{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:VP5PCEEZW4EADONLWPSJCOEOYF","short_pith_number":"pith:VP5PCEEZ","canonical_record":{"source":{"id":"cs/0603014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2006-03-02T18:31:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"37a59edb9aefb60efe7f8761511e8516a2a0e0c18eed94973cabb5dbf0b88fdd","abstract_canon_sha256":"560fa3c8788d720e2bf320305843a9b939260ad82f13272b1dd7b6dd9fb76250"},"schema_version":"1.0"},"canonical_sha256":"abfaf11099b70801b9abb3e491388ec159712e6c890507a8c09907fa16490196","source":{"kind":"arxiv","id":"cs/0603014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0603014","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0603014v1","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0603014","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"VP5PCEEZW4EA","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_16","alias_value":"VP5PCEEZW4EADONL","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_8","alias_value":"VP5PCEEZ","created_at":"2026-07-04T15:02:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:VP5PCEEZW4EADONLWPSJCOEOYF","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0603014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2006-03-02T18:31:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"37a59edb9aefb60efe7f8761511e8516a2a0e0c18eed94973cabb5dbf0b88fdd","abstract_canon_sha256":"560fa3c8788d720e2bf320305843a9b939260ad82f13272b1dd7b6dd9fb76250"},"schema_version":"1.0"},"canonical_sha256":"abfaf11099b70801b9abb3e491388ec159712e6c890507a8c09907fa16490196","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:02:51.375747Z","signature_b64":"gOhyhpjswJ03G1EueF3ZKQb08t23W/vwoV/2EHlZ0fA/mSqgXjWNxQSoG1+7f5Sw62jjiBNG+hSWfBE5/YIHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abfaf11099b70801b9abb3e491388ec159712e6c890507a8c09907fa16490196","last_reissued_at":"2026-07-04T15:02:51.375334Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:02:51.375334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0603014","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNYif6NZ6YNcAEvwce7Uhoqba5mJjNhDJqGzQkVsJqmXak3zaXuVlGYgewpQVi5AmrRfudClygwzo1mJPOnkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:04:27.025578Z"},"content_sha256":"85bdfad5408b01f65809636138fe23d6ac3484a8a9304545538ddfea12796f3c","schema_version":"1.0","event_id":"sha256:85bdfad5408b01f65809636138fe23d6ac3484a8a9304545538ddfea12796f3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:VP5PCEEZW4EADONLWPSJCOEOYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near orders and codes","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"C. Carvalho, C. Munuera, E. Silva, F. Torres","submitted_at":"2006-03-02T18:31:13Z","abstract_excerpt":"Hoholdt, van Lint and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this method are mainly those based on just one point. In this paper we introduce the concept of near order function with the aim of generalize this approach in such a way that a of wider family of Geometric Goppa codes can be studied on a more elementary setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0603014","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cs/0603014/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:02:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Fmpn/Lz3zm2c+xSdEd6F6Lj80bxEEat7HKX1kh6gdHGmfvN9i0HALy3rP6rkDBPlvcqtSlNX0HrBtOaVKUQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:04:27.026210Z"},"content_sha256":"915e7d7c37fc0b6dc59852a092f9970e8be1d99e91a11af85156687eb9120338","schema_version":"1.0","event_id":"sha256:915e7d7c37fc0b6dc59852a092f9970e8be1d99e91a11af85156687eb9120338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VP5PCEEZW4EADONLWPSJCOEOYF/bundle.json","state_url":"https://pith.science/pith/VP5PCEEZW4EADONLWPSJCOEOYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VP5PCEEZW4EADONLWPSJCOEOYF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T15:04:27Z","links":{"resolver":"https://pith.science/pith/VP5PCEEZW4EADONLWPSJCOEOYF","bundle":"https://pith.science/pith/VP5PCEEZW4EADONLWPSJCOEOYF/bundle.json","state":"https://pith.science/pith/VP5PCEEZW4EADONLWPSJCOEOYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VP5PCEEZW4EADONLWPSJCOEOYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VP5PCEEZW4EADONLWPSJCOEOYF","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":"560fa3c8788d720e2bf320305843a9b939260ad82f13272b1dd7b6dd9fb76250","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-03-02T18:31:13Z","title_canon_sha256":"37a59edb9aefb60efe7f8761511e8516a2a0e0c18eed94973cabb5dbf0b88fdd"},"schema_version":"1.0","source":{"id":"cs/0603014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0603014","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0603014v1","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0603014","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_12","alias_value":"VP5PCEEZW4EA","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_16","alias_value":"VP5PCEEZW4EADONL","created_at":"2026-07-04T15:02:51Z"},{"alias_kind":"pith_short_8","alias_value":"VP5PCEEZ","created_at":"2026-07-04T15:02:51Z"}],"graph_snapshots":[{"event_id":"sha256:915e7d7c37fc0b6dc59852a092f9970e8be1d99e91a11af85156687eb9120338","target":"graph","created_at":"2026-07-04T15:02:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cs/0603014/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hoholdt, van Lint and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this method are mainly those based on just one point. In this paper we introduce the concept of near order function with the aim of generalize this approach in such a way that a of wider family of Geometric Goppa codes can be studied on a more elementary setting.","authors_text":"C. Carvalho, C. Munuera, E. Silva, F. Torres","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2006-03-02T18:31:13Z","title":"Near orders and codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0603014","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":"sha256:85bdfad5408b01f65809636138fe23d6ac3484a8a9304545538ddfea12796f3c","target":"record","created_at":"2026-07-04T15:02:51Z","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":"560fa3c8788d720e2bf320305843a9b939260ad82f13272b1dd7b6dd9fb76250","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-03-02T18:31:13Z","title_canon_sha256":"37a59edb9aefb60efe7f8761511e8516a2a0e0c18eed94973cabb5dbf0b88fdd"},"schema_version":"1.0","source":{"id":"cs/0603014","kind":"arxiv","version":1}},"canonical_sha256":"abfaf11099b70801b9abb3e491388ec159712e6c890507a8c09907fa16490196","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abfaf11099b70801b9abb3e491388ec159712e6c890507a8c09907fa16490196","first_computed_at":"2026-07-04T15:02:51.375334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:51.375334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOhyhpjswJ03G1EueF3ZKQb08t23W/vwoV/2EHlZ0fA/mSqgXjWNxQSoG1+7f5Sw62jjiBNG+hSWfBE5/YIHAw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:51.375747Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0603014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85bdfad5408b01f65809636138fe23d6ac3484a8a9304545538ddfea12796f3c","sha256:915e7d7c37fc0b6dc59852a092f9970e8be1d99e91a11af85156687eb9120338"],"state_sha256":"6129a1c7b09038041c1f3b8cd80ecddfaa9046bbb10a593514b2261b1bdcde11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XUln0IDb5oeO8dXgeIh+I3zAwxGQAdnbNPqRqlt3upNnp6UceLC0ZG+s1n41akdsaBDGIdb1LWNxO9O2n9vzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T15:04:27.029154Z","bundle_sha256":"c308524857fef01957a92a4f4d680f23284ded6ca9dd4d4cc22a092d42ad5884"}}