{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZJ77LKL6IFAAHJ7MQWFFJLRFFS","short_pith_number":"pith:ZJ77LKL6","canonical_record":{"source":{"id":"1507.01095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-04T10:48:03Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"60325f6ca2720a3c17f7916ca202b6e73257d36beb6f8b05479acce3de8d66b1","abstract_canon_sha256":"eb439512cc57d1df8abc2d013b5a5dbd610aec29ba1ffed5713b1d153563d11b"},"schema_version":"1.0"},"canonical_sha256":"ca7ff5a97e414003a7ec858a54ae252c874241c4fae1913b054009e3950911b6","source":{"kind":"arxiv","id":"1507.01095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01095","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01095v1","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01095","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ77LKL6IFAA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ77LKL6IFAAHJ7M","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ77LKL6","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZJ77LKL6IFAAHJ7MQWFFJLRFFS","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-04T10:48:03Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"60325f6ca2720a3c17f7916ca202b6e73257d36beb6f8b05479acce3de8d66b1","abstract_canon_sha256":"eb439512cc57d1df8abc2d013b5a5dbd610aec29ba1ffed5713b1d153563d11b"},"schema_version":"1.0"},"canonical_sha256":"ca7ff5a97e414003a7ec858a54ae252c874241c4fae1913b054009e3950911b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:18.200206Z","signature_b64":"f6Bm0++Qbr/w0Y461iqNtsmpv4/vWl2vrX3DZ4m3DHb/ew2UIdruAsxaExzyB1rnGJrltyLyQ2NeBUmJOBmQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca7ff5a97e414003a7ec858a54ae252c874241c4fae1913b054009e3950911b6","last_reissued_at":"2026-05-18T01:37:18.199416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:18.199416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01095","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":"2026-05-18T01:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pnfVMlxDapS7anVUBgZ/9Qlbs6C/IaoO0RxOVrh/UttTXkvX38n1AiOU+W4b6ybt5ZlTmAM96u6d9yn+xr6bDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:24:43.193255Z"},"content_sha256":"bf009cc2be338926e85bcee505362292fa12e4666d4d39cff5c09c216c0e36e9","schema_version":"1.0","event_id":"sha256:bf009cc2be338926e85bcee505362292fa12e4666d4d39cff5c09c216c0e36e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZJ77LKL6IFAAHJ7MQWFFJLRFFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weight Enumerators and Higher Support Weights of Maximally Recoverable Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Satyanarayana V. Lokam, V. Lalitha","submitted_at":"2015-07-04T10:48:03Z","abstract_excerpt":"In this paper, we establish the matroid structures corresponding to data-local and local maximally recoverable codes (MRC). The matroid structures of these codes can be used to determine the associated Tutte polynomial. Greene proved that the weight enumerators of any code can be determined from its associated Tutte polynomial. We will use this result to derive explicit expressions for the weight enumerators of data-local and local MRC. Also, Britz proved that the higher support weights of any code can be determined from its associated Tutte polynomial. We will use this result to derive expres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01095","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0O3JCdNgwRJQd7TPE/2eu2MTovw/OnLcJr87K50iwaC/MAJZCA/Rt4UmGCzZB6CfFG32GJvmMSLa6FjghMLoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:24:43.194002Z"},"content_sha256":"df0f790a61fd61c06bf2150e9f1a6d454e4628ab15e9fddb105422f52a5c600b","schema_version":"1.0","event_id":"sha256:df0f790a61fd61c06bf2150e9f1a6d454e4628ab15e9fddb105422f52a5c600b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/bundle.json","state_url":"https://pith.science/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/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":"2026-06-10T01:24:43Z","links":{"resolver":"https://pith.science/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS","bundle":"https://pith.science/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/bundle.json","state":"https://pith.science/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJ77LKL6IFAAHJ7MQWFFJLRFFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZJ77LKL6IFAAHJ7MQWFFJLRFFS","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":"eb439512cc57d1df8abc2d013b5a5dbd610aec29ba1ffed5713b1d153563d11b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-04T10:48:03Z","title_canon_sha256":"60325f6ca2720a3c17f7916ca202b6e73257d36beb6f8b05479acce3de8d66b1"},"schema_version":"1.0","source":{"id":"1507.01095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01095","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01095v1","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01095","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ77LKL6IFAA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ77LKL6IFAAHJ7M","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ77LKL6","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:df0f790a61fd61c06bf2150e9f1a6d454e4628ab15e9fddb105422f52a5c600b","target":"graph","created_at":"2026-05-18T01:37:18Z","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"},"paper":{"abstract_excerpt":"In this paper, we establish the matroid structures corresponding to data-local and local maximally recoverable codes (MRC). The matroid structures of these codes can be used to determine the associated Tutte polynomial. Greene proved that the weight enumerators of any code can be determined from its associated Tutte polynomial. We will use this result to derive explicit expressions for the weight enumerators of data-local and local MRC. Also, Britz proved that the higher support weights of any code can be determined from its associated Tutte polynomial. We will use this result to derive expres","authors_text":"Satyanarayana V. Lokam, V. Lalitha","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-04T10:48:03Z","title":"Weight Enumerators and Higher Support Weights of Maximally Recoverable Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01095","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:bf009cc2be338926e85bcee505362292fa12e4666d4d39cff5c09c216c0e36e9","target":"record","created_at":"2026-05-18T01:37:18Z","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":"eb439512cc57d1df8abc2d013b5a5dbd610aec29ba1ffed5713b1d153563d11b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-04T10:48:03Z","title_canon_sha256":"60325f6ca2720a3c17f7916ca202b6e73257d36beb6f8b05479acce3de8d66b1"},"schema_version":"1.0","source":{"id":"1507.01095","kind":"arxiv","version":1}},"canonical_sha256":"ca7ff5a97e414003a7ec858a54ae252c874241c4fae1913b054009e3950911b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7ff5a97e414003a7ec858a54ae252c874241c4fae1913b054009e3950911b6","first_computed_at":"2026-05-18T01:37:18.199416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:18.199416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f6Bm0++Qbr/w0Y461iqNtsmpv4/vWl2vrX3DZ4m3DHb/ew2UIdruAsxaExzyB1rnGJrltyLyQ2NeBUmJOBmQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:18.200206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf009cc2be338926e85bcee505362292fa12e4666d4d39cff5c09c216c0e36e9","sha256:df0f790a61fd61c06bf2150e9f1a6d454e4628ab15e9fddb105422f52a5c600b"],"state_sha256":"c010e4ae72d8c8a8f697a6df3dae7a6ba0114418ccde4bf6f925618be379604d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7l+58RnEnfqdYmyBvZ3mnQbHZ1HkTsvOJlx17Vlbxg4C1avlFRRXHiLzmfBEX9qU2IeCRg3hXnRnfdTAk3VmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:24:43.198040Z","bundle_sha256":"cba5a4ebd75c81ee88dc2f4717572bf196d238be297797d88657d5b2510c51f0"}}