{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DMLVLPDJWAGG2JKVUKF44TRPED","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":"474ddb3df27649b6c1abc5385e75bc461f0d0da8118a8b25212d5548d5f7f9dd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-23T22:45:56Z","title_canon_sha256":"3d8d2d190a1b9498f318a67d9cdd109af65961a971f3da66b19d4c17fc2ce059"},"schema_version":"1.0","source":{"id":"1904.10562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10562","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10562v2","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10562","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"DMLVLPDJWAGG","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DMLVLPDJWAGG2JKV","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DMLVLPDJ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:f85f769e9bef6984902e302b2aaf91037c2909ecb607adb22baf1addd50e7a8b","target":"graph","created_at":"2026-05-17T23:45:51Z","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":"Suppose that $d \\geq 2$, and that $A \\subset [0,1]$ has sufficiently large dimension, $1 - \\epsilon_d < \\dim_H(A) < 1$. Then for any polynomial $P$ of degree $d$ with no constant term, there exists a point configuration $\\{ x, x-t,x-P(t) \\} \\subset A$ with $t \\approx_P 1$.","authors_text":"Ben Krause","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-23T22:45:56Z","title":"A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10562","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:beb30848942d67022d4ab17dbe5662ab486e70a6a5459244275970a6f00e209c","target":"record","created_at":"2026-05-17T23:45:51Z","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":"474ddb3df27649b6c1abc5385e75bc461f0d0da8118a8b25212d5548d5f7f9dd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-23T22:45:56Z","title_canon_sha256":"3d8d2d190a1b9498f318a67d9cdd109af65961a971f3da66b19d4c17fc2ce059"},"schema_version":"1.0","source":{"id":"1904.10562","kind":"arxiv","version":2}},"canonical_sha256":"1b1755bc69b00c6d2555a28bce4e2f20d609e45dc14ee4d603126d436fb418c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b1755bc69b00c6d2555a28bce4e2f20d609e45dc14ee4d603126d436fb418c5","first_computed_at":"2026-05-17T23:45:51.714263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:51.714263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/l/gqhXIjTm8BxYMI1O8VBj9MijI6ZK5HRzt14RgJFwjnzItF3z6pgko8dbMoJih7QydPet9MRWUQ4xPL/bDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:51.714756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beb30848942d67022d4ab17dbe5662ab486e70a6a5459244275970a6f00e209c","sha256:f85f769e9bef6984902e302b2aaf91037c2909ecb607adb22baf1addd50e7a8b"],"state_sha256":"68340b5f62b90b07afa6e4f5848a021b561976d279de14bbac63260a95222d3b"}