{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:THJC2L673WOWRTJZZOTYX3E6U4","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":"64ed27ce6cba23a5e92979042f843429c7636aeb19ef46c630dba5b78dd08eec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-02-05T18:27:16Z","title_canon_sha256":"271faae824aea54e36c04a3930f5c9c9838245f0eb2b736f611baf1888f249d9"},"schema_version":"1.0","source":{"id":"1602.02116","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02116","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02116v3","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02116","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"THJC2L673WOW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"THJC2L673WOWRTJZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"THJC2L67","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:d4ea335ca7b842721a37fed4d132036792bbb7d3fb771c28e24904a4002a2853","target":"graph","created_at":"2026-05-18T01:04:45Z","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":"Let $R=S/I$ be a graded algebra with $t_i$ and $T_i$ being the minimal and maximal shifts in the minimal $S$ resolution of $R$ at degree $i$. In this paper we prove that $t_n\\leq t_1+T_{n-1}$, for all $n$ and as a consequence, we show that for Gorenstein algebras of codimension $h$, the subadditivity of maximal shifts $T_i$ in the minimal resolution holds for $i \\geq h-1$, i.e, we show that $T_i \\leq T_a+T_{i-a}$ for $i\\geq h-1$.","authors_text":"Hema Srinivasan, Sabine El Khoury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-02-05T18:27:16Z","title":"A note on the subadditivity of Syzygies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02116","kind":"arxiv","version":3},"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":"sha256:440f5e0fb4a67a8a2017c14b93b66dfde4d2274980f123bd580da96a3d65bbb5","target":"record","created_at":"2026-05-18T01:04:45Z","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":"64ed27ce6cba23a5e92979042f843429c7636aeb19ef46c630dba5b78dd08eec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-02-05T18:27:16Z","title_canon_sha256":"271faae824aea54e36c04a3930f5c9c9838245f0eb2b736f611baf1888f249d9"},"schema_version":"1.0","source":{"id":"1602.02116","kind":"arxiv","version":3}},"canonical_sha256":"99d22d2fdfdd9d68cd39cba78bec9ea707c02fcfb8cab1622cb5f036241effd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99d22d2fdfdd9d68cd39cba78bec9ea707c02fcfb8cab1622cb5f036241effd5","first_computed_at":"2026-05-18T01:04:45.377356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:45.377356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVDE0drPpD/+4+q50n6/w8HDPrym0vke3OldQegjMk/2tW0Ig7u+R4bMijq+z3jcF+G4dJqrE701qCJpw9RzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:45.378065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02116","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:440f5e0fb4a67a8a2017c14b93b66dfde4d2274980f123bd580da96a3d65bbb5","sha256:d4ea335ca7b842721a37fed4d132036792bbb7d3fb771c28e24904a4002a2853"],"state_sha256":"b985843513d96e4d7b36edd5fa6a1e6556ed9d941f10c1bf8872e2bf784dfa86"}