{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BHUTBDCTBNNY2MIBRDCGVP2O2K","short_pith_number":"pith:BHUTBDCT","canonical_record":{"source":{"id":"1411.3397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-12T23:44:29Z","cross_cats_sorted":[],"title_canon_sha256":"afeb15495e66aa5531dba1bc1d1343c2095a40f9ce04eaf2d553a176ae90bc67","abstract_canon_sha256":"c11117cd3766019e14a8f5dd7c40f513b247e34948f26a90ff2881cd714bd73f"},"schema_version":"1.0"},"canonical_sha256":"09e9308c530b5b8d310188c46abf4ed2bc8af532d87087c3f15aeb4c17940644","source":{"kind":"arxiv","id":"1411.3397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3397","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3397v2","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3397","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"BHUTBDCTBNNY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BHUTBDCTBNNY2MIB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BHUTBDCT","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BHUTBDCTBNNY2MIBRDCGVP2O2K","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-12T23:44:29Z","cross_cats_sorted":[],"title_canon_sha256":"afeb15495e66aa5531dba1bc1d1343c2095a40f9ce04eaf2d553a176ae90bc67","abstract_canon_sha256":"c11117cd3766019e14a8f5dd7c40f513b247e34948f26a90ff2881cd714bd73f"},"schema_version":"1.0"},"canonical_sha256":"09e9308c530b5b8d310188c46abf4ed2bc8af532d87087c3f15aeb4c17940644","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:24.346090Z","signature_b64":"3w+3F0LhGyim0vIZLfDiQviVr+Ib1bYKvzxS7VBlN8nh/lO30ymP2lD6PVtGtMh/PtZPlIjYvkq6/kANHBZxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09e9308c530b5b8d310188c46abf4ed2bc8af532d87087c3f15aeb4c17940644","last_reissued_at":"2026-05-18T02:17:24.345389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:24.345389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3397","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":"2026-05-18T02:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVPKLE7h1YQCDSdy/Uld3CN+Xa2ofpiH1ryeWwhH47vyKjomkMgxYOVwkd3yKsOfMhuTM/W4o3IskjNh3aRwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:12:45.326608Z"},"content_sha256":"439a010542247d137ab6c13d3bece89afb144a2de43e20bbeca208b433d3c138","schema_version":"1.0","event_id":"sha256:439a010542247d137ab6c13d3bece89afb144a2de43e20bbeca208b433d3c138"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BHUTBDCTBNNY2MIBRDCGVP2O2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\gamma$-positivity of basic Eulerian polynomials via group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiang Zeng, Zhicong Lin","submitted_at":"2014-11-12T23:44:29Z","abstract_excerpt":"We provide combinatorial interpretation for the $\\gamma$-coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as well as the corresponding $\\gamma$-coefficients for derangements. Our results refine the classical $\\gamma$-positivity results for the Eulerian polynomials and the derangement polynomials. The main tools are Br\\\"and\\'en's modified Foata--Strehl action on permutations and the recent triple statistic (des, rix,aid) equidistibuted with (exc, fix, maj)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3397","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":"2026-05-18T02:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HsNuJshffC5wjv81AvsMXh2hhr1b2F/EIK1CY85gplO83SnTAAKU3AOxEnkbb9MJ4PCtNg+A2xcAMJHv0WbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:12:45.327309Z"},"content_sha256":"185240b3f1d98951dcce1d7abf263ab6be11976c5e05774fdbc709b730a3c885","schema_version":"1.0","event_id":"sha256:185240b3f1d98951dcce1d7abf263ab6be11976c5e05774fdbc709b730a3c885"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/bundle.json","state_url":"https://pith.science/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/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":"2026-06-06T16:12:45Z","links":{"resolver":"https://pith.science/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K","bundle":"https://pith.science/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/bundle.json","state":"https://pith.science/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BHUTBDCTBNNY2MIBRDCGVP2O2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BHUTBDCTBNNY2MIBRDCGVP2O2K","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":"c11117cd3766019e14a8f5dd7c40f513b247e34948f26a90ff2881cd714bd73f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-12T23:44:29Z","title_canon_sha256":"afeb15495e66aa5531dba1bc1d1343c2095a40f9ce04eaf2d553a176ae90bc67"},"schema_version":"1.0","source":{"id":"1411.3397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3397","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3397v2","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3397","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"BHUTBDCTBNNY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BHUTBDCTBNNY2MIB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BHUTBDCT","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:185240b3f1d98951dcce1d7abf263ab6be11976c5e05774fdbc709b730a3c885","target":"graph","created_at":"2026-05-18T02:17:24Z","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 provide combinatorial interpretation for the $\\gamma$-coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as well as the corresponding $\\gamma$-coefficients for derangements. Our results refine the classical $\\gamma$-positivity results for the Eulerian polynomials and the derangement polynomials. The main tools are Br\\\"and\\'en's modified Foata--Strehl action on permutations and the recent triple statistic (des, rix,aid) equidistibuted with (exc, fix, maj).","authors_text":"Jiang Zeng, Zhicong Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-12T23:44:29Z","title":"The $\\gamma$-positivity of basic Eulerian polynomials via group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3397","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":"sha256:439a010542247d137ab6c13d3bece89afb144a2de43e20bbeca208b433d3c138","target":"record","created_at":"2026-05-18T02:17:24Z","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":"c11117cd3766019e14a8f5dd7c40f513b247e34948f26a90ff2881cd714bd73f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-12T23:44:29Z","title_canon_sha256":"afeb15495e66aa5531dba1bc1d1343c2095a40f9ce04eaf2d553a176ae90bc67"},"schema_version":"1.0","source":{"id":"1411.3397","kind":"arxiv","version":2}},"canonical_sha256":"09e9308c530b5b8d310188c46abf4ed2bc8af532d87087c3f15aeb4c17940644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09e9308c530b5b8d310188c46abf4ed2bc8af532d87087c3f15aeb4c17940644","first_computed_at":"2026-05-18T02:17:24.345389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:24.345389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3w+3F0LhGyim0vIZLfDiQviVr+Ib1bYKvzxS7VBlN8nh/lO30ymP2lD6PVtGtMh/PtZPlIjYvkq6/kANHBZxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:24.346090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:439a010542247d137ab6c13d3bece89afb144a2de43e20bbeca208b433d3c138","sha256:185240b3f1d98951dcce1d7abf263ab6be11976c5e05774fdbc709b730a3c885"],"state_sha256":"6b770cdca548f6dbd2642781ee8b27fd2a7806e136539d379f352d1edca6a203"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63vXZouzIMExJE9EUUq8QyEdLj3xdNpzT1enBgy4l9w8mrEaVkkp1C98HU6t/igCN3rxtoDsdvgfBJ0YUzbJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:12:45.332729Z","bundle_sha256":"279846b9a259170daac82842859cadae58f70e245a5b1f1f58c25cd1426036e9"}}