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The number of copies of E in degree i equals the k-vector space dimension of the cohomology module Ext^i(k,R). These dimensions, known as Bass numbers, form an infinite sequence of invariants of R about which little is known. We prove that it is non-decreasing and grows exponentially if R is Golod, a non-trivial fiber product, or Teter, or"},"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":"0812.4672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-12-26T11:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"0c16863fb83f4a90a941922f2e9fb97e1423b6be2679d6714ff63fb0823228f7","abstract_canon_sha256":"7e33b08f2ed3550cce09d016b9258fc867f5f7c8f7bf7398a5c734cffd8188f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.842754Z","signature_b64":"R4CYILqlZ5UN+3gn+9GRSPKEvZbk5zeSAae6rIcJ26qb9McFvzTI0NPM2ZbJCYBgulohsb+arqmsOFcP4gmNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cd9467ec49537d8bac096d91b0accbba45d9d83a49a49eeef64b349a584ade9","last_reissued_at":"2026-05-18T02:58:10.842200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.842200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth in the minimal injective resolution of a local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Janet Striuli, Lars Winther Christensen, Oana Veliche","submitted_at":"2008-12-26T11:58:21Z","abstract_excerpt":"Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. 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