{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BI3X6UISLYJ5RQ6K2RPBZAHGXX","short_pith_number":"pith:BI3X6UIS","canonical_record":{"source":{"id":"1007.2870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-16T21:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"dae7a7951a8c72f3a90edb61a65d4067914bbd03eedb6e8221d22ace5ad19c36","abstract_canon_sha256":"c9bbdf4b5d72010e6021f5e47db01c6b9415c136fabdd65454a3086706eb3651"},"schema_version":"1.0"},"canonical_sha256":"0a377f51125e13d8c3cad45e1c80e6bdcef96a30f2e3e5c111a116bf86941122","source":{"kind":"arxiv","id":"1007.2870","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2870","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2870v2","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2870","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"BI3X6UISLYJ5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BI3X6UISLYJ5RQ6K","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BI3X6UIS","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BI3X6UISLYJ5RQ6K2RPBZAHGXX","target":"record","payload":{"canonical_record":{"source":{"id":"1007.2870","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-16T21:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"dae7a7951a8c72f3a90edb61a65d4067914bbd03eedb6e8221d22ace5ad19c36","abstract_canon_sha256":"c9bbdf4b5d72010e6021f5e47db01c6b9415c136fabdd65454a3086706eb3651"},"schema_version":"1.0"},"canonical_sha256":"0a377f51125e13d8c3cad45e1c80e6bdcef96a30f2e3e5c111a116bf86941122","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:53.072489Z","signature_b64":"G9Dg9TBwioRcjrLiIX0usb6KKQGD5HoireIY1fvTxRxXo+a8Y9XrQmRPAs/2OtJL4EV26xC11o0eKufHGNudDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a377f51125e13d8c3cad45e1c80e6bdcef96a30f2e3e5c111a116bf86941122","last_reissued_at":"2026-05-18T04:24:53.071994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:53.071994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.2870","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKZCAfERvkGhdIPinJ23B+7p1srSnOXl+2+jRtq8lpLOZcAJ3tJ8cU5ux2E0zuEE/Me8s7t/AhPlqeV4rzoqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:10:00.405377Z"},"content_sha256":"a2558202eafb0041a85ba5f4c0956143dbab72f43480d04364c184f05f290b2c","schema_version":"1.0","event_id":"sha256:a2558202eafb0041a85ba5f4c0956143dbab72f43480d04364c184f05f290b2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BI3X6UISLYJ5RQ6K2RPBZAHGXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Number System of the Permutations Generated by Cyclic Shift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"St\\'ephane Legendre","submitted_at":"2010-07-16T21:10:56Z","abstract_excerpt":"A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code describing the symmetry properties of the set of permutations generated by cyclic shift. This code is conjectured to be a combinatorial Gray code listing the set of permutations: this corresponds to an Hamiltonian path of minimal weight in an appropriate regular digraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2870","kind":"arxiv","version":2},"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":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2nv+JJpvJhcFBgR0aZ8niURNJxBMh0H3C9Sm9a05X6CLIMaTpm6g95tRBg0K3wvmNipwPAFveHagHSrKiKaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:10:00.405725Z"},"content_sha256":"917852df6f90410e7f4330faa68826d2add1dbbc0214fb3fe590815c66117fd0","schema_version":"1.0","event_id":"sha256:917852df6f90410e7f4330faa68826d2add1dbbc0214fb3fe590815c66117fd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/bundle.json","state_url":"https://pith.science/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/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":"2026-06-29T12:10:00Z","links":{"resolver":"https://pith.science/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX","bundle":"https://pith.science/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/bundle.json","state":"https://pith.science/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BI3X6UISLYJ5RQ6K2RPBZAHGXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BI3X6UISLYJ5RQ6K2RPBZAHGXX","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":"c9bbdf4b5d72010e6021f5e47db01c6b9415c136fabdd65454a3086706eb3651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-16T21:10:56Z","title_canon_sha256":"dae7a7951a8c72f3a90edb61a65d4067914bbd03eedb6e8221d22ace5ad19c36"},"schema_version":"1.0","source":{"id":"1007.2870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2870","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2870v2","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2870","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"BI3X6UISLYJ5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BI3X6UISLYJ5RQ6K","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BI3X6UIS","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:917852df6f90410e7f4330faa68826d2add1dbbc0214fb3fe590815c66117fd0","target":"graph","created_at":"2026-05-18T04:24:53Z","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 number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code describing the symmetry properties of the set of permutations generated by cyclic shift. This code is conjectured to be a combinatorial Gray code listing the set of permutations: this corresponds to an Hamiltonian path of minimal weight in an appropriate regular digraph.","authors_text":"St\\'ephane Legendre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-16T21:10:56Z","title":"The Number System of the Permutations Generated by Cyclic Shift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2870","kind":"arxiv","version":2},"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:a2558202eafb0041a85ba5f4c0956143dbab72f43480d04364c184f05f290b2c","target":"record","created_at":"2026-05-18T04:24:53Z","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":"c9bbdf4b5d72010e6021f5e47db01c6b9415c136fabdd65454a3086706eb3651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-16T21:10:56Z","title_canon_sha256":"dae7a7951a8c72f3a90edb61a65d4067914bbd03eedb6e8221d22ace5ad19c36"},"schema_version":"1.0","source":{"id":"1007.2870","kind":"arxiv","version":2}},"canonical_sha256":"0a377f51125e13d8c3cad45e1c80e6bdcef96a30f2e3e5c111a116bf86941122","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a377f51125e13d8c3cad45e1c80e6bdcef96a30f2e3e5c111a116bf86941122","first_computed_at":"2026-05-18T04:24:53.071994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.071994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G9Dg9TBwioRcjrLiIX0usb6KKQGD5HoireIY1fvTxRxXo+a8Y9XrQmRPAs/2OtJL4EV26xC11o0eKufHGNudDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.072489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2558202eafb0041a85ba5f4c0956143dbab72f43480d04364c184f05f290b2c","sha256:917852df6f90410e7f4330faa68826d2add1dbbc0214fb3fe590815c66117fd0"],"state_sha256":"093a5544a900282a45174676b8de98638ae385611d09898fe098d70fcc0a281e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V5mWfDou8v7UNxnzcvlynA8msOqVSOpXojIYXOjpAEsinXkYgIY9ta98zPPXEZ7wVj900BGjwDzZSt+jdczkBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:10:00.407549Z","bundle_sha256":"c112b4eb379151c6db580fe57016529c299a5e70ebcc1e37bffdae133fba766f"}}