{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EPQ5RGBILWFM4ONI3MVFNRW2OH","short_pith_number":"pith:EPQ5RGBI","canonical_record":{"source":{"id":"1805.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-06T17:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"8c65473a68c42e3c67ae29d7e27efca590d22797f8f1a72d9f5a44076ad07d94","abstract_canon_sha256":"9b031c7ae4e2baa7be07e47b69cee557bfa71853113d287001595f3971a85a26"},"schema_version":"1.0"},"canonical_sha256":"23e1d898285d8ace39a8db2a56c6da71c2cee89380683149fb739f4f52096255","source":{"kind":"arxiv","id":"1805.02254","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02254","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02254v2","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02254","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"EPQ5RGBILWFM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EPQ5RGBILWFM4ONI","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EPQ5RGBI","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EPQ5RGBILWFM4ONI3MVFNRW2OH","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-06T17:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"8c65473a68c42e3c67ae29d7e27efca590d22797f8f1a72d9f5a44076ad07d94","abstract_canon_sha256":"9b031c7ae4e2baa7be07e47b69cee557bfa71853113d287001595f3971a85a26"},"schema_version":"1.0"},"canonical_sha256":"23e1d898285d8ace39a8db2a56c6da71c2cee89380683149fb739f4f52096255","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:31.268976Z","signature_b64":"jBzkxbttIVpmTAmj3/ygVK7dGE2YWtbHKEZyiueqUCj2/91UosQ8nSGuNhv5U5DOq07FzvfFKUcrvgbQj0BzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e1d898285d8ace39a8db2a56c6da71c2cee89380683149fb739f4f52096255","last_reissued_at":"2026-05-18T00:05:31.268463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:31.268463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02254","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":"2026-05-18T00:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOVEmrrfbWdzw02HxcVjDg243Zx/CxyEAxHBe+FiGqsOeXiCzbfJOYEz3MOYyRSiknRfeD7+87Ele3Lp08vtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:36:07.173675Z"},"content_sha256":"b96ff6db563fa21ce25333e454986546f9babf0fba07d58deaf89709d9b650ed","schema_version":"1.0","event_id":"sha256:b96ff6db563fa21ce25333e454986546f9babf0fba07d58deaf89709d9b650ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EPQ5RGBILWFM4ONI3MVFNRW2OH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Lebedev","submitted_at":"2018-05-06T17:58:55Z","abstract_excerpt":"We show that if $\\varphi \\colon \\mathbb R\\rightarrow\\mathbb R$ is a continuous mapping and the set of nonlinearity of $\\varphi$ has nonzero Lebesgue measure, then $\\varphi$ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02254","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":"2026-05-18T00:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSBF/Y/qaZJGSOYORIT5dgiapZWsmUCcRWhAE49yH+xDe6QwQs22czCCY+MB5P1tLBXZw935H/5VcAEy77jBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:36:07.174026Z"},"content_sha256":"6b4711e1bd9ed056e4fc239797f3df710be2dc0264f46163ad72ed9c94012c89","schema_version":"1.0","event_id":"sha256:6b4711e1bd9ed056e4fc239797f3df710be2dc0264f46163ad72ed9c94012c89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/bundle.json","state_url":"https://pith.science/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/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":"2026-06-01T23:36:07Z","links":{"resolver":"https://pith.science/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH","bundle":"https://pith.science/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/bundle.json","state":"https://pith.science/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPQ5RGBILWFM4ONI3MVFNRW2OH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EPQ5RGBILWFM4ONI3MVFNRW2OH","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":"9b031c7ae4e2baa7be07e47b69cee557bfa71853113d287001595f3971a85a26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-06T17:58:55Z","title_canon_sha256":"8c65473a68c42e3c67ae29d7e27efca590d22797f8f1a72d9f5a44076ad07d94"},"schema_version":"1.0","source":{"id":"1805.02254","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02254","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02254v2","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02254","created_at":"2026-05-18T00:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"EPQ5RGBILWFM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EPQ5RGBILWFM4ONI","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EPQ5RGBI","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:6b4711e1bd9ed056e4fc239797f3df710be2dc0264f46163ad72ed9c94012c89","target":"graph","created_at":"2026-05-18T00:05:31Z","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 show that if $\\varphi \\colon \\mathbb R\\rightarrow\\mathbb R$ is a continuous mapping and the set of nonlinearity of $\\varphi$ has nonzero Lebesgue measure, then $\\varphi$ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.","authors_text":"Vladimir Lebedev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-06T17:58:55Z","title":"Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02254","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:b96ff6db563fa21ce25333e454986546f9babf0fba07d58deaf89709d9b650ed","target":"record","created_at":"2026-05-18T00:05:31Z","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":"9b031c7ae4e2baa7be07e47b69cee557bfa71853113d287001595f3971a85a26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-06T17:58:55Z","title_canon_sha256":"8c65473a68c42e3c67ae29d7e27efca590d22797f8f1a72d9f5a44076ad07d94"},"schema_version":"1.0","source":{"id":"1805.02254","kind":"arxiv","version":2}},"canonical_sha256":"23e1d898285d8ace39a8db2a56c6da71c2cee89380683149fb739f4f52096255","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23e1d898285d8ace39a8db2a56c6da71c2cee89380683149fb739f4f52096255","first_computed_at":"2026-05-18T00:05:31.268463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:31.268463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jBzkxbttIVpmTAmj3/ygVK7dGE2YWtbHKEZyiueqUCj2/91UosQ8nSGuNhv5U5DOq07FzvfFKUcrvgbQj0BzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:31.268976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02254","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b96ff6db563fa21ce25333e454986546f9babf0fba07d58deaf89709d9b650ed","sha256:6b4711e1bd9ed056e4fc239797f3df710be2dc0264f46163ad72ed9c94012c89"],"state_sha256":"111a24cdff2c1338d30aae244b9ceaa0114967204480dda7c69a186ae29976e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xKXiqQe5vICzsmKvZatjXw4q99CfIb16yYHRbSp45BWEtwBE/mWZFOCEgFjr674RM6Bp2tmnGkKE/0g71SXgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:36:07.175949Z","bundle_sha256":"bb196128be04445b6d7ccba8b6d99c8639795a58399830ecc8f6d0fec53bef56"}}