{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O4XAICTNM4ECQYTGY5TWGYRLOS","short_pith_number":"pith:O4XAICTN","canonical_record":{"source":{"id":"1403.2169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-10T08:53:10Z","cross_cats_sorted":[],"title_canon_sha256":"0e717732c30a962558c411d2f69802f3bf3042b9228b41d2d07e885c012af33d","abstract_canon_sha256":"2bb9c38a4631080993b82e13c365c9e8053cd4e56dfde9e7d2bb7e661756667b"},"schema_version":"1.0"},"canonical_sha256":"772e040a6d6708286266c76763622b7486aaa24228b5f08561cd336135852864","source":{"kind":"arxiv","id":"1403.2169","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2169","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2169v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2169","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"O4XAICTNM4EC","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O4XAICTNM4ECQYTG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O4XAICTN","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O4XAICTNM4ECQYTGY5TWGYRLOS","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-10T08:53:10Z","cross_cats_sorted":[],"title_canon_sha256":"0e717732c30a962558c411d2f69802f3bf3042b9228b41d2d07e885c012af33d","abstract_canon_sha256":"2bb9c38a4631080993b82e13c365c9e8053cd4e56dfde9e7d2bb7e661756667b"},"schema_version":"1.0"},"canonical_sha256":"772e040a6d6708286266c76763622b7486aaa24228b5f08561cd336135852864","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.050808Z","signature_b64":"Zrwbkn/eo48pbvslXuv9IUcrwaJT3FIlgtnCaRJjJ0sC93o8Mvk63LIEc5rvfHIDjs76e9EsOu75PkzZ512PDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"772e040a6d6708286266c76763622b7486aaa24228b5f08561cd336135852864","last_reissued_at":"2026-05-18T02:41:26.050329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.050329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2169","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvyHgOUZieD4LddJkB73QZ/4kXOjxNf76WYg0MZOBSvIFL+cKATs0ofZJPkmxb5qwUoTZXQm/Rl56nDy0RyICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:16.165923Z"},"content_sha256":"fcc2842ae1d426a5caab5064fba52ada42921bc3eeee0339620b285512e24eb7","schema_version":"1.0","event_id":"sha256:fcc2842ae1d426a5caab5064fba52ada42921bc3eeee0339620b285512e24eb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O4XAICTNM4ECQYTGY5TWGYRLOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sorting index and set-valued joint equidistributions of $\\mathcal{B}_n$ and $\\mathcal{D}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sen-Peng Eu, Tsai-Lien Wong, Yuan-Hsun Lo","submitted_at":"2014-03-10T08:53:10Z","abstract_excerpt":"The sorting indices $\\text{sor}_B$ and $\\text{sor}_D$ on the Coxeter groups of type $B$ and $D$ respectively are defined by Petersen and it is proved that $(\\text{inv}_B, \\text{rlmin})$ and $(\\text{sor}_B, \\ell'_B)$ have the same joint distribution for type $B$ while $\\text{inv}_D$ and $\\text{sor}_D$ have the same distribution for type $D$. These results, including a set-valued extension of type $B$ involving two equildistributed pairs of three statistics, are proved combinatorially by Chen et al. via two mappings $\\varphi:=\\text{(B-code)}^{-1}\\circ \\text{(A-code)}$ and $\\psi:=\\text{(D-code)}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2169","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":"2026-05-18T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vw6vgArDni/LZeNF16wCmr1pMkPKecfh8UskNDEwGkRH6yoVIJFKsIkSR6wbkirw0WvlyqYM7eQ8ZXTwvEJnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:16.166626Z"},"content_sha256":"ce4f9401a4620cfaaf4ecd7e761f557cea3ce265b42cfc01a94d7dc3f3c7cf0c","schema_version":"1.0","event_id":"sha256:ce4f9401a4620cfaaf4ecd7e761f557cea3ce265b42cfc01a94d7dc3f3c7cf0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/bundle.json","state_url":"https://pith.science/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