_canon_sha256":"3a0c842366e580d6b259b11e73747e4b3de5dca6e44b505d84e197d3a61bff00"},"schema_version":"1.0","source":{"id":"1404.1557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1557","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1557v1","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1557","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"YX6PVKXN3KSP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YX6PVKXN3KSP5CZ6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YX6PVKXN","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:81b9d48a2357105aa7356c33d8c31726a3161c1b34a46467be2e06f186deea44","target":"graph","created_at":"2026-05-18T02:54:46Z","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":"I show that a trivial modification of a standard proof of the Roth's Theorem on triples in arithmetic progression would lead to the following Theorem: If A is a \"large set\" that is its elements are monotone increasing integers and the sum of reciprocals of its elements diverges then the sequence contains an arithmetic progression of length three.","authors_text":"Gabor Korvin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-06T08:57:11Z","title":"Short Note: Every Large Set of Integers Contains a Three Term Arithmetic Progression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1557","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":"sha256:2674a666bcd4b053e56b323ddaaba11acdcc0201ba9f84b8595ebe7ae3bdfe99","target":"record","created_at":"2026-05-18T02:54:46Z","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":"330b88ca5cc89ef22d6b803a3adb4f65818217ee82d0f581f46442adb5a98a48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-06T08:57:11Z","title_canon_sha256":"3a0c842366e580d6b259b11e73747e4b3de5dca6e44b505d84e197d3a61bff00"},"schema_version":"1.0","source":{"id":"1404.1557","kind":"arxiv","version":1}},"canonical_sha256":"c5fcfaaaeddaa4fe8b3eebbd116c962a79c00bc50e619d16d2fd4671e6cd73a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5fcfaaaeddaa4fe8b3eebbd116c962a79c00bc50e619d16d2fd4671e6cd73a8","first_computed_at":"2026-05-18T02:54:46.020865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:46.020865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C0dQ1r2mjkxKIiOd9880mlLBU2VwcBetr6O4mnLKl9DKsim36ac8qoUXYmELMsQaGOIr9eXJAPwzs0n/t1puAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:46.021291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2674a666bcd4b053e56b323ddaaba11acdcc0201ba9f84b8595ebe7ae3bdfe99","sha256:81b9d48a2357105aa7356c33d8c31726a3161c1b34a46467be2e06f186deea44"],"state_sha256":"aa6d524d4344c2716059db7e2757368ad414c25ade76af290e3c81904166a803"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhduZAXVwErYbZ46Sj9z8DKYBDWtuFGAI0UMmoALf+a8w9ym5UuhFmCvB4LG/19/ipRViaqaRat113ol9NfqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:18:46.162927Z","bundle_sha256":"13a1c0d875001eb89bd1272f55534fd8503cdb0b8ee0717b1dac40f1751e1e9a"}}