{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:TPRCWJCV6RJVSP5CNYQ742OOM5","short_pith_number":"pith:TPRCWJCV","schema_version":"1.0","canonical_sha256":"9be22b2455f453593fa26e21fe69ce67568f36dc5cbe8ff3a8c343c0af495142","source":{"kind":"arxiv","id":"0802.2088","version":1},"attestation_state":"computed","paper":{"title":"Toric surface codes and Minkowski length of polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Evgenia Soprunova, Ivan Soprunov","submitted_at":"2008-02-14T19:54:49Z","abstract_excerpt":"In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily computed for any given P."},"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":"0802.2088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-02-14T19:54:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cfc7f2966ae47a909881fd6cd88ec6e2eef92254f9ca8d0978a4fc6e1a42f0ac","abstract_canon_sha256":"971e2c51d88f328aed0931a74befa07188f37262cb236d9958b202f77975ce79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:54.590224Z","signature_b64":"2zlcOLp5X29iVtrsGgUIjgjAaRYE75huq33gTeeSVnX1crAVcOwr7+TlgC/j7GSS8FePIeaoQ7CW0kZsUEWjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9be22b2455f453593fa26e21fe69ce67568f36dc5cbe8ff3a8c343c0af495142","last_reissued_at":"2026-05-18T01:38:54.589499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:54.589499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric surface codes and Minkowski length of polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Evgenia Soprunova, Ivan Soprunov","submitted_at":"2008-02-14T19:54:49Z","abstract_excerpt":"In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily computed for any given P."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2088","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":"0802.2088","created_at":"2026-05-18T01:38:54.589618+00:00"},{"alias_kind":"arxiv_version","alias_value":"0802.2088v1","created_at":"2026-05-18T01:38:54.589618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2088","created_at":"2026-05-18T01:38:54.589618+00:00"},{"alias_kind":"pith_short_12","alias_value":"TPRCWJCV6RJV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"TPRCWJCV6RJVSP5C","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"TPRCWJCV","created_at":"2026-05-18T12:25:58.018023+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/TPRCWJCV6RJVSP5CNYQ742OOM5","json":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5.json","graph_json":"https://pith.science/api/pith-number/TPRCWJCV6RJVSP5CNYQ742OOM5/graph.json","events_json":"https://pith.science/api/pith-number/TPRCWJCV6RJVSP5CNYQ742OOM5/events.json","paper":"https://pith.science/paper/TPRCWJCV"},"agent_actions":{"view_html":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5","download_json":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5.json","view_paper":"https://pith.science/paper/TPRCWJCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0802.2088&json=true","fetch_graph":"https://pith.science/api/pith-number/TPRCWJCV6RJVSP5CNYQ742OOM5/graph.json","fetch_events":"https://pith.science/api/pith-number/TPRCWJCV6RJVSP5CNYQ742OOM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5/action/storage_attestation","attest_author":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5/action/author_attestation","sign_citation":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5/action/citation_signature","submit_replication":"https://pith.science/pith/TPRCWJCV6RJVSP5CNYQ742OOM5/action/replication_record"}},"created_at":"2026-05-18T01:38:54.589618+00:00","updated_at":"2026-05-18T01:38:54.589618+00:00"}