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As a corollary we show that $2^{{n \\choose [n/2]}} \\leq |\\Semistar(D)| \\leq 2^{2^n}$ if $n = |\\Max(D)|$ is finite; we compute $|\\Semistar(D)|$ if $|\\Max(D)| \\leq 7$; and we show that if $\\Max(D)$ is infinite then $\\Semistar(D)$ has cardinality $2^{2^{|\\Max(D)|}}$."},"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":"1110.1898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-10T00:53:34Z","cross_cats_sorted":[],"title_canon_sha256":"8520682f631e214f17289310244eed48f6fba81e06af4fefd22ca52fda49d38b","abstract_canon_sha256":"f98cde5f0e243daa71fad94c548f48e11fad9c9f36c1aef878cd8678bfd4f9d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.379429Z","signature_b64":"acb/qZc3mRhPFrg8+bz2c9McAIRyJ/Ki34Zu4U9NkFw8O/F2rlmaE0XMFLvGb0DF7HuBu8rAsHy31i1r49OiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"299f26ce83f8c1ea9a4e903f452ae5b7d3b0fb1a9d8f7215e950c1ba33ce98e4","last_reissued_at":"2026-05-18T04:11:19.378972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.378972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semistar operations on Dedekind domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jesse Elliott","submitted_at":"2011-10-10T00:53:34Z","abstract_excerpt":"We give an explicit description of the lattice $\\Semistar(D)$ of all semistar operations on any Dedekind domain $D$ from its set $\\Max(D)$ of maximal ideals. 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As a corollary we show that $2^{{n \\choose [n/2]}} \\leq |\\Semistar(D)| \\leq 2^{2^n}$ if $n = |\\Max(D)|$ is finite; we compute $|\\Semistar(D)|$ if $|\\Max(D)| \\leq 7$; and we show that if $\\Max(D)$ is infinite then $\\Semistar(D)$ has cardinality $2^{2^{|\\Max(D)|}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1898","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":"1110.1898","created_at":"2026-05-18T04:11:19.379032+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1898v1","created_at":"2026-05-18T04:11:19.379032+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1898","created_at":"2026-05-18T04:11:19.379032+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGPSNTUD7DA6","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGPSNTUD7DA6VGSO","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGPSNTUD","created_at":"2026-05-18T12:26:28.662955+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/FGPSNTUD7DA6VGSOSA7UKKXFW7","json":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7.json","graph_json":"https://pith.science/api/pith-number/FGPSNTUD7DA6VGSOSA7UKKXFW7/graph.json","events_json":"https://pith.science/api/pith-number/FGPSNTUD7DA6VGSOSA7UKKXFW7/events.json","paper":"https://pith.science/paper/FGPSNTUD"},"agent_actions":{"view_html":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7","download_json":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7.json","view_paper":"https://pith.science/paper/FGPSNTUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1898&json=true","fetch_graph":"https://pith.science/api/pith-number/FGPSNTUD7DA6VGSOSA7UKKXFW7/graph.json","fetch_events":"https://pith.science/api/pith-number/FGPSNTUD7DA6VGSOSA7UKKXFW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7/action/storage_attestation","attest_author":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7/action/author_attestation","sign_citation":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7/action/citation_signature","submit_replication":"https://pith.science/pith/FGPSNTUD7DA6VGSOSA7UKKXFW7/action/replication_record"}},"created_at":"2026-05-18T04:11:19.379032+00:00","updated_at":"2026-05-18T04:11:19.379032+00:00"}