{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L3LWL62UPCOQDJCGA62W6HZ4OH","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":"1536795a01d811c8365e8048b308aebfbaec6c3ff0b8e64914cf061378703426","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-09-05T10:36:14Z","title_canon_sha256":"f57f87bd4f0f838dc02f218b8b39b1033421f3bc27e349d2d0b79db1f15d0e86"},"schema_version":"1.0","source":{"id":"1809.01426","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01426","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01426v2","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01426","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"L3LWL62UPCOQ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L3LWL62UPCOQDJCG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L3LWL62U","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:21bf713bfb987fe7ed9ee21f1e16cf3730387395688359665eb8f73072f59e3d","target":"graph","created_at":"2026-05-17T23:47:39Z","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 consider a variation on a classical avoidance problem from combinatorics on words that has been introduced by Mousavi and Shallit at DLT 2013. Let $\\texttt{pexp}_i(w)$ be the supremum of the exponent over the products of $i$ factors of the word $w$. The repetition threshold $\\texttt{RT}_i(k)$ is then the infimum of $\\texttt{pexp}_i(w)$ over all words $w\\in\\Sigma^\\omega_k$. Mousavi and Shallit obtained that $\\texttt{RT}_i(2)=2i$ and $\\texttt{RT}_2(3)=\\tfrac{13}4$. We show that $\\texttt{RT}_i(3)=\\tfrac{3i}2+\\tfrac14$ if $i$ is even and $\\texttt{RT}_i(3)=\\tfrac{3i}2+\\tfrac16$ if $i$ is odd and","authors_text":"Kamellia Reshadi, Pamela Fleischmann, Pascal Ochem","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-09-05T10:36:14Z","title":"Repetition avoidance in products of factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01426","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:dfd6b0bc4061f00c35a1f60e63cca2f911448b4b987d10e5de0e04f121662724","target":"record","created_at":"2026-05-17T23:47:39Z","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":"1536795a01d811c8365e8048b308aebfbaec6c3ff0b8e64914cf061378703426","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-09-05T10:36:14Z","title_canon_sha256":"f57f87bd4f0f838dc02f218b8b39b1033421f3bc27e349d2d0b79db1f15d0e86"},"schema_version":"1.0","source":{"id":"1809.01426","kind":"arxiv","version":2}},"canonical_sha256":"5ed765fb54789d01a44607b56f1f3c71fa4a3f6c29fdde753c2a36f1120fba54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed765fb54789d01a44607b56f1f3c71fa4a3f6c29fdde753c2a36f1120fba54","first_computed_at":"2026-05-17T23:47:39.809895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:39.809895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bpwZySCuTg5jhaNSqtdAfjhQoVfnDbExG77xbAM0psQ8ESxN57vqQssRjzCyBiqQ2msPhe2QeXHFDmlFhlgUBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:39.810288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01426","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfd6b0bc4061f00c35a1f60e63cca2f911448b4b987d10e5de0e04f121662724","sha256:21bf713bfb987fe7ed9ee21f1e16cf3730387395688359665eb8f73072f59e3d"],"state_sha256":"978e9fbc437833ce6ff17122d915ad9ef7d33cf5489071b151ae450dfeab7ac9"}