{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MFB7JE34VYSWM4QTXJI2AD5PV7","short_pith_number":"pith:MFB7JE34","canonical_record":{"source":{"id":"2410.00127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T18:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"ada00d3d12aeb4e9caa2308c0c8f0aa59ef57a48c3bcf4e4d679fe521e5f2e9e","abstract_canon_sha256":"ffffdfdd71401c1f2f496d1276334f4fa31529f6057e125f150e4104d9c149ad"},"schema_version":"1.0"},"canonical_sha256":"6143f4937cae25667213ba51a00fafafd008ba48bea137c44726a4d5b143936d","source":{"kind":"arxiv","id":"2410.00127","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00127","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00127v3","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00127","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"MFB7JE34VYSW","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"MFB7JE34VYSWM4QT","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"MFB7JE34","created_at":"2026-07-02T00:18:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MFB7JE34VYSWM4QTXJI2AD5PV7","target":"record","payload":{"canonical_record":{"source":{"id":"2410.00127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T18:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"ada00d3d12aeb4e9caa2308c0c8f0aa59ef57a48c3bcf4e4d679fe521e5f2e9e","abstract_canon_sha256":"ffffdfdd71401c1f2f496d1276334f4fa31529f6057e125f150e4104d9c149ad"},"schema_version":"1.0"},"canonical_sha256":"6143f4937cae25667213ba51a00fafafd008ba48bea137c44726a4d5b143936d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:09.683309Z","signature_b64":"/E2a5Skz/IGZB0t2XFM1XoJ3P5/Nm+MPOlomfO5TV1OV2+kNcCQpbdVr1oHK4LOpRJFWtZwTXBIEtO7H7nzlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6143f4937cae25667213ba51a00fafafd008ba48bea137c44726a4d5b143936d","last_reissued_at":"2026-07-02T00:18:09.682379Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:09.682379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.00127","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-02T00:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPZzfURdIbsSGp8eBFnl0kldS2XQ3vkF9r3+mbuxUbrZq8P3pemINDrnFnSIPrFvtjqaYamyd1akX0WtGTDNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:30:04.655067Z"},"content_sha256":"61600434165d1fd6be43cc50518489f1b5234e59a0e2badbdd5b3aca701f01e3","schema_version":"1.0","event_id":"sha256:61600434165d1fd6be43cc50518489f1b5234e59a0e2badbdd5b3aca701f01e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MFB7JE34VYSWM4QTXJI2AD5PV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rook matroids and log-concavity of $P$-Eulerian polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aryaman Jal, Per Alexandersson","submitted_at":"2024-09-30T18:09:30Z","abstract_excerpt":"We define and study rook matroids, the bases of which correspond to non-nesting rook placements on a skew Ferrers board. We show that rook matroids are a subclass of both transversal matroids and positroids; they also bear a subtle relationship to lattice path matroids that centers around not having the quaternary matroid $Q_{6}$ as a minor. The enumerative and distributional properties of non-nesting rook placements stand in contrast to those of usual rook placements: the non-nesting rook polynomial is not real-rooted in general, and is instead ultra-log-concave. We leverage this property tog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00127","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.00127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-02T00:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cHhuQqSIoSwvR1vmgUZnSUCezLf1NEguAfGU+bQPsCMOHM0+mty31B5ATo8gk4eEARJMA+gLC7V9yCE0zF6XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:30:04.655511Z"},"content_sha256":"acea0c44a5ebb515d734abe1c182cfc3ad0183e408211d62c05a9d8b819a464f","schema_version":"1.0","event_id":"sha256:acea0c44a5ebb515d734abe1c182cfc3ad0183e408211d62c05a9d8b819a464f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/bundle.json","state_url":"https://pith.science/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/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":"2026-07-02T22:30:04Z","links":{"resolver":"https://pith.science/pith/MFB7JE34VYSWM4QTXJI2AD5PV7","bundle":"https://pith.science/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/bundle.json","state":"https://pith.science/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFB7JE34VYSWM4QTXJI2AD5PV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MFB7JE34VYSWM4QTXJI2AD5PV7","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":"ffffdfdd71401c1f2f496d1276334f4fa31529f6057e125f150e4104d9c149ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T18:09:30Z","title_canon_sha256":"ada00d3d12aeb4e9caa2308c0c8f0aa59ef57a48c3bcf4e4d679fe521e5f2e9e"},"schema_version":"1.0","source":{"id":"2410.00127","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00127","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00127v3","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00127","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"MFB7JE34VYSW","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_16","alias_value":"MFB7JE34VYSWM4QT","created_at":"2026-07-02T00:18:09Z"},{"alias_kind":"pith_short_8","alias_value":"MFB7JE34","created_at":"2026-07-02T00:18:09Z"}],"graph_snapshots":[{"event_id":"sha256:acea0c44a5ebb515d734abe1c182cfc3ad0183e408211d62c05a9d8b819a464f","target":"graph","created_at":"2026-07-02T00:18:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.00127/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study rook matroids, the bases of which correspond to non-nesting rook placements on a skew Ferrers board. We show that rook matroids are a subclass of both transversal matroids and positroids; they also bear a subtle relationship to lattice path matroids that centers around not having the quaternary matroid $Q_{6}$ as a minor. The enumerative and distributional properties of non-nesting rook placements stand in contrast to those of usual rook placements: the non-nesting rook polynomial is not real-rooted in general, and is instead ultra-log-concave. We leverage this property tog","authors_text":"Aryaman Jal, Per Alexandersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T18:09:30Z","title":"Rook matroids and log-concavity of $P$-Eulerian polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00127","kind":"arxiv","version":3},"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":"sha256:61600434165d1fd6be43cc50518489f1b5234e59a0e2badbdd5b3aca701f01e3","target":"record","created_at":"2026-07-02T00:18:09Z","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":"ffffdfdd71401c1f2f496d1276334f4fa31529f6057e125f150e4104d9c149ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-09-30T18:09:30Z","title_canon_sha256":"ada00d3d12aeb4e9caa2308c0c8f0aa59ef57a48c3bcf4e4d679fe521e5f2e9e"},"schema_version":"1.0","source":{"id":"2410.00127","kind":"arxiv","version":3}},"canonical_sha256":"6143f4937cae25667213ba51a00fafafd008ba48bea137c44726a4d5b143936d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6143f4937cae25667213ba51a00fafafd008ba48bea137c44726a4d5b143936d","first_computed_at":"2026-07-02T00:18:09.682379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:09.682379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/E2a5Skz/IGZB0t2XFM1XoJ3P5/Nm+MPOlomfO5TV1OV2+kNcCQpbdVr1oHK4LOpRJFWtZwTXBIEtO7H7nzlAA==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:09.683309Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00127","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61600434165d1fd6be43cc50518489f1b5234e59a0e2badbdd5b3aca701f01e3","sha256:acea0c44a5ebb515d734abe1c182cfc3ad0183e408211d62c05a9d8b819a464f"],"state_sha256":"0d33f3171bbb8b25bbf4f461ce12f6752a04dbb583759d78a2e901400c7064f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"voB7gvl2jPiqkTnKgxQnkI1YKeA8YmajxjIJx7u9nA1yx0HugJwdpk+/b9fQWpTauqeKEfyImg8gPOwbXtTaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:30:04.657587Z","bundle_sha256":"e8707089822c5be68a71d432c5097755d5bf1afa2036cc6c93a6347035102bdd"}}