{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YSQ54CURVN6B3SQALD7BOWSQUQ","short_pith_number":"pith:YSQ54CUR","schema_version":"1.0","canonical_sha256":"c4a1de0a91ab7c1dca0058fe175a50a42ea6a4f050fb137ef4bb64e5d5c3fbed","source":{"kind":"arxiv","id":"1405.5806","version":1},"attestation_state":"computed","paper":{"title":"On the Hyperhomology of the Small Gobelin in Codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Luis N\\'u\\~nez-Betancourt, Xavier G\\'omez-Mont","submitted_at":"2014-05-22T16:01:11Z","abstract_excerpt":"Given a zero-dimensional Gorenstein algebra $\\mathbb{B}$ and two syzygies between two elements $f_1,f_2\\in\\mathbb{B}$, one constructs a double complex of $\\mathbb{B}$-modules, ${\\cal G}_\\mathbb{B},$ called the small Gobelin. We describe an inductive procedure to construct the even and odd hyperhomologies of this complex. For high degrees, the difference $\\dim \\mathbb{H}_{j+2}({\\cal G}_\\mathbb{B}) - \\dim\\mathbb{H}_j({\\cal G}_\\mathbb{B})$ is constant, but possibly with a different value for even and odd degrees. We describe two flags of ideals in $\\mathbb{B}$ which codify the above differences o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.5806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-22T16:01:11Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0675f2a3e99add7efcc00584e17a7ecf1c14102465ed284671e80896b5eb0da5","abstract_canon_sha256":"30c94afe08d18746dc25fdb5a673cc817c3101a886c52743028ba8a5d0c41f5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:15.554481Z","signature_b64":"Uxccgh5ZpcO5e+tiVqcP0LxH+z0YEiP2LlaDOXowf6CMjYOl7rjf26e0LydEvZZ7S7z8lat+51rBFNNuNx/OCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4a1de0a91ab7c1dca0058fe175a50a42ea6a4f050fb137ef4bb64e5d5c3fbed","last_reissued_at":"2026-05-18T02:51:15.554059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:15.554059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Hyperhomology of the Small Gobelin in Codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Luis N\\'u\\~nez-Betancourt, Xavier G\\'omez-Mont","submitted_at":"2014-05-22T16:01:11Z","abstract_excerpt":"Given a zero-dimensional Gorenstein algebra $\\mathbb{B}$ and two syzygies between two elements $f_1,f_2\\in\\mathbb{B}$, one constructs a double complex of $\\mathbb{B}$-modules, ${\\cal G}_\\mathbb{B},$ called the small Gobelin. We describe an inductive procedure to construct the even and odd hyperhomologies of this complex. For high degrees, the difference $\\dim \\mathbb{H}_{j+2}({\\cal G}_\\mathbb{B}) - \\dim\\mathbb{H}_j({\\cal G}_\\mathbb{B})$ is constant, but possibly with a different value for even and odd degrees. We describe two flags of ideals in $\\mathbb{B}$ which codify the above differences o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5806","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1405.5806","created_at":"2026-05-18T02:51:15.554121+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5806v1","created_at":"2026-05-18T02:51:15.554121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5806","created_at":"2026-05-18T02:51:15.554121+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSQ54CURVN6B","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSQ54CURVN6B3SQA","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSQ54CUR","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ","json":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ.json","graph_json":"https://pith.science/api/pith-number/YSQ54CURVN6B3SQALD7BOWSQUQ/graph.json","events_json":"https://pith.science/api/pith-number/YSQ54CURVN6B3SQALD7BOWSQUQ/events.json","paper":"https://pith.science/paper/YSQ54CUR"},"agent_actions":{"view_html":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ","download_json":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ.json","view_paper":"https://pith.science/paper/YSQ54CUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5806&json=true","fetch_graph":"https://pith.science/api/pith-number/YSQ54CURVN6B3SQALD7BOWSQUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YSQ54CURVN6B3SQALD7BOWSQUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ/action/storage_attestation","attest_author":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ/action/author_attestation","sign_citation":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ/action/citation_signature","submit_replication":"https://pith.science/pith/YSQ54CURVN6B3SQALD7BOWSQUQ/action/replication_record"}},"created_at":"2026-05-18T02:51:15.554121+00:00","updated_at":"2026-05-18T02:51:15.554121+00:00"}