{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:726F4GQZ2JE7QZA4NAFYTASIJV","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":"17c940afdaeea6018e533d88457285d63ff488c44db59e59819d9b92ea494c0b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2023-06-25T13:29:49Z","title_canon_sha256":"02743f37ce59f094a357a8ea0bc303b32d3c18b67df36c63248b73e78918dfc8"},"schema_version":"1.0","source":{"id":"2306.14243","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.14243","created_at":"2026-07-05T06:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"2306.14243v4","created_at":"2026-07-05T06:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.14243","created_at":"2026-07-05T06:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"726F4GQZ2JE7","created_at":"2026-07-05T06:58:41Z"},{"alias_kind":"pith_short_16","alias_value":"726F4GQZ2JE7QZA4","created_at":"2026-07-05T06:58:41Z"},{"alias_kind":"pith_short_8","alias_value":"726F4GQZ","created_at":"2026-07-05T06:58:41Z"}],"graph_snapshots":[{"event_id":"sha256:d1e490372cdc91b9bce1a0c2c11190347dbd50cbe26a1c0a6992253563cab1eb","target":"graph","created_at":"2026-07-05T06:58:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.14243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $I$ be a graded ideal of a standard graded polynomial ring $S$ with coefficients in a field $K$. The asymptotic behaviour of the $\\text{v}$-number of the powers of $I$ is investigated. Natural lower and upper bounds which are linear functions in $k$ are determined for $\\text{v}(I^k)$. We call $\\text{v}(I^k)$ the $\\text{v}$-function of $I$. We prove that $\\text{v}(I^k)$ is a linear function in $k$ for $k$ large enough, of the form $\\text{v}(I^k)=\\alpha(I)k+b$, where $\\alpha(I)$ is the initial degree of $I$, and $b\\in\\mathbb{Z}$ is a suitable integer. For this aim, we construct new blowup al","authors_text":"Antonino Ficarra, Emanuele Sgroi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2023-06-25T13:29:49Z","title":"Asymptotic behaviour of the $\\text{v}$-number of homogeneous ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.14243","kind":"arxiv","version":4},"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":"sha256:266e9fb0eca410ec1dd6975d9b6911eefe8e839350347b2ea4247933780f36ed","target":"record","created_at":"2026-07-05T06:58:41Z","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":"17c940afdaeea6018e533d88457285d63ff488c44db59e59819d9b92ea494c0b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2023-06-25T13:29:49Z","title_canon_sha256":"02743f37ce59f094a357a8ea0bc303b32d3c18b67df36c63248b73e78918dfc8"},"schema_version":"1.0","source":{"id":"2306.14243","kind":"arxiv","version":4}},"canonical_sha256":"febc5e1a19d249f8641c680b8982484d6fa8c57f9ca8e949c53c7569be82f12c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"febc5e1a19d249f8641c680b8982484d6fa8c57f9ca8e949c53c7569be82f12c","first_computed_at":"2026-07-05T06:58:41.129111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:58:41.129111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8X4OVwWkyvZLBvcr7VNVMQB1KIdC7O6IWY3kW/ne6VGxbnhY+cxmuQgXnDT/DzCsPQEyXlVqZtYBRvSRrYtzBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:58:41.129667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.14243","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:266e9fb0eca410ec1dd6975d9b6911eefe8e839350347b2ea4247933780f36ed","sha256:d1e490372cdc91b9bce1a0c2c11190347dbd50cbe26a1c0a6992253563cab1eb"],"state_sha256":"0f46a8dfe527259382e7320058dac7855e20f68238026560676759dbe33b07bc"}