{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VFCN2B2XDB7LAIYEBXKM2GSRFZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81d54a278d4fd346ccef995fa4fa972d475de2d02604e834a8a9ad9002619160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-04T17:07:23Z","title_canon_sha256":"c28e56b7b804c69ebe89844125333afb7926435a9b9770feafebbaa958df93f4"},"schema_version":"1.0","source":{"id":"1207.1060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1060","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1060v1","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1060","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"VFCN2B2XDB7L","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VFCN2B2XDB7LAIYE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VFCN2B2X","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1d6f3088447b921057cce959a6ce8b905f7c39a8316beddd134b0b6279d2575a","target":"graph","created_at":"2026-05-18T03:51:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we work with several divisors of a module $E \\subseteq G \\simeq R^{e}$ having rank $e$, such as the classical Fitting ideals of $E$ and of $G/E$, and the more recently introduced (generic) Bourbaki ideals $I(E)$ (A. Simis, B. Ulrich, and W. Vasconcelos [18]) or ideal norms $[[E]]_R$ (O. Villamayor [22]). We found several relations and equalities among them which allow to describe in some cases universal properties with respect to $E$ of their blow ups. As a byproduct we are also able to obtain lower bounds for the analytic spread $\\ell(\\bigwedge^{e}E)$ related with the algebraic ","authors_text":"Ana L. Branco Correia, Santiago Zarzuela","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-04T17:07:23Z","title":"Divisors of a module and blow up"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1060","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c0d965ff6e52b8de917dfcd2e36f9a191cf0c9f2f43136391a3ea2d3ad543c81","target":"record","created_at":"2026-05-18T03:51:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81d54a278d4fd346ccef995fa4fa972d475de2d02604e834a8a9ad9002619160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-04T17:07:23Z","title_canon_sha256":"c28e56b7b804c69ebe89844125333afb7926435a9b9770feafebbaa958df93f4"},"schema_version":"1.0","source":{"id":"1207.1060","kind":"arxiv","version":1}},"canonical_sha256":"a944dd0757187eb023040dd4cd1a512e59f396f35ccf6d5da0098a34964fd52b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a944dd0757187eb023040dd4cd1a512e59f396f35ccf6d5da0098a34964fd52b","first_computed_at":"2026-05-18T03:51:47.623285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:47.623285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dtGj4+dayfkBYz3yPfC4ro6OcU/K2UhdlWNKdHsh4uKw4+6Hj9cD0Ujk6J5yrN7DTwlIvMsy2g4BuDja+NlaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:47.624130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0d965ff6e52b8de917dfcd2e36f9a191cf0c9f2f43136391a3ea2d3ad543c81","sha256:1d6f3088447b921057cce959a6ce8b905f7c39a8316beddd134b0b6279d2575a"],"state_sha256":"7d79f26959a1d51139a19f9088f7fe2fff316b8935864d4a321e83dd3ceb044b"}