{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NSJ4VBT2ZECETTXT62LEPEL2JP","short_pith_number":"pith:NSJ4VBT2","canonical_record":{"source":{"id":"1401.5568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-22T06:54:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"18d6a7cf26ea40f21152b4e3bb73b0e9d9f85eea1451158b55be6a13c36460a2","abstract_canon_sha256":"b79125d3249f92bfa693483837092ce29718405807281b9cc8a09e3e7360d7e5"},"schema_version":"1.0"},"canonical_sha256":"6c93ca867ac90449cef3f69647917a4bc2b55bc96861761162a9f2289486dd80","source":{"kind":"arxiv","id":"1401.5568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5568","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5568v1","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5568","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"NSJ4VBT2ZECE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NSJ4VBT2ZECETTXT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NSJ4VBT2","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NSJ4VBT2ZECETTXT62LEPEL2JP","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-22T06:54:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"18d6a7cf26ea40f21152b4e3bb73b0e9d9f85eea1451158b55be6a13c36460a2","abstract_canon_sha256":"b79125d3249f92bfa693483837092ce29718405807281b9cc8a09e3e7360d7e5"},"schema_version":"1.0"},"canonical_sha256":"6c93ca867ac90449cef3f69647917a4bc2b55bc96861761162a9f2289486dd80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:25.923724Z","signature_b64":"h9oSCZbvU27MCroVw4UCuIm/Hjw6AmR8/v6ET8DNtHcoyKbO1K0RMKvhOw9QlCsokE5vWh6WD9guPZ2g8XKDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c93ca867ac90449cef3f69647917a4bc2b55bc96861761162a9f2289486dd80","last_reissued_at":"2026-05-18T03:01:25.922969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:25.922969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5568","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":"2026-05-18T03:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWm4rsiwlF7GpNLdp7uEkuxxxSH4zkiqrYFoHWuV2ltECVU0Uhmyxe3hpqS8nkZ4Cv8hP7OdpkURWKi4TxyvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:42:34.053238Z"},"content_sha256":"5bb25ffbb67a88e4e3fc0202cf4ed39a690a8cece68e29319feb41a41d35f5b0","schema_version":"1.0","event_id":"sha256:5bb25ffbb67a88e4e3fc0202cf4ed39a690a8cece68e29319feb41a41d35f5b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NSJ4VBT2ZECETTXT62LEPEL2JP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the group of alternating colored permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"David Garber, Eli Bagno, Toufik Mansour","submitted_at":"2014-01-22T06:54:40Z","abstract_excerpt":"The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\\mathbb{Z}_r \\wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of $\\mathbb{Z}_{\\frac{r}{2}} \\wr S_n$ and use this point of view to give another expression for the length function. We also use this covering to lift several known parameters of $\\mathbb{Z}_{\\frac{r}{2}} \\wr S_n$ to the group of alternating colored permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5568","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":"2026-05-18T03:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"975mwIrBspGWE9fikebfk1qPEcg7SWBhId+efyq6aLlKslxdp14xJPmNlhnIopPf3xa1i7HY4hvecTstUhfvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:42:34.053644Z"},"content_sha256":"ed309f0892217dee24a9de71ad0505f420d2fce1480c33abe47507b56c74a6b5","schema_version":"1.0","event_id":"sha256:ed309f0892217dee24a9de71ad0505f420d2fce1480c33abe47507b56c74a6b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/bundle.json","state_url":"https://pith.science/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/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":"2026-05-27T19:42:34Z","links":{"resolver":"https://pith.science/pith/NSJ4VBT2ZECETTXT62LEPEL2JP","bundle":"https://pith.science/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/bundle.json","state":"https://pith.science/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSJ4VBT2ZECETTXT62LEPEL2JP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NSJ4VBT2ZECETTXT62LEPEL2JP","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":"b79125d3249f92bfa693483837092ce29718405807281b9cc8a09e3e7360d7e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-22T06:54:40Z","title_canon_sha256":"18d6a7cf26ea40f21152b4e3bb73b0e9d9f85eea1451158b55be6a13c36460a2"},"schema_version":"1.0","source":{"id":"1401.5568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5568","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5568v1","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5568","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"NSJ4VBT2ZECE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NSJ4VBT2ZECETTXT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NSJ4VBT2","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ed309f0892217dee24a9de71ad0505f420d2fce1480c33abe47507b56c74a6b5","target":"graph","created_at":"2026-05-18T03:01:25Z","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":"The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\\mathbb{Z}_r \\wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of $\\mathbb{Z}_{\\frac{r}{2}} \\wr S_n$ and use this point of view to give another expression for the length function. We also use this covering to lift several known parameters of $\\mathbb{Z}_{\\frac{r}{2}} \\wr S_n$ to the group of alternating colored permutations.","authors_text":"David Garber, Eli Bagno, Toufik Mansour","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-22T06:54:40Z","title":"On the group of alternating colored permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5568","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":"sha256:5bb25ffbb67a88e4e3fc0202cf4ed39a690a8cece68e29319feb41a41d35f5b0","target":"record","created_at":"2026-05-18T03:01:25Z","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":"b79125d3249f92bfa693483837092ce29718405807281b9cc8a09e3e7360d7e5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-22T06:54:40Z","title_canon_sha256":"18d6a7cf26ea40f21152b4e3bb73b0e9d9f85eea1451158b55be6a13c36460a2"},"schema_version":"1.0","source":{"id":"1401.5568","kind":"arxiv","version":1}},"canonical_sha256":"6c93ca867ac90449cef3f69647917a4bc2b55bc96861761162a9f2289486dd80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c93ca867ac90449cef3f69647917a4bc2b55bc96861761162a9f2289486dd80","first_computed_at":"2026-05-18T03:01:25.922969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:25.922969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h9oSCZbvU27MCroVw4UCuIm/Hjw6AmR8/v6ET8DNtHcoyKbO1K0RMKvhOw9QlCsokE5vWh6WD9guPZ2g8XKDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:25.923724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bb25ffbb67a88e4e3fc0202cf4ed39a690a8cece68e29319feb41a41d35f5b0","sha256:ed309f0892217dee24a9de71ad0505f420d2fce1480c33abe47507b56c74a6b5"],"state_sha256":"5d540d019e28e3702cf50951d6e18e55818a9c4b955165e5c58712c4fb1fe2da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Hl/6EtMaSoFFwh3z+26SI5ywrGo0C2JfZFpYm0Quab9eXlzX4LC4KS8U1bc8qCaaD2vc5WQnxCJcaLJlaK9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:42:34.056595Z","bundle_sha256":"cdae85f42632bbde83c3afe0e78bedbef3a552f10ce934f3c07f0c10c7289d18"}}