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The smallest number $s$ for which there exist $\\varphi_1, \\ldots, \\varphi_s \\in Hom_R(\\omega_R,R)$ with $tr(\\omega_R)=\\varphi_1(\\omega_R) + \\cdots + \\varphi_s(\\omega_R)$ is called the Teter number of $R$. We say that $R$ is of Teter type if $s = 1$. It is shown that $R$ is not of Teter type if $R$ is generically Gore"},"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":"2112.04237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2021-12-08T11:32:05Z","cross_cats_sorted":[],"title_canon_sha256":"7923d9607c01960198dfb94b89c6c5b298bccbc52d619a3ac72fc023d950504f","abstract_canon_sha256":"c9df05bca3457c31fe70882fe517670ddf61ecd9ef23b7d57cd646f1de4dd4c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:40:54.219948Z","signature_b64":"Hy8bWDlod8KhRVEvQ9Fh7RR+e/Ee1NPhCgqqrLEPNaY+nV6VhdqTzIxyIivge+r3Kg2GXm/1nqAY48/JTZGHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a407cf5350ac20d746ad8e258094f2821b694a887f4007ca0685a1e90a4eb36","last_reissued_at":"2026-07-05T03:40:54.219555Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:40:54.219555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rings of Teter type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"J\\\"urgen Herzog, Oleksandra Gasanova, Somayeh Moradi, Takayuki Hibi","submitted_at":"2021-12-08T11:32:05Z","abstract_excerpt":"Let $R$ be a Cohen--Macaulay local $K$-algebra or a standard graded $K$-algebra over a field $K$ with a canonical module $\\omega_R$. The trace of $\\omega_R$ is the ideal $tr(\\omega_R)$ of $R$ which is the sum of those ideals $\\varphi(\\omega_R)$ with $\\varphi\\in Hom_R(\\omega_R,R)$. The smallest number $s$ for which there exist $\\varphi_1, \\ldots, \\varphi_s \\in Hom_R(\\omega_R,R)$ with $tr(\\omega_R)=\\varphi_1(\\omega_R) + \\cdots + \\varphi_s(\\omega_R)$ is called the Teter number of $R$. We say that $R$ is of Teter type if $s = 1$. It is shown that $R$ is not of Teter type if $R$ is generically Gore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04237","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.04237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2112.04237","created_at":"2026-07-05T03:40:54.219619+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.04237v2","created_at":"2026-07-05T03:40:54.219619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04237","created_at":"2026-07-05T03:40:54.219619+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJAHZ5JVBLBA","created_at":"2026-07-05T03:40:54.219619+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJAHZ5JVBLBA25DK","created_at":"2026-07-05T03:40:54.219619+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJAHZ5JV","created_at":"2026-07-05T03:40:54.219619+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/LJAHZ5JVBLBA25DK3DRFQCKPFA","json":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA.json","graph_json":"https://pith.science/api/pith-number/LJAHZ5JVBLBA25DK3DRFQCKPFA/graph.json","events_json":"https://pith.science/api/pith-number/LJAHZ5JVBLBA25DK3DRFQCKPFA/events.json","paper":"https://pith.science/paper/LJAHZ5JV"},"agent_actions":{"view_html":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA","download_json":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA.json","view_paper":"https://pith.science/paper/LJAHZ5JV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.04237&json=true","fetch_graph":"https://pith.science/api/pith-number/LJAHZ5JVBLBA25DK3DRFQCKPFA/graph.json","fetch_events":"https://pith.science/api/pith-number/LJAHZ5JVBLBA25DK3DRFQCKPFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA/action/storage_attestation","attest_author":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA/action/author_attestation","sign_citation":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA/action/citation_signature","submit_replication":"https://pith.science/pith/LJAHZ5JVBLBA25DK3DRFQCKPFA/action/replication_record"}},"created_at":"2026-07-05T03:40:54.219619+00:00","updated_at":"2026-07-05T03:40:54.219619+00:00"}