{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:H67MJCE742E2CHH24VKPL2DQNZ","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":"76429c9fb1f53602d45b9d169d2a0a8e88000542ef40587349f0d4ef38eea2f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-21T18:58:34Z","title_canon_sha256":"793f315359511c23ec764f2805021bc8098c5deb8a700976caafbd049b652b98"},"schema_version":"1.0","source":{"id":"1308.4659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4659","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4659v1","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4659","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"H67MJCE742E2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H67MJCE742E2CHH2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H67MJCE7","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:7fd61db19c7f37519e0f06d184135cb4ba462dfad5a3db4bd43ab719f667230b","target":"graph","created_at":"2026-05-18T03:15:21Z","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, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X_1,...,X_n]/a of a polynomial ring over a field K by ideals a=L+P which are the sum of a piecewise lex-segment ideal L, as defined by Shakin, and a pure powers ideal P. Our main results extend Abedelfatah's recent work on the Eisenbud-Green-Harris conjecture, Shakin's generalization of Macaulay and Bigatti-Hulett-Pardue theorems on Betti numbers and, when char(K)=0, Mermin-Murai theorem on the Lex-Plus-Power inequality, from monomial regular sequences to a larger class of ideal","authors_text":"Enrico Sbarra, Giulio Caviglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-21T18:58:34Z","title":"Distractions of Shakin rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4659","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":"sha256:56b6db398134df60b630b1fdbc93cdcaa467ce915c29635def1cb03e6750d843","target":"record","created_at":"2026-05-18T03:15:21Z","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":"76429c9fb1f53602d45b9d169d2a0a8e88000542ef40587349f0d4ef38eea2f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-21T18:58:34Z","title_canon_sha256":"793f315359511c23ec764f2805021bc8098c5deb8a700976caafbd049b652b98"},"schema_version":"1.0","source":{"id":"1308.4659","kind":"arxiv","version":1}},"canonical_sha256":"3fbec4889fe689a11cfae554f5e8706e5fa1aa21d959540dfd53b7d6db2b9b3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fbec4889fe689a11cfae554f5e8706e5fa1aa21d959540dfd53b7d6db2b9b3d","first_computed_at":"2026-05-18T03:15:21.362417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:21.362417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LgPSydKJvDUYYbW3VWP9d01CzEiQixgAONHNwJvrGnFaFsmVVETwCoSTDf00dtjg+vXDG8Qt1c4r2zjzpERGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:21.363003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56b6db398134df60b630b1fdbc93cdcaa467ce915c29635def1cb03e6750d843","sha256:7fd61db19c7f37519e0f06d184135cb4ba462dfad5a3db4bd43ab719f667230b"],"state_sha256":"979f15729c299bdba63b7244cc313240cbc9e27b1eb6f48c548ece8775c32efe"}