{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LEQ4KLJHMVQBP6TCDAB5R6BTUF","short_pith_number":"pith:LEQ4KLJH","schema_version":"1.0","canonical_sha256":"5921c52d27656017fa621803d8f833a16cecb6e303768f970ff5c7406befd87e","source":{"kind":"arxiv","id":"1807.08916","version":2},"attestation_state":"computed","paper":{"title":"Representation type of surfaces in $\\mathbb{P}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Sukmoon Huh","submitted_at":"2018-07-24T06:00:49Z","abstract_excerpt":"The goal of this article is to prove that every surface with a regular point in the three-dimensional projective space of degree at least four, is of wild representation type under the condition that either $X$ is integral or $\\mathrm{Pic}(X) \\cong \\langle \\Oo_X(1) \\rangle$; we construct families of arbitrarily large dimension of indecomposable pairwise non-isomorphic aCM vector bundles. On the other hand, we prove that every non-integral aCM scheme of arbitrary dimension at least two, is also very wild in a sense that there exist arbitrarily large dimensional families of pairwise non-isomorph"},"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":"1807.08916","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-24T06:00:49Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"577b1702a8025ad51e2af08b79c1479e3a8c67831c2ee00269761fd4617c80c0","abstract_canon_sha256":"d37eeb2411cbf056fa6a1172ec668bd1e47237131c14e08e47d63d8f3994095e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:51.852945Z","signature_b64":"OqjOWjXkHDaLR9IzkLoofklprpzfka8D28Mw43s+BPxiHcXYQHq2SWp1ITaA4q7OrLYui7bL+qcYdbr2opKEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5921c52d27656017fa621803d8f833a16cecb6e303768f970ff5c7406befd87e","last_reissued_at":"2026-05-18T00:09:51.852377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:51.852377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representation type of surfaces in $\\mathbb{P}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Sukmoon Huh","submitted_at":"2018-07-24T06:00:49Z","abstract_excerpt":"The goal of this article is to prove that every surface with a regular point in the three-dimensional projective space of degree at least four, is of wild representation type under the condition that either $X$ is integral or $\\mathrm{Pic}(X) \\cong \\langle \\Oo_X(1) \\rangle$; we construct families of arbitrarily large dimension of indecomposable pairwise non-isomorphic aCM vector bundles. On the other hand, we prove that every non-integral aCM scheme of arbitrary dimension at least two, is also very wild in a sense that there exist arbitrarily large dimensional families of pairwise non-isomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08916","kind":"arxiv","version":2},"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":"1807.08916","created_at":"2026-05-18T00:09:51.852485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08916v2","created_at":"2026-05-18T00:09:51.852485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08916","created_at":"2026-05-18T00:09:51.852485+00:00"},{"alias_kind":"pith_short_12","alias_value":"LEQ4KLJHMVQB","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LEQ4KLJHMVQBP6TC","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LEQ4KLJH","created_at":"2026-05-18T12:32:37.024351+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/LEQ4KLJHMVQBP6TCDAB5R6BTUF","json":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF.json","graph_json":"https://pith.science/api/pith-number/LEQ4KLJHMVQBP6TCDAB5R6BTUF/graph.json","events_json":"https://pith.science/api/pith-number/LEQ4KLJHMVQBP6TCDAB5R6BTUF/events.json","paper":"https://pith.science/paper/LEQ4KLJH"},"agent_actions":{"view_html":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF","download_json":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF.json","view_paper":"https://pith.science/paper/LEQ4KLJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08916&json=true","fetch_graph":"https://pith.science/api/pith-number/LEQ4KLJHMVQBP6TCDAB5R6BTUF/graph.json","fetch_events":"https://pith.science/api/pith-number/LEQ4KLJHMVQBP6TCDAB5R6BTUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF/action/storage_attestation","attest_author":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF/action/author_attestation","sign_citation":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF/action/citation_signature","submit_replication":"https://pith.science/pith/LEQ4KLJHMVQBP6TCDAB5R6BTUF/action/replication_record"}},"created_at":"2026-05-18T00:09:51.852485+00:00","updated_at":"2026-05-18T00:09:51.852485+00:00"}