{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XN7AOH27MV6J2EEOVFTUK27PIP","short_pith_number":"pith:XN7AOH27","canonical_record":{"source":{"id":"1708.00642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-02T08:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"3e684768163d764fca86564a528a46db0b1a0e79433eadc95347b0549f662b54","abstract_canon_sha256":"cc6cf576ad128a305ced41f7430611631dae0a05e404db4eb9726ba0585720fc"},"schema_version":"1.0"},"canonical_sha256":"bb7e071f5f657c9d108ea967456bef43e7cc48709e15ee739cb07f9f1b81e32c","source":{"kind":"arxiv","id":"1708.00642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00642","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00642v1","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00642","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"XN7AOH27MV6J","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XN7AOH27MV6J2EEO","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XN7AOH27","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XN7AOH27MV6J2EEOVFTUK27PIP","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-02T08:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"3e684768163d764fca86564a528a46db0b1a0e79433eadc95347b0549f662b54","abstract_canon_sha256":"cc6cf576ad128a305ced41f7430611631dae0a05e404db4eb9726ba0585720fc"},"schema_version":"1.0"},"canonical_sha256":"bb7e071f5f657c9d108ea967456bef43e7cc48709e15ee739cb07f9f1b81e32c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:38.522414Z","signature_b64":"IWkp+ehbRmo6kgw1lgE6oajdgk13rfDaUXoOejJ/PMbEtrYgE5lmQSlZgE9eSomGD2uALMrUwjCPduMIZGb+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb7e071f5f657c9d108ea967456bef43e7cc48709e15ee739cb07f9f1b81e32c","last_reissued_at":"2026-05-17T23:43:38.521845Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:38.521845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00642","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":"2026-05-17T23:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eLntPpNRtKJ92iCydBn0hD141dSdq2mj2QUgzIJb1WxIj8gB4UFpRmrmGtkyAGMVrvkHCB+JsI/lFx0g3eVSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:15:28.031071Z"},"content_sha256":"989d2d13d65881221b55900b173cc8f3525c4b29646cbd34ae8df98d07e9baff","schema_version":"1.0","event_id":"sha256:989d2d13d65881221b55900b173cc8f3525c4b29646cbd34ae8df98d07e9baff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XN7AOH27MV6J2EEOVFTUK27PIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A separation result for countable unions of Borel rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dominique Lecomte (IMJ)","submitted_at":"2017-08-02T08:28:31Z","abstract_excerpt":"We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a countable union of ${\\bf\\Sigma}^0_1 \\!\\times\\! {\\bf\\Sigma}^0_\\xi$ sets, or by a ${\\bf\\Pi}^0_1 \\!\\times\\! {\\bf\\Pi}^0_\\xi$ set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00642","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":"2026-05-17T23:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izSTv9aJuzxwF/bd1Ern5RzhGlQ57XM9O/GbTm70NhPbF1mos/l0VfPaxorvSm6PDhlUYaYJQi27x/uZYeRACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:15:28.031433Z"},"content_sha256":"4a8843f2627765d601492bdfa31f39f599c58fe8b770033d2fd2c7ef98bcd9b8","schema_version":"1.0","event_id":"sha256:4a8843f2627765d601492bdfa31f39f599c58fe8b770033d2fd2c7ef98bcd9b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XN7AOH27MV6J2EEOVFTUK27PIP/bundle.json","state_url":"https://pith.science/pith/XN7AOH27MV6J2EEOVFTUK27PIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XN7AOH27MV6J2EEOVFTUK27PIP/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":"2026-07-01T21:15:28Z","links":{"resolver":"https://pith.science/pith/XN7AOH27MV6J2EEOVFTUK27PIP","bundle":"https://pith.science/pith/XN7AOH27MV6J2EEOVFTUK27PIP/bundle.json","state":"https://pith.science/pith/XN7AOH27MV6J2EEOVFTUK27PIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XN7AOH27MV6J2EEOVFTUK27PIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XN7AOH27MV6J2EEOVFTUK27PIP","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":"cc6cf576ad128a305ced41f7430611631dae0a05e404db4eb9726ba0585720fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-02T08:28:31Z","title_canon_sha256":"3e684768163d764fca86564a528a46db0b1a0e79433eadc95347b0549f662b54"},"schema_version":"1.0","source":{"id":"1708.00642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00642","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00642v1","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00642","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"XN7AOH27MV6J","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XN7AOH27MV6J2EEO","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XN7AOH27","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:4a8843f2627765d601492bdfa31f39f599c58fe8b770033d2fd2c7ef98bcd9b8","target":"graph","created_at":"2026-05-17T23:43:38Z","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 provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a countable union of ${\\bf\\Sigma}^0_1 \\!\\times\\! {\\bf\\Sigma}^0_\\xi$ sets, or by a ${\\bf\\Pi}^0_1 \\!\\times\\! {\\bf\\Pi}^0_\\xi$ set.","authors_text":"Dominique Lecomte (IMJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-02T08:28:31Z","title":"A separation result for countable unions of Borel rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00642","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":"sha256:989d2d13d65881221b55900b173cc8f3525c4b29646cbd34ae8df98d07e9baff","target":"record","created_at":"2026-05-17T23:43:38Z","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":"cc6cf576ad128a305ced41f7430611631dae0a05e404db4eb9726ba0585720fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-02T08:28:31Z","title_canon_sha256":"3e684768163d764fca86564a528a46db0b1a0e79433eadc95347b0549f662b54"},"schema_version":"1.0","source":{"id":"1708.00642","kind":"arxiv","version":1}},"canonical_sha256":"bb7e071f5f657c9d108ea967456bef43e7cc48709e15ee739cb07f9f1b81e32c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb7e071f5f657c9d108ea967456bef43e7cc48709e15ee739cb07f9f1b81e32c","first_computed_at":"2026-05-17T23:43:38.521845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:38.521845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWkp+ehbRmo6kgw1lgE6oajdgk13rfDaUXoOejJ/PMbEtrYgE5lmQSlZgE9eSomGD2uALMrUwjCPduMIZGb+Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:38.522414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:989d2d13d65881221b55900b173cc8f3525c4b29646cbd34ae8df98d07e9baff","sha256:4a8843f2627765d601492bdfa31f39f599c58fe8b770033d2fd2c7ef98bcd9b8"],"state_sha256":"39128d59f797b7864115462d8480e4e53a43a8eaec35cb4f4b8b1ad2b1c9d0ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7RH2z4ex0u84303tcEStIdP4YkAdSTXpghsCsWvNMYkG5w5sh/mIwdZFKidZ51tmqZxU0bLGZMV/zkWdeKgYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:15:28.033350Z","bundle_sha256":"c5584e357319f4b2934d90d8b951187821e143fd2e369e62239ad2812c05e278"}}