{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q4QFICV5MKUWAFD2UH6F3D2Y6S","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":"92362baaaecd16eaf7af9971e0d3cb835337baea081457bb26a52072eb6195fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-27T15:27:25Z","title_canon_sha256":"b048423b26de32cc30728dfca48f7eb910ba9fda8808a6c0dcdb641068f70650"},"schema_version":"1.0","source":{"id":"1201.5799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5799","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5799v2","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5799","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"Q4QFICV5MKUW","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q4QFICV5MKUWAFD2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q4QFICV5","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:01776e63859444ddcdcfa2774ab1d25e3c0675c040ff514046ae1d11ac13d4d4","target":"graph","created_at":"2026-05-18T01:21:05Z","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 prove that in NTP_2 theories if p is a dependent type with dp-rank >= \\kappa, then this can be witnessed by indiscernible sequences of tuples satisfying p. If p has dp-rank infinity, then this can be witnessed by singletons (in any theory).","authors_text":"Itay Kaplan, Pierre Simon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-27T15:27:25Z","title":"Witnessing dp-rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5799","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":"sha256:3fbd734ffd31ec85eafa0464aa84660152b51040b3d74679fc8c52e353f071fa","target":"record","created_at":"2026-05-18T01:21:05Z","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":"92362baaaecd16eaf7af9971e0d3cb835337baea081457bb26a52072eb6195fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-01-27T15:27:25Z","title_canon_sha256":"b048423b26de32cc30728dfca48f7eb910ba9fda8808a6c0dcdb641068f70650"},"schema_version":"1.0","source":{"id":"1201.5799","kind":"arxiv","version":2}},"canonical_sha256":"8720540abd62a960147aa1fc5d8f58f4bb9460ce0d5b31b39431ff57aee8302b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8720540abd62a960147aa1fc5d8f58f4bb9460ce0d5b31b39431ff57aee8302b","first_computed_at":"2026-05-18T01:21:05.796847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:05.796847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lbk5wCKT9ImKRkYEmNPkY/c9pD512bsCZyM/pIcOIR8rqyswByUxdqZJBNoNYfGKyf/9vWpXZrO42OIGOYToDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:05.797482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fbd734ffd31ec85eafa0464aa84660152b51040b3d74679fc8c52e353f071fa","sha256:01776e63859444ddcdcfa2774ab1d25e3c0675c040ff514046ae1d11ac13d4d4"],"state_sha256":"df8568ceec7e1f340186eaba2097e106ba1741b6d4bcd349e4ff8a54a9b84e19"}