{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7SYL3IKJMS6TOU7TMPJ2QXO2QB","short_pith_number":"pith:7SYL3IKJ","canonical_record":{"source":{"id":"1611.04580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-11-14T20:59:04Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"ebfba7874eb8db4e658e2814b257259b28dd1bbb2a7892f1ed9731c3dbc3623c","abstract_canon_sha256":"8308f0dc8b6d448b94707c2e1da746194aa524c7b2d91714e613299998334d4d"},"schema_version":"1.0"},"canonical_sha256":"fcb0bda14964bd3753f363d3a85dda8062c95393bad20184ef2c802b40d89bac","source":{"kind":"arxiv","id":"1611.04580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04580","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04580v1","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04580","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"7SYL3IKJMS6T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7SYL3IKJMS6TOU7T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7SYL3IKJ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7SYL3IKJMS6TOU7TMPJ2QXO2QB","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-11-14T20:59:04Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"ebfba7874eb8db4e658e2814b257259b28dd1bbb2a7892f1ed9731c3dbc3623c","abstract_canon_sha256":"8308f0dc8b6d448b94707c2e1da746194aa524c7b2d91714e613299998334d4d"},"schema_version":"1.0"},"canonical_sha256":"fcb0bda14964bd3753f363d3a85dda8062c95393bad20184ef2c802b40d89bac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:12.760097Z","signature_b64":"XOY48s+hu0E5xMKa73nWtiJAH6+V6kfCDXeaHE7AHppPKO6aFw97u/ZGM1I28sBNu8MnUYN6ERwH+0e8JIeXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcb0bda14964bd3753f363d3a85dda8062c95393bad20184ef2c802b40d89bac","last_reissued_at":"2026-05-18T00:59:12.759588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:12.759588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04580","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":"2026-05-18T00:59:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgdvzRzQQ0ejbLTOab5VP9YIbNauHJMHkn5rJiViWUs4qqil+ySW8EbrFBmLZv8VKOaK+yMof9HEyLvBRkK5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:51:15.124008Z"},"content_sha256":"51bcc12541b996e40c655e12f6e44c927db6c5f3d9d8f48b5b7c5b1a3dc1d053","schema_version":"1.0","event_id":"sha256:51bcc12541b996e40c655e12f6e44c927db6c5f3d9d8f48b5b7c5b1a3dc1d053"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7SYL3IKJMS6TOU7TMPJ2QXO2QB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some conjectures on codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.FL","authors_text":"Clelia De Felice","submitted_at":"2016-11-14T20:59:04Z","abstract_excerpt":"Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04580","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":"2026-05-18T00:59:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAxB0rz6JVX03X7FVcmSD0ylXFPEtabtD+UjJKSYXN+o16XR6K7UgDL1ExmYpKOsFbKrKyZ+v27ymvKkdVUBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:51:15.124746Z"},"content_sha256":"a85f9b7ee349ed82e1843dbd779534c291f1b95892d36b34ec6689673c459eb0","schema_version":"1.0","event_id":"sha256:a85f9b7ee349ed82e1843dbd779534c291f1b95892d36b34ec6689673c459eb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/bundle.json","state_url":"https://pith.science/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/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":"2026-06-09T18:51:15Z","links":{"resolver":"https://pith.science/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB","bundle":"https://pith.science/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/bundle.json","state":"https://pith.science/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SYL3IKJMS6TOU7TMPJ2QXO2QB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7SYL3IKJMS6TOU7TMPJ2QXO2QB","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":"8308f0dc8b6d448b94707c2e1da746194aa524c7b2d91714e613299998334d4d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-11-14T20:59:04Z","title_canon_sha256":"ebfba7874eb8db4e658e2814b257259b28dd1bbb2a7892f1ed9731c3dbc3623c"},"schema_version":"1.0","source":{"id":"1611.04580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04580","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04580v1","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04580","created_at":"2026-05-18T00:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"7SYL3IKJMS6T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7SYL3IKJMS6TOU7T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7SYL3IKJ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:a85f9b7ee349ed82e1843dbd779534c291f1b95892d36b34ec6689673c459eb0","target":"graph","created_at":"2026-05-18T00:59:12Z","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":"Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.","authors_text":"Clelia De Felice","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-11-14T20:59:04Z","title":"Some conjectures on codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04580","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":"sha256:51bcc12541b996e40c655e12f6e44c927db6c5f3d9d8f48b5b7c5b1a3dc1d053","target":"record","created_at":"2026-05-18T00:59:12Z","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":"8308f0dc8b6d448b94707c2e1da746194aa524c7b2d91714e613299998334d4d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-11-14T20:59:04Z","title_canon_sha256":"ebfba7874eb8db4e658e2814b257259b28dd1bbb2a7892f1ed9731c3dbc3623c"},"schema_version":"1.0","source":{"id":"1611.04580","kind":"arxiv","version":1}},"canonical_sha256":"fcb0bda14964bd3753f363d3a85dda8062c95393bad20184ef2c802b40d89bac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb0bda14964bd3753f363d3a85dda8062c95393bad20184ef2c802b40d89bac","first_computed_at":"2026-05-18T00:59:12.759588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:12.759588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XOY48s+hu0E5xMKa73nWtiJAH6+V6kfCDXeaHE7AHppPKO6aFw97u/ZGM1I28sBNu8MnUYN6ERwH+0e8JIeXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:12.760097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51bcc12541b996e40c655e12f6e44c927db6c5f3d9d8f48b5b7c5b1a3dc1d053","sha256:a85f9b7ee349ed82e1843dbd779534c291f1b95892d36b34ec6689673c459eb0"],"state_sha256":"a4d57a47491acdc68b3eda31239d5de6fe3d3dc6e7171c9e1b7d2c85cf4a7343"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LX0yXDzvO/lASbBdGAqMFqF3/u+CxQNI/fdZDDAPWwGbRwkziOaqFZ96nqJqTxpngOt2XSQZnoj9TAMZbBcfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:51:15.129042Z","bundle_sha256":"434cde1468635ccd3062622426beddce19f27fcbb248e2f7b452f1fca9db3ad7"}}