{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7ML5PWRMIXORVCBJKWZGXPWZYO","short_pith_number":"pith:7ML5PWRM","canonical_record":{"source":{"id":"1311.5173","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T19:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"ba2d2606947369c289ae484ea780964a56d7757531f2c4cffe412fc4fa25db1d","abstract_canon_sha256":"391b0d2b71a9b59f5c69971229fc763792b6475df4f938a0f930840a8885b59a"},"schema_version":"1.0"},"canonical_sha256":"fb17d7da2c45dd1a882955b26bbed9c38431c0ae0fd4a42741556ee24f2ee800","source":{"kind":"arxiv","id":"1311.5173","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5173","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5173v5","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5173","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"7ML5PWRMIXOR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7ML5PWRMIXORVCBJ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7ML5PWRM","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7ML5PWRMIXORVCBJKWZGXPWZYO","target":"record","payload":{"canonical_record":{"source":{"id":"1311.5173","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T19:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"ba2d2606947369c289ae484ea780964a56d7757531f2c4cffe412fc4fa25db1d","abstract_canon_sha256":"391b0d2b71a9b59f5c69971229fc763792b6475df4f938a0f930840a8885b59a"},"schema_version":"1.0"},"canonical_sha256":"fb17d7da2c45dd1a882955b26bbed9c38431c0ae0fd4a42741556ee24f2ee800","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:56.526042Z","signature_b64":"OVL5FKDknjTrgLTZT/0dkK3yIeBXN8xaUVO1rUWueEWJpTeK9B391YvTWWL2ejfOP8vv20cuacVD1/YfqxGuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb17d7da2c45dd1a882955b26bbed9c38431c0ae0fd4a42741556ee24f2ee800","last_reissued_at":"2026-05-17T23:52:56.525311Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:56.525311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.5173","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJufVScy5NDHa/qm5ZKYQNE1HmtpWDXsMC9cgDt1LTuwrfUkSLKhikO1XfV7E/dTHJIxro9ECrWH0pnWQ5dsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:50:00.819219Z"},"content_sha256":"0296d77f8adca6df7779a9ac60fe7203592067bd449b860696245d7122e37446","schema_version":"1.0","event_id":"sha256:0296d77f8adca6df7779a9ac60fe7203592067bd449b860696245d7122e37446"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7ML5PWRMIXORVCBJKWZGXPWZYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signed Mahonian polynomials for major and sorting indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huilan Chang, Sen-Peng Eu, Shishuo Fu, Yuan-Hsun Lo, Zhicong Lin","submitted_at":"2013-11-20T19:00:31Z","abstract_excerpt":"We derive some new signed Mahonian polynomials over the complex reflection group $G(r,1,n)=C_r\\wr\\mathfrak{S}_n$, where the \"sign\" is taken to be any of the $2r$ $1$-dim characters and the \"Mahonian\" statistics are the $\\mathsf{lmaj}$ defined by Bagno and the $\\mathsf{sor}$ defined by Eu et al. Various new signed Mahonian polynomials over Coxeter groups of types $B_n$ and $D_n$ are derived as well. We also investigate the signed counting polynomials on $G(r,1,n)$ for those statistics with the distribution $[r]_q[2r]_q\\cdots [nr]_q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5173","kind":"arxiv","version":5},"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":"2026-05-17T23:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXPAUkFr4kmG5t0/R7oo92jeKqwJz8KJo1vJ/+Vg17/UVmaPmrHE03IU76+bSAu55Tw0cUIeclaLcEoh5PTGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:50:00.819584Z"},"content_sha256":"1b093349eacad7dd0c2eb289a52711a482f91d4f25a98cab23a2a8fd77a9231b","schema_version":"1.0","event_id":"sha256:1b093349eacad7dd0c2eb289a52711a482f91d4f25a98cab23a2a8fd77a9231b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/bundle.json","state_url":"https://pith.science/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/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":"2026-05-26T11:50:00Z","links":{"resolver":"https://pith.science/pith/7ML5PWRMIXORVCBJKWZGXPWZYO","bundle":"https://pith.science/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/bundle.json","state":"https://pith.science/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ML5PWRMIXORVCBJKWZGXPWZYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7ML5PWRMIXORVCBJKWZGXPWZYO","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":"391b0d2b71a9b59f5c69971229fc763792b6475df4f938a0f930840a8885b59a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T19:00:31Z","title_canon_sha256":"ba2d2606947369c289ae484ea780964a56d7757531f2c4cffe412fc4fa25db1d"},"schema_version":"1.0","source":{"id":"1311.5173","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5173","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5173v5","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5173","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"7ML5PWRMIXOR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7ML5PWRMIXORVCBJ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7ML5PWRM","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:1b093349eacad7dd0c2eb289a52711a482f91d4f25a98cab23a2a8fd77a9231b","target":"graph","created_at":"2026-05-17T23:52:56Z","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":"We derive some new signed Mahonian polynomials over the complex reflection group $G(r,1,n)=C_r\\wr\\mathfrak{S}_n$, where the \"sign\" is taken to be any of the $2r$ $1$-dim characters and the \"Mahonian\" statistics are the $\\mathsf{lmaj}$ defined by Bagno and the $\\mathsf{sor}$ defined by Eu et al. Various new signed Mahonian polynomials over Coxeter groups of types $B_n$ and $D_n$ are derived as well. We also investigate the signed counting polynomials on $G(r,1,n)$ for those statistics with the distribution $[r]_q[2r]_q\\cdots [nr]_q$.","authors_text":"Huilan Chang, Sen-Peng Eu, Shishuo Fu, Yuan-Hsun Lo, Zhicong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T19:00:31Z","title":"Signed Mahonian polynomials for major and sorting indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5173","kind":"arxiv","version":5},"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":"sha256:0296d77f8adca6df7779a9ac60fe7203592067bd449b860696245d7122e37446","target":"record","created_at":"2026-05-17T23:52:56Z","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":"391b0d2b71a9b59f5c69971229fc763792b6475df4f938a0f930840a8885b59a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T19:00:31Z","title_canon_sha256":"ba2d2606947369c289ae484ea780964a56d7757531f2c4cffe412fc4fa25db1d"},"schema_version":"1.0","source":{"id":"1311.5173","kind":"arxiv","version":5}},"canonical_sha256":"fb17d7da2c45dd1a882955b26bbed9c38431c0ae0fd4a42741556ee24f2ee800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb17d7da2c45dd1a882955b26bbed9c38431c0ae0fd4a42741556ee24f2ee800","first_computed_at":"2026-05-17T23:52:56.525311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:56.525311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OVL5FKDknjTrgLTZT/0dkK3yIeBXN8xaUVO1rUWueEWJpTeK9B391YvTWWL2ejfOP8vv20cuacVD1/YfqxGuBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:56.526042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5173","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0296d77f8adca6df7779a9ac60fe7203592067bd449b860696245d7122e37446","sha256:1b093349eacad7dd0c2eb289a52711a482f91d4f25a98cab23a2a8fd77a9231b"],"state_sha256":"df9a9d0b7b8ba396245c4e4ffc3a4b31f6eaca26cc3b407db7ee2714576e8d87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMC3MhOEgOsK623Kv55s/rfiHoRncnm29wgNXbFYzfMKcIUrKuBTqp1vsiGdS/OE+2tgAXjNO740a0+7XVJoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:50:00.822544Z","bundle_sha256":"0ba12abbac28902ce21c066fe89b9424c7110736511255d9849b9f25c129f2ef"}}