{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BZ3X3ZXGBLPTUWQ7NX36VMM6N3","short_pith_number":"pith:BZ3X3ZXG","schema_version":"1.0","canonical_sha256":"0e777de6e60adf3a5a1f6df7eab19e6ed45db3512110293e86bfca24b423c4fb","source":{"kind":"arxiv","id":"1712.08516","version":2},"attestation_state":"computed","paper":{"title":"A syntactic approach to the MacNeille completion of $\\bold\\Lambda^{\\ast}$, the free monoid over an ordered alphabet $\\bold \\Lambda$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hans-J\\\"urgen Bandelt, Maurice Pouzet","submitted_at":"2017-12-22T15:29:07Z","abstract_excerpt":"Let $\\Lambda^{\\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\\Lambda^{\\ast}$, where it extends the divisibility ordering of words. The MacNeille completion of $\\Lambda^{\\ast}$ constitutes a complete lattice ordered monoid and is realized by the system of \"closed\" lower sets in $\\Lambda^*$ (ordered by inclusion) or its isomorphic copy formed of the \"closed\" upper sets (ordered by reverse inclusion). Under some additional hypothesis on $\\Lambda$, one can easily identify the closed "},"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":"1712.08516","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-12-22T15:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"579392ef5e0177bbb1c9b1690edccd62972528fbbe606ffaddfe27ec983d7009","abstract_canon_sha256":"2a54ce4efbfad86b3faf7bcfa19ea30dc35b778d6698d451262785cbef53aba2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:44.498893Z","signature_b64":"SE/XQsPCXtT5B7Jzdg2k67I9AKedXhb/xLkLwp9H6L3CAKzyJVp1aexO6/aprc2pQaeb0QWpGTjjtnNIgAHJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e777de6e60adf3a5a1f6df7eab19e6ed45db3512110293e86bfca24b423c4fb","last_reissued_at":"2026-05-18T00:16:44.498224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:44.498224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A syntactic approach to the MacNeille completion of $\\bold\\Lambda^{\\ast}$, the free monoid over an ordered alphabet $\\bold \\Lambda$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hans-J\\\"urgen Bandelt, Maurice Pouzet","submitted_at":"2017-12-22T15:29:07Z","abstract_excerpt":"Let $\\Lambda^{\\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\\Lambda^{\\ast}$, where it extends the divisibility ordering of words. The MacNeille completion of $\\Lambda^{\\ast}$ constitutes a complete lattice ordered monoid and is realized by the system of \"closed\" lower sets in $\\Lambda^*$ (ordered by inclusion) or its isomorphic copy formed of the \"closed\" upper sets (ordered by reverse inclusion). Under some additional hypothesis on $\\Lambda$, one can easily identify the closed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08516","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":"1712.08516","created_at":"2026-05-18T00:16:44.498354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.08516v2","created_at":"2026-05-18T00:16:44.498354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08516","created_at":"2026-05-18T00:16:44.498354+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ3X3ZXGBLPT","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ3X3ZXGBLPTUWQ7","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ3X3ZXG","created_at":"2026-05-18T12:31:08.081275+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/BZ3X3ZXGBLPTUWQ7NX36VMM6N3","json":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3.json","graph_json":"https://pith.science/api/pith-number/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/graph.json","events_json":"https://pith.science/api/pith-number/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/events.json","paper":"https://pith.science/paper/BZ3X3ZXG"},"agent_actions":{"view_html":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3","download_json":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3.json","view_paper":"https://pith.science/paper/BZ3X3ZXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.08516&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/action/storage_attestation","attest_author":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/action/author_attestation","sign_citation":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/action/citation_signature","submit_replication":"https://pith.science/pith/BZ3X3ZXGBLPTUWQ7NX36VMM6N3/action/replication_record"}},"created_at":"2026-05-18T00:16:44.498354+00:00","updated_at":"2026-05-18T00:16:44.498354+00:00"}