{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B7QITVZYDSBQYKQ423IMDKYD7B","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":"dfd1736fbcafe28726b3a764aac8a2f098022466ad085d89d16eaf5d61cc1f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-26T01:14:09Z","title_canon_sha256":"973525eab4efa59823ea9e5e9fa63621314c48ac13fa5c77c3b9016e7d9f0306"},"schema_version":"1.0","source":{"id":"1403.6549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6549","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6549v1","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6549","created_at":"2026-05-18T02:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"B7QITVZYDSBQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B7QITVZYDSBQYKQ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B7QITVZY","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:10024887990e8b9a8b9666928a070b952fd6a0ab2a5d73c5d0807399cb108f92","target":"graph","created_at":"2026-05-18T02:55:28Z","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":"We study transformations of finite modules over Noetherian local rings that attach to a module $M$ a graded module $H^{0}_{\\mathfrak{m}}( \\mathrm{gr}_{I}(M))$ defined via partial systems of parameters of $M$. Despite the generality of the process, which are called $\\mathbf{j}$-transforms, in numerous cases they have interesting cohomological properties. We focus on deriving the Hilbert functions of $\\mathbf{j}$-transforms and studying the significance of the vanishing of some of its coefficients.","authors_text":"Jooyoun Hong, Shiro Goto, Wolmer V. Vasconcelos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-26T01:14:09Z","title":"Hilbert polynomials of j-transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6549","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:ee4ba9508490081d1cd0090939634b564aecc731740d463e7a18e439a683dd2a","target":"record","created_at":"2026-05-18T02:55:28Z","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":"dfd1736fbcafe28726b3a764aac8a2f098022466ad085d89d16eaf5d61cc1f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-03-26T01:14:09Z","title_canon_sha256":"973525eab4efa59823ea9e5e9fa63621314c48ac13fa5c77c3b9016e7d9f0306"},"schema_version":"1.0","source":{"id":"1403.6549","kind":"arxiv","version":1}},"canonical_sha256":"0fe089d7381c830c2a1cd6d0c1ab03f875da339af80d03984e859a9c2778d7ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fe089d7381c830c2a1cd6d0c1ab03f875da339af80d03984e859a9c2778d7ce","first_computed_at":"2026-05-18T02:55:28.652588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:28.652588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYroByZLtF/ePxdjkJJRwV+hhOYxiv8uQn5IjIb44rWzTNT4F77HRnBsekNMn2tiNZPE4qfBY7cY6VQH5juBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:28.653254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee4ba9508490081d1cd0090939634b564aecc731740d463e7a18e439a683dd2a","sha256:10024887990e8b9a8b9666928a070b952fd6a0ab2a5d73c5d0807399cb108f92"],"state_sha256":"339f918956c7a24b47a91a14b9f0610a431d84a0df91bdfcc7e9073094cb9852"}