{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YW7GLOBBXJXOYC6Q25LHH6OP2Y","short_pith_number":"pith:YW7GLOBB","canonical_record":{"source":{"id":"2605.29439","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-28T06:33:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"294786f6660c14c41395dcb334d31cf574aa6af2aa93710db1c79c2f91163740","abstract_canon_sha256":"57595616664e56a30dd8bca83ef6c1a6fc15634c190a56f39ed4907a4c671eb3"},"schema_version":"1.0"},"canonical_sha256":"c5be65b821ba6eec0bd0d75673f9cfd63e844718bbc34cfc57248069c431201c","source":{"kind":"arxiv","id":"2605.29439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29439","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29439v1","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29439","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"YW7GLOBBXJXO","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_16","alias_value":"YW7GLOBBXJXOYC6Q","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_8","alias_value":"YW7GLOBB","created_at":"2026-05-29T01:05:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YW7GLOBBXJXOYC6Q25LHH6OP2Y","target":"record","payload":{"canonical_record":{"source":{"id":"2605.29439","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-28T06:33:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"294786f6660c14c41395dcb334d31cf574aa6af2aa93710db1c79c2f91163740","abstract_canon_sha256":"57595616664e56a30dd8bca83ef6c1a6fc15634c190a56f39ed4907a4c671eb3"},"schema_version":"1.0"},"canonical_sha256":"c5be65b821ba6eec0bd0d75673f9cfd63e844718bbc34cfc57248069c431201c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:39.083664Z","signature_b64":"pQrZjKIr2PxRPE5Hz8uEOn901ozRVGlOsqYBjQAnIqairhtH0RACC/VEqsP1Ndlwv9KIrouC3bNakevhfo4VBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5be65b821ba6eec0bd0d75673f9cfd63e844718bbc34cfc57248069c431201c","last_reissued_at":"2026-05-29T01:05:39.083102Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:39.083102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.29439","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":"2026-05-29T01:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XAhh1SEUxozV1vhlCfsOW6kwkA1ZjcCHvTnDXez9OKt+vaH/wLDxanDVhvzvNV4VMv0JogQV7AWVOVlywmpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:28:52.262405Z"},"content_sha256":"36a4622033224a9cfeddd8de3c681f530fbf09d4fdcc501a00b0f49ca480faab","schema_version":"1.0","event_id":"sha256:36a4622033224a9cfeddd8de3c681f530fbf09d4fdcc501a00b0f49ca480faab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YW7GLOBBXJXOYC6Q25LHH6OP2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Maximal Length of MDS Elliptic Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chang-An Zhao, Chuangqiang Hu, Haojie Chen, Junjie Huang","submitted_at":"2026-05-28T06:33:38Z","abstract_excerpt":"The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\\mathbb{F}_q$, let $\\operatorname{MEC}(k,q)$ denote the maximal length of a $q$-ary MDS elliptic code of dimension $k$. It was recently shown that $\\operatorname{MEC}(k,q)\\le\\frac{q+1}{2}+\\sqrt{q}$ for $q\\ge289$ and $3\\le k\\le(q+1-2\\sqrt{q})/10$, with equality for odd $k$ when $q$ is an odd square. This paper investigates the remaining open cases, namely even dimension $k$, non-square $q$ and fields of characterist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29439","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/2605.29439/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":"2026-05-29T01:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2i8o+2VjGsWwWN7DhyiNOVpslkqvolyQ/i+AAnbY8jf1YirbXU+ECGqHUPQWoLxTscFhMj6ocT7vIDWHCtoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:28:52.262786Z"},"content_sha256":"562d351ccf3602daee43f8f4dbd9d48c72c4b45cc4df958f23f982537496d1a8","schema_version":"1.0","event_id":"sha256:562d351ccf3602daee43f8f4dbd9d48c72c4b45cc4df958f23f982537496d1a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/bundle.json","state_url":"https://pith.science/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/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":"2026-05-30T05:28:52Z","links":{"resolver":"https://pith.science/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y","bundle":"https://pith.science/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/bundle.json","state":"https://pith.science/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YW7GLOBBXJXOYC6Q25LHH6OP2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YW7GLOBBXJXOYC6Q25LHH6OP2Y","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":"57595616664e56a30dd8bca83ef6c1a6fc15634c190a56f39ed4907a4c671eb3","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-28T06:33:38Z","title_canon_sha256":"294786f6660c14c41395dcb334d31cf574aa6af2aa93710db1c79c2f91163740"},"schema_version":"1.0","source":{"id":"2605.29439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29439","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29439v1","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29439","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"YW7GLOBBXJXO","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_16","alias_value":"YW7GLOBBXJXOYC6Q","created_at":"2026-05-29T01:05:39Z"},{"alias_kind":"pith_short_8","alias_value":"YW7GLOBB","created_at":"2026-05-29T01:05:39Z"}],"graph_snapshots":[{"event_id":"sha256:562d351ccf3602daee43f8f4dbd9d48c72c4b45cc4df958f23f982537496d1a8","target":"graph","created_at":"2026-05-29T01:05:39Z","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/2605.29439/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\\mathbb{F}_q$, let $\\operatorname{MEC}(k,q)$ denote the maximal length of a $q$-ary MDS elliptic code of dimension $k$. It was recently shown that $\\operatorname{MEC}(k,q)\\le\\frac{q+1}{2}+\\sqrt{q}$ for $q\\ge289$ and $3\\le k\\le(q+1-2\\sqrt{q})/10$, with equality for odd $k$ when $q$ is an odd square. This paper investigates the remaining open cases, namely even dimension $k$, non-square $q$ and fields of characterist","authors_text":"Chang-An Zhao, Chuangqiang Hu, Haojie Chen, Junjie Huang","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-28T06:33:38Z","title":"On the Maximal Length of MDS Elliptic Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29439","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":"sha256:36a4622033224a9cfeddd8de3c681f530fbf09d4fdcc501a00b0f49ca480faab","target":"record","created_at":"2026-05-29T01:05:39Z","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":"57595616664e56a30dd8bca83ef6c1a6fc15634c190a56f39ed4907a4c671eb3","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-28T06:33:38Z","title_canon_sha256":"294786f6660c14c41395dcb334d31cf574aa6af2aa93710db1c79c2f91163740"},"schema_version":"1.0","source":{"id":"2605.29439","kind":"arxiv","version":1}},"canonical_sha256":"c5be65b821ba6eec0bd0d75673f9cfd63e844718bbc34cfc57248069c431201c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5be65b821ba6eec0bd0d75673f9cfd63e844718bbc34cfc57248069c431201c","first_computed_at":"2026-05-29T01:05:39.083102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:39.083102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pQrZjKIr2PxRPE5Hz8uEOn901ozRVGlOsqYBjQAnIqairhtH0RACC/VEqsP1Ndlwv9KIrouC3bNakevhfo4VBQ==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:39.083664Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36a4622033224a9cfeddd8de3c681f530fbf09d4fdcc501a00b0f49ca480faab","sha256:562d351ccf3602daee43f8f4dbd9d48c72c4b45cc4df958f23f982537496d1a8"],"state_sha256":"7808860bb43a69f8dbd2d41508888584d805ab291da8f99eb2081ca50dda72bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OyVq/TW6cECIBpaXSeOpHyScud1R7WbDhDidVz+aCrjuN3SWpEEGOQd6WrgvlQLhtmYs6sHGpiSeJAmxPYSuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:28:52.264876Z","bundle_sha256":"12431cb3d06ff4e692f0e850b819a85c9295b8d1648fc88ad844304ca4bd675f"}}