/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":"2026-05-26T19:11:16Z","links":{"resolver":"https://pith.science/pith/O4XAICTNM4ECQYTGY5TWGYRLOS","bundle":"https://pith.science/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/bundle.json","state":"https://pith.science/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4XAICTNM4ECQYTGY5TWGYRLOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O4XAICTNM4ECQYTGY5TWGYRLOS","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":"2bb9c38a4631080993b82e13c365c9e8053cd4e56dfde9e7d2bb7e661756667b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-10T08:53:10Z","title_canon_sha256":"0e717732c30a962558c411d2f69802f3bf3042b9228b41d2d07e885c012af33d"},"schema_version":"1.0","source":{"id":"1403.2169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2169","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2169v2","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2169","created_at":"2026-05-18T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"O4XAICTNM4EC","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O4XAICTNM4ECQYTG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O4XAICTN","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ce4f9401a4620cfaaf4ecd7e761f557cea3ce265b42cfc01a94d7dc3f3c7cf0c","target":"graph","created_at":"2026-05-18T02:41:26Z","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 sorting indices $\\text{sor}_B$ and $\\text{sor}_D$ on the Coxeter groups of type $B$ and $D$ respectively are defined by Petersen and it is proved that $(\\text{inv}_B, \\text{rlmin})$ and $(\\text{sor}_B, \\ell'_B)$ have the same joint distribution for type $B$ while $\\text{inv}_D$ and $\\text{sor}_D$ have the same distribution for type $D$. These results, including a set-valued extension of type $B$ involving two equildistributed pairs of three statistics, are proved combinatorially by Chen et al. via two mappings $\\varphi:=\\text{(B-code)}^{-1}\\circ \\text{(A-code)}$ and $\\psi:=\\text{(D-code)}^","authors_text":"Sen-Peng Eu, Tsai-Lien Wong, Yuan-Hsun Lo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-10T08:53:10Z","title":"The sorting index and set-valued joint equidistributions of $\\mathcal{B}_n$ and $\\mathcal{D}_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2169","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:fcc2842ae1d426a5caab5064fba52ada42921bc3eeee0339620b285512e24eb7","target":"record","created_at":"2026-05-18T02:41:26Z","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":"2bb9c38a4631080993b82e13c365c9e8053cd4e56dfde9e7d2bb7e661756667b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-10T08:53:10Z","title_canon_sha256":"0e717732c30a962558c411d2f69802f3bf3042b9228b41d2d07e885c012af33d"},"schema_version":"1.0","source":{"id":"1403.2169","kind":"arxiv","version":2}},"canonical_sha256":"772e040a6d6708286266c76763622b7486aaa24228b5f08561cd336135852864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"772e040a6d6708286266c76763622b7486aaa24228b5f08561cd336135852864","first_computed_at":"2026-05-18T02:41:26.050329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:26.050329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zrwbkn/eo48pbvslXuv9IUcrwaJT3FIlgtnCaRJjJ0sC93o8Mvk63LIEc5rvfHIDjs76e9EsOu75PkzZ512PDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:26.050808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcc2842ae1d426a5caab5064fba52ada42921bc3eeee0339620b285512e24eb7","sha256:ce4f9401a4620cfaaf4ecd7e761f557cea3ce265b42cfc01a94d7dc3f3c7cf0c"],"state_sha256":"cffb8d1f1e75a5c9dd8e3342fe98930dc3f3e306962a02982ca8e2f689ff2069"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7bCrlXJTHpKwBlyff1PZIORKnlU+HTnsFaxP/nAbpljVfC6MLIP/9vk7MD8pBC8ssmMn2DWfU49SdmANh7D+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:11:16.170439Z","bundle_sha256":"c5b6b3053a69bab0dd7dddc61e3878206ecd5372303fe10558c5fe36b608d937"}}