{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VJKY3WCYZR4Q7Y5ZAL7O5VTP6U","short_pith_number":"pith:VJKY3WCY","schema_version":"1.0","canonical_sha256":"aa558dd858cc790fe3b902feeed66ff510c9443bf0508aa8197ef69fc40719ba","source":{"kind":"arxiv","id":"1710.10616","version":1},"attestation_state":"computed","paper":{"title":"$k$-Foldability of Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Beth Bjorkman, Danny Rorabaugh, Garner Cochran, Heather Smith, Jennifer Wise, Lauren Keough, Mitch Phillipson, Rachel Kirsch, Wei Gao","submitted_at":"2017-10-29T13:44:59Z","abstract_excerpt":"We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet $\\{A_1, \\overline{A}_1, \\ldots, A_m, \\overline{A}_m\\}$ in which $\\overline{A}_i$ is called the complement of $A_i$. A word $w$ is foldable if can be wrapped around a rooted plane tree $T$, starting at the root and working counterclockwise such that one letter labels each half edge and the two letters labeling the same edge are complements. The tree $T$ is called $w$-valid.\n  We define a bijection between "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.10616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-29T13:44:59Z","cross_cats_sorted":[],"title_canon_sha256":"33e42cea8d1273875e083bd210888d7c981b52c565342026c80513df77ed0c2a","abstract_canon_sha256":"b71516a318dd4806613e37212f452e6e51e3a073c5757acfd2c29a3f07f7b4c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:56.886227Z","signature_b64":"CYo1fShNwaDBuEQAQpPP553Y+dpNP4TJq2HO5JU9xbJBaAdJFQGNFqU5+lHET6icyyPIWX7ozD7tEOX2szMFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa558dd858cc790fe3b902feeed66ff510c9443bf0508aa8197ef69fc40719ba","last_reissued_at":"2026-05-17T23:45:56.885797Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:56.885797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$k$-Foldability of Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Beth Bjorkman, Danny Rorabaugh, Garner Cochran, Heather Smith, Jennifer Wise, Lauren Keough, Mitch Phillipson, Rachel Kirsch, Wei Gao","submitted_at":"2017-10-29T13:44:59Z","abstract_excerpt":"We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet $\\{A_1, \\overline{A}_1, \\ldots, A_m, \\overline{A}_m\\}$ in which $\\overline{A}_i$ is called the complement of $A_i$. A word $w$ is foldable if can be wrapped around a rooted plane tree $T$, starting at the root and working counterclockwise such that one letter labels each half edge and the two letters labeling the same edge are complements. The tree $T$ is called $w$-valid.\n  We define a bijection between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10616","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.10616","created_at":"2026-05-17T23:45:56.885872+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10616v1","created_at":"2026-05-17T23:45:56.885872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10616","created_at":"2026-05-17T23:45:56.885872+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJKY3WCYZR4Q","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJKY3WCYZR4Q7Y5Z","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJKY3WCY","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U","json":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U.json","graph_json":"https://pith.science/api/pith-number/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/graph.json","events_json":"https://pith.science/api/pith-number/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/events.json","paper":"https://pith.science/paper/VJKY3WCY"},"agent_actions":{"view_html":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U","download_json":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U.json","view_paper":"https://pith.science/paper/VJKY3WCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10616&json=true","fetch_graph":"https://pith.science/api/pith-number/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/graph.json","fetch_events":"https://pith.science/api/pith-number/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/action/storage_attestation","attest_author":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/action/author_attestation","sign_citation":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/action/citation_signature","submit_replication":"https://pith.science/pith/VJKY3WCYZR4Q7Y5ZAL7O5VTP6U/action/replication_record"}},"created_at":"2026-05-17T23:45:56.885872+00:00","updated_at":"2026-05-17T23:45:56.885872+00:00"}