{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XZTPVFHZ3L5PZPCB6PA774EWG2","short_pith_number":"pith:XZTPVFHZ","canonical_record":{"source":{"id":"1403.1818","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CO","submitted_at":"2014-03-07T17:30:57Z","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"title_canon_sha256":"02c1b4311483a0fdc714b175eb040efbecf982a1511f42df51cb9a65212a6926","abstract_canon_sha256":"6f51127a5fcac00007b23c5ffa78e13f256d2e7db4103c28cc310731e477de5d"},"schema_version":"1.0"},"canonical_sha256":"be66fa94f9dafafcbc41f3c1fff0963689b9b446f2ced86bb506f26d4ece60b9","source":{"kind":"arxiv","id":"1403.1818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1818","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1818v1","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1818","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"XZTPVFHZ3L5P","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZTPVFHZ3L5PZPCB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZTPVFHZ","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XZTPVFHZ3L5PZPCB6PA774EWG2","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1818","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CO","submitted_at":"2014-03-07T17:30:57Z","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"title_canon_sha256":"02c1b4311483a0fdc714b175eb040efbecf982a1511f42df51cb9a65212a6926","abstract_canon_sha256":"6f51127a5fcac00007b23c5ffa78e13f256d2e7db4103c28cc310731e477de5d"},"schema_version":"1.0"},"canonical_sha256":"be66fa94f9dafafcbc41f3c1fff0963689b9b446f2ced86bb506f26d4ece60b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:52.496347Z","signature_b64":"qO2O968QG8rpXerIwZ5Cva3jDFl+OQlTh6n/gkBZfU42aqr1vuwxeJZuyD87y/PWsmZDkI7TPHOaYe1c4PqpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be66fa94f9dafafcbc41f3c1fff0963689b9b446f2ced86bb506f26d4ece60b9","last_reissued_at":"2026-05-18T02:56:52.495906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:52.495906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1818","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":"2026-05-18T02:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5Ntm3+fCdo8TzBbkgTFxgDkJ8gonVeoi6RMvc9IuY4F0MURE8GMZeA3icafFonp42hrvtPFOIVbQFKVeZT/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:20:40.462243Z"},"content_sha256":"d50b66cc3a1389eb9ea15e0a086cca1ec212bbc9a3f43686e3edcbe84d719dfd","schema_version":"1.0","event_id":"sha256:d50b66cc3a1389eb9ea15e0a086cca1ec212bbc9a3f43686e3edcbe84d719dfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XZTPVFHZ3L5PZPCB6PA774EWG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gray Codes and Overlap Cycles for Restricted Weight Words","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["cs.DM","cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Glenn Hurlbert, Victoria Horan","submitted_at":"2014-03-07T17:30:57Z","abstract_excerpt":"A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been considered in the past, we provide a new, simple Gray code for fixed-weight m-ary strings. In addition, we consider a relatively new type of Gray code known as overlap cycles and prove basic existence results concerning overlap cycles for fixed-weight and weight-range m-ary words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1818","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":"2026-05-18T02:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPgwNfcr3z0A9pyNvg5dcInczPeXy1W17jwmV21osV7EP4ZwJH8i1y17aenI+gmm321KNdAG1Hke5ztA1/SWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:20:40.462601Z"},"content_sha256":"735010987dd7bd13345187427a01d9484313c64d0d1329efe8e3f841cc55224f","schema_version":"1.0","event_id":"sha256:735010987dd7bd13345187427a01d9484313c64d0d1329efe8e3f841cc55224f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/bundle.json","state_url":"https://pith.science/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/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":"2026-06-27T09:20:40Z","links":{"resolver":"https://pith.science/pith/XZTPVFHZ3L5PZPCB6PA774EWG2","bundle":"https://pith.science/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/bundle.json","state":"https://pith.science/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZTPVFHZ3L5PZPCB6PA774EWG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XZTPVFHZ3L5PZPCB6PA774EWG2","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":"6f51127a5fcac00007b23c5ffa78e13f256d2e7db4103c28cc310731e477de5d","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CO","submitted_at":"2014-03-07T17:30:57Z","title_canon_sha256":"02c1b4311483a0fdc714b175eb040efbecf982a1511f42df51cb9a65212a6926"},"schema_version":"1.0","source":{"id":"1403.1818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1818","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1818v1","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1818","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"XZTPVFHZ3L5P","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZTPVFHZ3L5PZPCB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZTPVFHZ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:735010987dd7bd13345187427a01d9484313c64d0d1329efe8e3f841cc55224f","target":"graph","created_at":"2026-05-18T02:56:52Z","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":"A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been considered in the past, we provide a new, simple Gray code for fixed-weight m-ary strings. In addition, we consider a relatively new type of Gray code known as overlap cycles and prove basic existence results concerning overlap cycles for fixed-weight and weight-range m-ary words.","authors_text":"Glenn Hurlbert, Victoria Horan","cross_cats":["cs.DM","cs.IT","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CO","submitted_at":"2014-03-07T17:30:57Z","title":"Gray Codes and Overlap Cycles for Restricted Weight Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1818","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:d50b66cc3a1389eb9ea15e0a086cca1ec212bbc9a3f43686e3edcbe84d719dfd","target":"record","created_at":"2026-05-18T02:56:52Z","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":"6f51127a5fcac00007b23c5ffa78e13f256d2e7db4103c28cc310731e477de5d","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CO","submitted_at":"2014-03-07T17:30:57Z","title_canon_sha256":"02c1b4311483a0fdc714b175eb040efbecf982a1511f42df51cb9a65212a6926"},"schema_version":"1.0","source":{"id":"1403.1818","kind":"arxiv","version":1}},"canonical_sha256":"be66fa94f9dafafcbc41f3c1fff0963689b9b446f2ced86bb506f26d4ece60b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be66fa94f9dafafcbc41f3c1fff0963689b9b446f2ced86bb506f26d4ece60b9","first_computed_at":"2026-05-18T02:56:52.495906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:52.495906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qO2O968QG8rpXerIwZ5Cva3jDFl+OQlTh6n/gkBZfU42aqr1vuwxeJZuyD87y/PWsmZDkI7TPHOaYe1c4PqpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:52.496347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50b66cc3a1389eb9ea15e0a086cca1ec212bbc9a3f43686e3edcbe84d719dfd","sha256:735010987dd7bd13345187427a01d9484313c64d0d1329efe8e3f841cc55224f"],"state_sha256":"2f1f6fada109313308ea763ac2609422a13cb193573d4f7693153c0f1583b069"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3AUJlwxhvg9qH/OacoOF1QtXS2YUPTgrJONrWK7JNwSxdD9L4tYa6767aQ1/IP+vKm7n6OJpT8Nn6CsM+4a/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:20:40.464475Z","bundle_sha256":"dc7bbaede0e2eb9fb75674a1a0f1a0f5603a3df28d565fdd549228c09899ffed"}}