{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QEBPQAPOPWFCYOBWQJIIYLQ3ZP","short_pith_number":"pith:QEBPQAPO","canonical_record":{"source":{"id":"2505.04581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-07T17:20:38Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"78c32ad38a95edf0d7cc4973c9b9b5cba6aae3e6c506da0272d6f48e2bdab059","abstract_canon_sha256":"c790d7199aa64c948b84a510ba65192f1e9534d4ea2741bae8f3eea5a6e98e81"},"schema_version":"1.0"},"canonical_sha256":"8102f801ee7d8a2c383682508c2e1bcbd627d58ad9b66f231f7d41c87fbbe591","source":{"kind":"arxiv","id":"2505.04581","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04581","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04581v2","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04581","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"QEBPQAPOPWFC","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"QEBPQAPOPWFCYOBW","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"QEBPQAPO","created_at":"2026-07-05T11:04:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QEBPQAPOPWFCYOBWQJIIYLQ3ZP","target":"record","payload":{"canonical_record":{"source":{"id":"2505.04581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-07T17:20:38Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"78c32ad38a95edf0d7cc4973c9b9b5cba6aae3e6c506da0272d6f48e2bdab059","abstract_canon_sha256":"c790d7199aa64c948b84a510ba65192f1e9534d4ea2741bae8f3eea5a6e98e81"},"schema_version":"1.0"},"canonical_sha256":"8102f801ee7d8a2c383682508c2e1bcbd627d58ad9b66f231f7d41c87fbbe591","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:50.562849Z","signature_b64":"B3f2P5CNB0N5nbUuqE1eTl5neywpNIgLrQSsoG61Jj9pLQJY9f1aGid5UaQc5YWLR0aT5RdF7OL8JCv5mBUODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8102f801ee7d8a2c383682508c2e1bcbd627d58ad9b66f231f7d41c87fbbe591","last_reissued_at":"2026-07-05T11:04:50.562449Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:50.562449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.04581","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":"2026-07-05T11:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgoEMWL4Zyr+aWH2C+vq1zpOXvZzBGSAJ9pnGPu0wQFL7XoG3LRf+d9Y3YtwfbNn1XIc/YwkdFfVSO0MBiTZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:13:31.316026Z"},"content_sha256":"da2c2a82fd4e81ce262cc1c908582ce3553bff4c45453dcf29bafd021a9a22e7","schema_version":"1.0","event_id":"sha256:da2c2a82fd4e81ce262cc1c908582ce3553bff4c45453dcf29bafd021a9a22e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QEBPQAPOPWFCYOBWQJIIYLQ3ZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matchings in Corona graph and classical symmetric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Yau Wing Li","submitted_at":"2025-05-07T17:20:38Z","abstract_excerpt":"We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits in Types AIII and CII. Moreover, we prove a conjecture of Can and Ugurlu concerning the non-integrality of the coefficients of the polynomial that interpolates the number of orbits in Type BI."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04581","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.04581/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":"2026-07-05T11:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2G995dM60B9+iaqACYLrRCPlAF0Q9DVgE+YPkEzLwhPWo+gG1SIenwVMi5z8GgC+wBvFiqlqzanHvhLf6EmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:13:31.316532Z"},"content_sha256":"d6e472f8178cd18308902e336864b6f22db4455a1326a152c4f9ab332510feab","schema_version":"1.0","event_id":"sha256:d6e472f8178cd18308902e336864b6f22db4455a1326a152c4f9ab332510feab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/bundle.json","state_url":"https://pith.science/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/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":"2026-08-16T11:13:31Z","links":{"resolver":"https://pith.science/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP","bundle":"https://pith.science/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/bundle.json","state":"https://pith.science/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEBPQAPOPWFCYOBWQJIIYLQ3ZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QEBPQAPOPWFCYOBWQJIIYLQ3ZP","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":"c790d7199aa64c948b84a510ba65192f1e9534d4ea2741bae8f3eea5a6e98e81","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-07T17:20:38Z","title_canon_sha256":"78c32ad38a95edf0d7cc4973c9b9b5cba6aae3e6c506da0272d6f48e2bdab059"},"schema_version":"1.0","source":{"id":"2505.04581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04581","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04581v2","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04581","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"QEBPQAPOPWFC","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"QEBPQAPOPWFCYOBW","created_at":"2026-07-05T11:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"QEBPQAPO","created_at":"2026-07-05T11:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:d6e472f8178cd18308902e336864b6f22db4455a1326a152c4f9ab332510feab","target":"graph","created_at":"2026-07-05T11:04:50Z","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/2505.04581/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an alternative combinatorial parametrization of Borel orbits in classical symmetric varieties using matchings of the Corona graph. As an application, we obtain ultra log-concavity and unimodality for the number of Borel orbits in Types AIII and CII. Moreover, we prove a conjecture of Can and Ugurlu concerning the non-integrality of the coefficients of the polynomial that interpolates the number of orbits in Type BI.","authors_text":"Yau Wing Li","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-07T17:20:38Z","title":"Matchings in Corona graph and classical symmetric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04581","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:da2c2a82fd4e81ce262cc1c908582ce3553bff4c45453dcf29bafd021a9a22e7","target":"record","created_at":"2026-07-05T11:04:50Z","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":"c790d7199aa64c948b84a510ba65192f1e9534d4ea2741bae8f3eea5a6e98e81","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-07T17:20:38Z","title_canon_sha256":"78c32ad38a95edf0d7cc4973c9b9b5cba6aae3e6c506da0272d6f48e2bdab059"},"schema_version":"1.0","source":{"id":"2505.04581","kind":"arxiv","version":2}},"canonical_sha256":"8102f801ee7d8a2c383682508c2e1bcbd627d58ad9b66f231f7d41c87fbbe591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8102f801ee7d8a2c383682508c2e1bcbd627d58ad9b66f231f7d41c87fbbe591","first_computed_at":"2026-07-05T11:04:50.562449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:50.562449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3f2P5CNB0N5nbUuqE1eTl5neywpNIgLrQSsoG61Jj9pLQJY9f1aGid5UaQc5YWLR0aT5RdF7OL8JCv5mBUODQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:50.562849Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.04581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da2c2a82fd4e81ce262cc1c908582ce3553bff4c45453dcf29bafd021a9a22e7","sha256:d6e472f8178cd18308902e336864b6f22db4455a1326a152c4f9ab332510feab"],"state_sha256":"631905c2bb02979ab4792204b1937990fc063e69e6056af52542b1e7537dbacf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMtvyo7PfxHZcqHErxJ+IR8Tt02TaVDjle3Zv6DzNQVj66mOm1idGq6h1QYRmMJbULjmwlU3r6ObGflyKXWBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:13:31.321381Z","bundle_sha256":"91dd4456e5e8214c0b770c5aa027699fd767d2e6e64b53f509216794565c50f9"}}