{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BMHAKC5G3UXX2NZFQEHM3KNOV6","short_pith_number":"pith:BMHAKC5G","canonical_record":{"source":{"id":"1611.04973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-15T18:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"ce4f57532c57fdc9a053b3e940786d9ff31eb6f477d362eb41551795b2d0bc77","abstract_canon_sha256":"7f803cef0b9fb24369ab7fe9f38453ae7096d6db5062c2c589b2858a8074de99"},"schema_version":"1.0"},"canonical_sha256":"0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e","source":{"kind":"arxiv","id":"1611.04973","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04973","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04973v2","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04973","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"BMHAKC5G3UXX","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BMHAKC5G3UXX2NZF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BMHAKC5G","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BMHAKC5G3UXX2NZFQEHM3KNOV6","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-15T18:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"ce4f57532c57fdc9a053b3e940786d9ff31eb6f477d362eb41551795b2d0bc77","abstract_canon_sha256":"7f803cef0b9fb24369ab7fe9f38453ae7096d6db5062c2c589b2858a8074de99"},"schema_version":"1.0"},"canonical_sha256":"0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:36.956351Z","signature_b64":"yVSCWpoLGH6qSqXqGkQAsnJ9Z0wY3B70LmJhxXIPCTYUU4PNuhgFXXsR3QI9FQtsCtxLvJ+xfCzw1VpOMiU+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e","last_reissued_at":"2026-05-18T00:57:36.955732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:36.955732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04973","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":"2026-05-18T00:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGTfwC/SfY4RLkVn7V051kaGLhDTqsy7n4Vq8SBbZqcjtHMrxumXQjqGxxmDQLs+pnGsitIgA17lem3Ihr62Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:01:28.480041Z"},"content_sha256":"0419403ae96fb941f010b7d24c22e7ed9085fb7fb1fce9b28a6f390a648f34be","schema_version":"1.0","event_id":"sha256:0419403ae96fb941f010b7d24c22e7ed9085fb7fb1fce9b28a6f390a648f34be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BMHAKC5G3UXX2NZFQEHM3KNOV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Macdonald symmetry at $q=1$ and a new class of inv-preserving bijections on words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jennifer Morse, Maria Gillespie, Ryan Kaliszewski","submitted_at":"2016-11-15T18:17:15Z","abstract_excerpt":"We give a direct combinatorial proof of the $q,t$-symmetry relation $\\tilde H_{\\mu}(X;q,t)=\\tilde H_{\\mu'}(X;t,q)$ in the Macdonald polynomials $\\tilde H_\\mu$ at the specialization $q=1$. The bijection demonstrates that the Macdonald inv statistic on the permutations of any given row of a Young diagram filling is Mahonian. Moreover, our bijection gives rise a family of new bijections on words that preserves the classical Mahonian inv statistic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04973","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":"2026-05-18T00:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3sYSQ0BrvswsirPaAD/wmlh/7J7J5mCnOWjPdgqQRXmD9m9MmSqV0b/hGzlRFvUD3/Kj8oklfg7HI5+iuCVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:01:28.480698Z"},"content_sha256":"e4f3fd0ef1c3fbbb7f68773f6d86e6a53caa275852a1bab5d950301ccc616dfb","schema_version":"1.0","event_id":"sha256:e4f3fd0ef1c3fbbb7f68773f6d86e6a53caa275852a1bab5d950301ccc616dfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/bundle.json","state_url":"https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/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":"2026-05-31T04:01:28Z","links":{"resolver":"https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6","bundle":"https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/bundle.json","state":"https://pith.science/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMHAKC5G3UXX2NZFQEHM3KNOV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BMHAKC5G3UXX2NZFQEHM3KNOV6","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":"7f803cef0b9fb24369ab7fe9f38453ae7096d6db5062c2c589b2858a8074de99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-15T18:17:15Z","title_canon_sha256":"ce4f57532c57fdc9a053b3e940786d9ff31eb6f477d362eb41551795b2d0bc77"},"schema_version":"1.0","source":{"id":"1611.04973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04973","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04973v2","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04973","created_at":"2026-05-18T00:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"BMHAKC5G3UXX","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BMHAKC5G3UXX2NZF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BMHAKC5G","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:e4f3fd0ef1c3fbbb7f68773f6d86e6a53caa275852a1bab5d950301ccc616dfb","target":"graph","created_at":"2026-05-18T00:57:36Z","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 give a direct combinatorial proof of the $q,t$-symmetry relation $\\tilde H_{\\mu}(X;q,t)=\\tilde H_{\\mu'}(X;t,q)$ in the Macdonald polynomials $\\tilde H_\\mu$ at the specialization $q=1$. The bijection demonstrates that the Macdonald inv statistic on the permutations of any given row of a Young diagram filling is Mahonian. Moreover, our bijection gives rise a family of new bijections on words that preserves the classical Mahonian inv statistic.","authors_text":"Jennifer Morse, Maria Gillespie, Ryan Kaliszewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-15T18:17:15Z","title":"Macdonald symmetry at $q=1$ and a new class of inv-preserving bijections on words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04973","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":"sha256:0419403ae96fb941f010b7d24c22e7ed9085fb7fb1fce9b28a6f390a648f34be","target":"record","created_at":"2026-05-18T00:57:36Z","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":"7f803cef0b9fb24369ab7fe9f38453ae7096d6db5062c2c589b2858a8074de99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-15T18:17:15Z","title_canon_sha256":"ce4f57532c57fdc9a053b3e940786d9ff31eb6f477d362eb41551795b2d0bc77"},"schema_version":"1.0","source":{"id":"1611.04973","kind":"arxiv","version":2}},"canonical_sha256":"0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b0e050ba6dd2f7d3725810ecda9aeaf8d305a4e48d22e6bcde7280f8878421e","first_computed_at":"2026-05-18T00:57:36.955732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:36.955732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yVSCWpoLGH6qSqXqGkQAsnJ9Z0wY3B70LmJhxXIPCTYUU4PNuhgFXXsR3QI9FQtsCtxLvJ+xfCzw1VpOMiU+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:36.956351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0419403ae96fb941f010b7d24c22e7ed9085fb7fb1fce9b28a6f390a648f34be","sha256:e4f3fd0ef1c3fbbb7f68773f6d86e6a53caa275852a1bab5d950301ccc616dfb"],"state_sha256":"50f58395160fe721ffdfed8ab6bd4546365ee8b7ff623832165de29294e962ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x61AKSlUPBew9vx8T80Se99AQhbzyliCN3ejHbUj4EE8RdBAS7MDb9DQwTYzOSNee4qBsZL8CpdHhjy1PSP6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:01:28.483954Z","bundle_sha256":"29e0ac470d9bd81538f49d3214a15a609fcb6505d5701264bfc0f01d027a551d"}}