{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YD7LYKWIC5Y3LMIVYHNWL6IOHR","short_pith_number":"pith:YD7LYKWI","canonical_record":{"source":{"id":"1506.07489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-06-24T18:16:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c18ccf5b7d738cef4cc8ca02acd016b57f7974dc0cac7ab1315d0ce55e88f908","abstract_canon_sha256":"74bdfc6641e604611c11787af104d5c8386837111df16c19b59391efb0ff6b06"},"schema_version":"1.0"},"canonical_sha256":"c0febc2ac81771b5b115c1db65f90e3c5d50d79921da70deb52f4e08db3be00f","source":{"kind":"arxiv","id":"1506.07489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07489","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07489v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07489","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"YD7LYKWIC5Y3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YD7LYKWIC5Y3LMIV","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YD7LYKWI","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YD7LYKWIC5Y3LMIVYHNWL6IOHR","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-06-24T18:16:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c18ccf5b7d738cef4cc8ca02acd016b57f7974dc0cac7ab1315d0ce55e88f908","abstract_canon_sha256":"74bdfc6641e604611c11787af104d5c8386837111df16c19b59391efb0ff6b06"},"schema_version":"1.0"},"canonical_sha256":"c0febc2ac81771b5b115c1db65f90e3c5d50d79921da70deb52f4e08db3be00f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:53.924674Z","signature_b64":"AcvfQczcinQIH7wWrSVYT4hSUruat+9f4t/84WrCdg51QtDXPUMLHt4ldrMOGIYOyE6TC4PWyrKfWmhRUDilAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0febc2ac81771b5b115c1db65f90e3c5d50d79921da70deb52f4e08db3be00f","last_reissued_at":"2026-05-18T01:39:53.924042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:53.924042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07489","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":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4eGkIp6wSECUxyXxjxb7wTxgksbk//y6fuBDW2UHDD7yMFQimQjSUntJiaO1qcedgiYdEA6S/AAlemcRPCV5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:13:51.604532Z"},"content_sha256":"14928f98fe86b074528490c831e27fe8094baa4f1db164078090f658130c6387","schema_version":"1.0","event_id":"sha256:14928f98fe86b074528490c831e27fe8094baa4f1db164078090f658130c6387"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YD7LYKWIC5Y3LMIVYHNWL6IOHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indiscernible arrays and rational functions with algebraic constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.LO","authors_text":"Elad Levi","submitted_at":"2015-06-24T18:16:14Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic zero and $P(x,y)\\in k[x,y]$ be a polynomial which depends on all its variables. $P$ has an algebraic constraint if the set $\\{(P(a,b),(P(a',b'),P(a',b),P(a,b')\\,|\\,a,a',b,b'\\in k\\}$ does not have the maximal Zariski-dimension. Tao proved that if $P$ has an algebraic constraint then it can be decomposed: there exists $Q,F,G\\in k[x]$ such that $P(x_{1},x_{2})=Q(F(x_{1})+G(x_{2}))$, or $P(x_{1},x_{2})=Q(F(x_{1})\\cdot G(x_{2}))$. In this paper we give an answer to a question raised by Hrushovski and Zilber regarding 3-dimensional indiscern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07489","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":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jtaqzn2UM/DGVpc9q/f/CYRPWhdIiZC9fBgi/IVBQXfuYFgmcp70WayAKRm0SovVkIRIZJtSRbnCnrenKACCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:13:51.605269Z"},"content_sha256":"ced332515202e471fc5ca9ed83878020a5c901405e071e51601c8d929024f613","schema_version":"1.0","event_id":"sha256:ced332515202e471fc5ca9ed83878020a5c901405e071e51601c8d929024f613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/bundle.json","state_url":"https://pith.science/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/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":"2026-06-11T20:13:51Z","links":{"resolver":"https://pith.science/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR","bundle":"https://pith.science/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/bundle.json","state":"https://pith.science/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YD7LYKWIC5Y3LMIVYHNWL6IOHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YD7LYKWIC5Y3LMIVYHNWL6IOHR","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":"74bdfc6641e604611c11787af104d5c8386837111df16c19b59391efb0ff6b06","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-06-24T18:16:14Z","title_canon_sha256":"c18ccf5b7d738cef4cc8ca02acd016b57f7974dc0cac7ab1315d0ce55e88f908"},"schema_version":"1.0","source":{"id":"1506.07489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07489","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07489v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07489","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"YD7LYKWIC5Y3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YD7LYKWIC5Y3LMIV","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YD7LYKWI","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:ced332515202e471fc5ca9ed83878020a5c901405e071e51601c8d929024f613","target":"graph","created_at":"2026-05-18T01:39:53Z","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":"Let $k$ be an algebraically closed field of characteristic zero and $P(x,y)\\in k[x,y]$ be a polynomial which depends on all its variables. $P$ has an algebraic constraint if the set $\\{(P(a,b),(P(a',b'),P(a',b),P(a,b')\\,|\\,a,a',b,b'\\in k\\}$ does not have the maximal Zariski-dimension. Tao proved that if $P$ has an algebraic constraint then it can be decomposed: there exists $Q,F,G\\in k[x]$ such that $P(x_{1},x_{2})=Q(F(x_{1})+G(x_{2}))$, or $P(x_{1},x_{2})=Q(F(x_{1})\\cdot G(x_{2}))$. In this paper we give an answer to a question raised by Hrushovski and Zilber regarding 3-dimensional indiscern","authors_text":"Elad Levi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-06-24T18:16:14Z","title":"Indiscernible arrays and rational functions with algebraic constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07489","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":"sha256:14928f98fe86b074528490c831e27fe8094baa4f1db164078090f658130c6387","target":"record","created_at":"2026-05-18T01:39:53Z","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":"74bdfc6641e604611c11787af104d5c8386837111df16c19b59391efb0ff6b06","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-06-24T18:16:14Z","title_canon_sha256":"c18ccf5b7d738cef4cc8ca02acd016b57f7974dc0cac7ab1315d0ce55e88f908"},"schema_version":"1.0","source":{"id":"1506.07489","kind":"arxiv","version":1}},"canonical_sha256":"c0febc2ac81771b5b115c1db65f90e3c5d50d79921da70deb52f4e08db3be00f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0febc2ac81771b5b115c1db65f90e3c5d50d79921da70deb52f4e08db3be00f","first_computed_at":"2026-05-18T01:39:53.924042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:53.924042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AcvfQczcinQIH7wWrSVYT4hSUruat+9f4t/84WrCdg51QtDXPUMLHt4ldrMOGIYOyE6TC4PWyrKfWmhRUDilAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:53.924674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14928f98fe86b074528490c831e27fe8094baa4f1db164078090f658130c6387","sha256:ced332515202e471fc5ca9ed83878020a5c901405e071e51601c8d929024f613"],"state_sha256":"d532f3742eebf366ee12b2e2e65746a63a02685fec2df224c8c6929e92991114"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NtQEj17itcoKcrAacsSI6tQG5KJIdSTVQ1Vz5OkzUI2BVhRymkCaddMlS5h0y9nTexjIwijeO+ofRdCVupGMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:13:51.609523Z","bundle_sha256":"4b7e7ea9bc2fe7cc03076549f9b880b5da67e87e4fa4c0e4a8f391e34648c26d"}}