{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZMBWSSWW22NTM3CG3BTJP5CVYJ","short_pith_number":"pith:ZMBWSSWW","schema_version":"1.0","canonical_sha256":"cb03694ad6d69b366c46d86697f455c259d2e2784db9351483886eda1c22301f","source":{"kind":"arxiv","id":"1501.00377","version":1},"attestation_state":"computed","paper":{"title":"The index of a string consisting of 4 blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heping Zhang, Jianxin Wei","submitted_at":"2015-01-02T10:32:44Z","abstract_excerpt":"Generalized Fibonacci cube $Q_{d}(f)$, introduced by Ili\\'{c}, Klav\\v{z}ar and Rho, is the graph obtained from the $d$-hypercube $Q_{d}$ by removing all vertices that contain $f$ as a substring. The smallest integer $d$ such that $Q_{d}(f)$ is not an isometric subgraph of $Q_{d}$ is called the index of $f$. A non-extendable sequence of contiguous equal digits in a string $\\mu$ is called a block of $\\mu$. The question that determine the index of a string consisting of at most 3 blocks is solved by Ili\\'{c}, Klav\\v{z}ar and Rho. This question is further studied and the index of a string consisti"},"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":"1501.00377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-02T10:32:44Z","cross_cats_sorted":[],"title_canon_sha256":"68bea88b6142c00bed5e7130a4042f94bc450dd7a24a4e1cb5e9417acdcec83b","abstract_canon_sha256":"fbd3e1d8eb06be29abc4e67dfe4705abca30b248290c21e3c08c87de6f3232d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:09.351908Z","signature_b64":"9DXkADqrkIQz1GUynw8Z21YwPGN1RsFf+GM41jPJCQapsn+8mD1VYNHV4WN2tRHRDz3GG4vKwjidd+jZdjH6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb03694ad6d69b366c46d86697f455c259d2e2784db9351483886eda1c22301f","last_reissued_at":"2026-05-18T02:30:09.351289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:09.351289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The index of a string consisting of 4 blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heping Zhang, Jianxin Wei","submitted_at":"2015-01-02T10:32:44Z","abstract_excerpt":"Generalized Fibonacci cube $Q_{d}(f)$, introduced by Ili\\'{c}, Klav\\v{z}ar and Rho, is the graph obtained from the $d$-hypercube $Q_{d}$ by removing all vertices that contain $f$ as a substring. The smallest integer $d$ such that $Q_{d}(f)$ is not an isometric subgraph of $Q_{d}$ is called the index of $f$. A non-extendable sequence of contiguous equal digits in a string $\\mu$ is called a block of $\\mu$. The question that determine the index of a string consisting of at most 3 blocks is solved by Ili\\'{c}, Klav\\v{z}ar and Rho. This question is further studied and the index of a string consisti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00377","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":"1501.00377","created_at":"2026-05-18T02:30:09.351393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00377v1","created_at":"2026-05-18T02:30:09.351393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00377","created_at":"2026-05-18T02:30:09.351393+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMBWSSWW22NT","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMBWSSWW22NTM3CG","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMBWSSWW","created_at":"2026-05-18T12:29:52.810259+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/ZMBWSSWW22NTM3CG3BTJP5CVYJ","json":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ.json","graph_json":"https://pith.science/api/pith-number/ZMBWSSWW22NTM3CG3BTJP5CVYJ/graph.json","events_json":"https://pith.science/api/pith-number/ZMBWSSWW22NTM3CG3BTJP5CVYJ/events.json","paper":"https://pith.science/paper/ZMBWSSWW"},"agent_actions":{"view_html":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ","download_json":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ.json","view_paper":"https://pith.science/paper/ZMBWSSWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00377&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMBWSSWW22NTM3CG3BTJP5CVYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMBWSSWW22NTM3CG3BTJP5CVYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ/action/storage_attestation","attest_author":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ/action/author_attestation","sign_citation":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ/action/citation_signature","submit_replication":"https://pith.science/pith/ZMBWSSWW22NTM3CG3BTJP5CVYJ/action/replication_record"}},"created_at":"2026-05-18T02:30:09.351393+00:00","updated_at":"2026-05-18T02:30:09.351393+00:00"}