{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LIU5VM4CJ723YZ743BJOFE6VAM","short_pith_number":"pith:LIU5VM4C","schema_version":"1.0","canonical_sha256":"5a29dab3824ff5bc67fcd852e293d50324bc7b8d12dd468e970d0cb0b04b0f2d","source":{"kind":"arxiv","id":"1311.2318","version":2},"attestation_state":"computed","paper":{"title":"Counting the Palstars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"math.CO","authors_text":"Jeffrey Shallit, L. Bruce Richmond","submitted_at":"2013-11-10T23:27:54Z","abstract_excerpt":"A palstar (after Knuth, Morris, and Pratt) is a concatenation of even-length palindromes. We show that, asymptotically, there are $\\Theta(\\alpha_k^n)$ palstars of length $2n$ over a $k$-letter alphabet, where $\\alpha_k$ is a constant such that $2k-1 < \\alpha_k < 2k-{1 \\over 2}$. In particular, $\\alpha_2 \\doteq 3.33513193$."},"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":"1311.2318","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-10T23:27:54Z","cross_cats_sorted":["cs.DM","cs.FL"],"title_canon_sha256":"1a7b497413c94e825496fbda2695453d5814735ecd5ddd8926026a20e063311f","abstract_canon_sha256":"98e173f9aa722da07d672f3b979e30c2085319065697b3c73bae88ef7d49f72e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:53.903950Z","signature_b64":"MSUnUQbTycXct23cPtcQrfaXTyHeo8dnOD507A83mHh3/9RAdEWg3XJu+8W46YsMOOlrbj7itlMCnLTnhgq4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a29dab3824ff5bc67fcd852e293d50324bc7b8d12dd468e970d0cb0b04b0f2d","last_reissued_at":"2026-05-18T02:49:53.903374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:53.903374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting the Palstars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL"],"primary_cat":"math.CO","authors_text":"Jeffrey Shallit, L. Bruce Richmond","submitted_at":"2013-11-10T23:27:54Z","abstract_excerpt":"A palstar (after Knuth, Morris, and Pratt) is a concatenation of even-length palindromes. We show that, asymptotically, there are $\\Theta(\\alpha_k^n)$ palstars of length $2n$ over a $k$-letter alphabet, where $\\alpha_k$ is a constant such that $2k-1 < \\alpha_k < 2k-{1 \\over 2}$. In particular, $\\alpha_2 \\doteq 3.33513193$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2318","kind":"arxiv","version":2},"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":"1311.2318","created_at":"2026-05-18T02:49:53.903480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.2318v2","created_at":"2026-05-18T02:49:53.903480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2318","created_at":"2026-05-18T02:49:53.903480+00:00"},{"alias_kind":"pith_short_12","alias_value":"LIU5VM4CJ723","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LIU5VM4CJ723YZ74","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LIU5VM4C","created_at":"2026-05-18T12:27:51.066281+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/LIU5VM4CJ723YZ743BJOFE6VAM","json":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM.json","graph_json":"https://pith.science/api/pith-number/LIU5VM4CJ723YZ743BJOFE6VAM/graph.json","events_json":"https://pith.science/api/pith-number/LIU5VM4CJ723YZ743BJOFE6VAM/events.json","paper":"https://pith.science/paper/LIU5VM4C"},"agent_actions":{"view_html":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM","download_json":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM.json","view_paper":"https://pith.science/paper/LIU5VM4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.2318&json=true","fetch_graph":"https://pith.science/api/pith-number/LIU5VM4CJ723YZ743BJOFE6VAM/graph.json","fetch_events":"https://pith.science/api/pith-number/LIU5VM4CJ723YZ743BJOFE6VAM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM/action/storage_attestation","attest_author":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM/action/author_attestation","sign_citation":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM/action/citation_signature","submit_replication":"https://pith.science/pith/LIU5VM4CJ723YZ743BJOFE6VAM/action/replication_record"}},"created_at":"2026-05-18T02:49:53.903480+00:00","updated_at":"2026-05-18T02:49:53.903480+00:00"}