{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RGHJ4RQFO2WRJPWEONSACGXK5X","short_pith_number":"pith:RGHJ4RQF","canonical_record":{"source":{"id":"1902.00767","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-02T19:06:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"178a1ce14ba2dd15d864b0ee13679d75314f4188a7f2b2b407678f644d60981e","abstract_canon_sha256":"14de17ff0e5bcc6d0e98a532e133ddcf5e6f8cef3c360b54ef8de6c257c53e9f"},"schema_version":"1.0"},"canonical_sha256":"898e9e460576ad14bec47364011aeaeddebf23954fe62f4799766febb20e14b5","source":{"kind":"arxiv","id":"1902.00767","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00767","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00767v5","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00767","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"RGHJ4RQFO2WR","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_16","alias_value":"RGHJ4RQFO2WRJPWE","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_8","alias_value":"RGHJ4RQF","created_at":"2026-07-05T01:19:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RGHJ4RQFO2WRJPWEONSACGXK5X","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00767","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-02T19:06:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"178a1ce14ba2dd15d864b0ee13679d75314f4188a7f2b2b407678f644d60981e","abstract_canon_sha256":"14de17ff0e5bcc6d0e98a532e133ddcf5e6f8cef3c360b54ef8de6c257c53e9f"},"schema_version":"1.0"},"canonical_sha256":"898e9e460576ad14bec47364011aeaeddebf23954fe62f4799766febb20e14b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:19:49.341304Z","signature_b64":"fu5dxfVwy/DtoPMJ4EBTyXG++u8Zgoiu6xN+ZOyvR0jXJrIp0c5CeDNNpIidiBGFmajncu9rMRHHj5tj1aONDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"898e9e460576ad14bec47364011aeaeddebf23954fe62f4799766febb20e14b5","last_reissued_at":"2026-07-05T01:19:49.340858Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:19:49.340858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00767","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Z4ZeSODH0JTEPzRGr3q1O1vOlacap+Pd5o8LZWgTQBJneuw4fxYEmUgCmcwlHKsNvEF0SgOg+EXShof5dfPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:05:25.643963Z"},"content_sha256":"40785e64b4e53bea10345e0fc35d3f7835f61a28d457067d8d8fd5e0e54774a0","schema_version":"1.0","event_id":"sha256:40785e64b4e53bea10345e0fc35d3f7835f61a28d457067d8d8fd5e0e54774a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RGHJ4RQFO2WRJPWEONSACGXK5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties of high rank subvarieties of affine spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"David Kazhdan, Tamar Ziegler","submitted_at":"2019-02-02T19:06:03Z","abstract_excerpt":"We use tools of additive combinatorics for the study of subvarieties defined by {\\it high rank} families of polynomials in high dimensional $\\mathbb{F} _q$-vector spaces. In the first, analytic part of the paper we prove a number properties of high rank systems of polynomials. In the second, we use these properties to deduce results in Algebraic Geometry, such as an effective Stillman conjecture over algebraically closed fields, an analogue of Nullstellensatz for varieties over finite fields, and a strengthening of a recent result of [5]. We also show that for $k$-varieties $\\mathbb X \\subset "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00767","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.00767/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvzKGoRYt2hiPyEbmbQWPjN5heonnet4XXQ1WirXHn0mocL2ScVs7b9yVCq/RS8znUPkbwfa6y2orDqsKw6UCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:05:25.645973Z"},"content_sha256":"cb50da23628603329523d96a72205b1364a08fbdb945381d9bf818be53069ce0","schema_version":"1.0","event_id":"sha256:cb50da23628603329523d96a72205b1364a08fbdb945381d9bf818be53069ce0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/bundle.json","state_url":"https://pith.science/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/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":"2026-08-08T20:05:25Z","links":{"resolver":"https://pith.science/pith/RGHJ4RQFO2WRJPWEONSACGXK5X","bundle":"https://pith.science/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/bundle.json","state":"https://pith.science/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGHJ4RQFO2WRJPWEONSACGXK5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RGHJ4RQFO2WRJPWEONSACGXK5X","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":"14de17ff0e5bcc6d0e98a532e133ddcf5e6f8cef3c360b54ef8de6c257c53e9f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-02T19:06:03Z","title_canon_sha256":"178a1ce14ba2dd15d864b0ee13679d75314f4188a7f2b2b407678f644d60981e"},"schema_version":"1.0","source":{"id":"1902.00767","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00767","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00767v5","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00767","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"RGHJ4RQFO2WR","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_16","alias_value":"RGHJ4RQFO2WRJPWE","created_at":"2026-07-05T01:19:49Z"},{"alias_kind":"pith_short_8","alias_value":"RGHJ4RQF","created_at":"2026-07-05T01:19:49Z"}],"graph_snapshots":[{"event_id":"sha256:cb50da23628603329523d96a72205b1364a08fbdb945381d9bf818be53069ce0","target":"graph","created_at":"2026-07-05T01:19:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.00767/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use tools of additive combinatorics for the study of subvarieties defined by {\\it high rank} families of polynomials in high dimensional $\\mathbb{F} _q$-vector spaces. In the first, analytic part of the paper we prove a number properties of high rank systems of polynomials. In the second, we use these properties to deduce results in Algebraic Geometry, such as an effective Stillman conjecture over algebraically closed fields, an analogue of Nullstellensatz for varieties over finite fields, and a strengthening of a recent result of [5]. We also show that for $k$-varieties $\\mathbb X \\subset ","authors_text":"David Kazhdan, Tamar Ziegler","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-02T19:06:03Z","title":"Properties of high rank subvarieties of affine spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00767","kind":"arxiv","version":5},"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":"sha256:40785e64b4e53bea10345e0fc35d3f7835f61a28d457067d8d8fd5e0e54774a0","target":"record","created_at":"2026-07-05T01:19:49Z","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":"14de17ff0e5bcc6d0e98a532e133ddcf5e6f8cef3c360b54ef8de6c257c53e9f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-02T19:06:03Z","title_canon_sha256":"178a1ce14ba2dd15d864b0ee13679d75314f4188a7f2b2b407678f644d60981e"},"schema_version":"1.0","source":{"id":"1902.00767","kind":"arxiv","version":5}},"canonical_sha256":"898e9e460576ad14bec47364011aeaeddebf23954fe62f4799766febb20e14b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"898e9e460576ad14bec47364011aeaeddebf23954fe62f4799766febb20e14b5","first_computed_at":"2026-07-05T01:19:49.340858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:19:49.340858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fu5dxfVwy/DtoPMJ4EBTyXG++u8Zgoiu6xN+ZOyvR0jXJrIp0c5CeDNNpIidiBGFmajncu9rMRHHj5tj1aONDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:19:49.341304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00767","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40785e64b4e53bea10345e0fc35d3f7835f61a28d457067d8d8fd5e0e54774a0","sha256:cb50da23628603329523d96a72205b1364a08fbdb945381d9bf818be53069ce0"],"state_sha256":"86975fa0af23f86e472c55858b9d0f3ad8b5505174a71ae1aa07e2166cda910b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQjgnjW/ac+HXI7GXPFMFem3Vub/loTiCHHIPoO1eQxuPBGqGdGCrQ76zKrTtkBy+DgZ8LVZV+6gZiinLTG3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T20:05:25.652515Z","bundle_sha256":"ee0952206cc18b38aca02683f71b642c7772624072bb4d932e3c50e8c1e2b8a4"}}