{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2YYJHJGRAT34BPZSG3X6UNOROB","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":"6ee4338e202076079daeb4fec14c7a51819706dec3e74e13e03c29002407e2e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-08-22T00:48:55Z","title_canon_sha256":"92c9a6522e97f25272d00a77f4618c98effac5a348ce2654c0a4c9f2efa6a229"},"schema_version":"1.0","source":{"id":"1708.06462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06462","created_at":"2026-05-18T00:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06462v1","created_at":"2026-05-18T00:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06462","created_at":"2026-05-18T00:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"2YYJHJGRAT34","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YYJHJGRAT34BPZS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YYJHJGR","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:a1e5ee0bea74bc77f8be0a144a8a20341fbf87b110ae2fb38dbf8eee4eadcaf8","target":"graph","created_at":"2026-05-18T00:37:41Z","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":"Fraenkel and Simpson showed that the number of distinct squares in a word of length n is bounded from above by 2n, since at most two distinct squares have their rightmost, or last, occurrence begin at each position. Improvements by Ilie to $2n-\\Theta(\\log n)$ and by Deza et al. to 11n/6 rely on the study of combinatorics of FS-double-squares, when the maximum number of two last occurrences of squares begin. In this paper, we first study how to maximize runs of FS-double-squares in the prefix of a word. We show that for a given positive integer m, the minimum length of a word beginning with m F","authors_text":"F. Blanchet-Sadri (Department of Computer Science, S. Osborne (Department of Computer Science, University of North Carolina)","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-08-22T00:48:55Z","title":"Constructing Words with High Distinct Square Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06462","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:e35fb53c0dc80d4bec1e3080380bb090006338dfc0baf05eb5c478eeb13032e6","target":"record","created_at":"2026-05-18T00:37:41Z","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":"6ee4338e202076079daeb4fec14c7a51819706dec3e74e13e03c29002407e2e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-08-22T00:48:55Z","title_canon_sha256":"92c9a6522e97f25272d00a77f4618c98effac5a348ce2654c0a4c9f2efa6a229"},"schema_version":"1.0","source":{"id":"1708.06462","kind":"arxiv","version":1}},"canonical_sha256":"d63093a4d104f7c0bf3236efea35d17066776ebd8576ec2f3360a313a34b4af8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d63093a4d104f7c0bf3236efea35d17066776ebd8576ec2f3360a313a34b4af8","first_computed_at":"2026-05-18T00:37:41.434017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:41.434017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZWMQNhjHf0NIuputDs1sTX6mxG4RGAVDtpBPmFskogbsGDZzYEhOcvv98+k45PLFJJd5eoWMoU34RSD34WbjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:41.434690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e35fb53c0dc80d4bec1e3080380bb090006338dfc0baf05eb5c478eeb13032e6","sha256:a1e5ee0bea74bc77f8be0a144a8a20341fbf87b110ae2fb38dbf8eee4eadcaf8"],"state_sha256":"356e5fae0a7979c9d6a526440be1c3490063e1a7ad09b905eb6c9e657a10c746"}