{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OGXVBI3MNGGGRLXAKX5KDVDVSU","short_pith_number":"pith:OGXVBI3M","canonical_record":{"source":{"id":"1704.02701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-10T04:00:36Z","cross_cats_sorted":[],"title_canon_sha256":"0ffb840c9693b9b7fe72e30838725e7d567bb0735f65085724d78b9cd9e9af74","abstract_canon_sha256":"9443885438a52083bbd307881a1bd1ce9c3400cda52d4c8d22de289148c8d23f"},"schema_version":"1.0"},"canonical_sha256":"71af50a36c698c68aee055faa1d4759511c72e77e3a567773b997a117cc06021","source":{"kind":"arxiv","id":"1704.02701","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02701","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02701v1","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02701","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"pith_short_12","alias_value":"OGXVBI3MNGGG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OGXVBI3MNGGGRLXA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OGXVBI3M","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OGXVBI3MNGGGRLXAKX5KDVDVSU","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-10T04:00:36Z","cross_cats_sorted":[],"title_canon_sha256":"0ffb840c9693b9b7fe72e30838725e7d567bb0735f65085724d78b9cd9e9af74","abstract_canon_sha256":"9443885438a52083bbd307881a1bd1ce9c3400cda52d4c8d22de289148c8d23f"},"schema_version":"1.0"},"canonical_sha256":"71af50a36c698c68aee055faa1d4759511c72e77e3a567773b997a117cc06021","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:44.677786Z","signature_b64":"l5/Rg/F9GIrJD3eEG4rHOI7DQZ08TrtoNFQqzUT5/pOvB8xRXvraOy3w1MHpOAJ7LqY1zSUcX3qFY6hzPZ1qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71af50a36c698c68aee055faa1d4759511c72e77e3a567773b997a117cc06021","last_reissued_at":"2026-05-18T00:46:44.677152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:44.677152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02701","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBltVGbq9kL+iViSSLV6kyJODQFiTRud7Dt+0EXbD49nEVQjx5Sx6aU/YggIDqjkTY9ImJu8KJPzGzhuzQfjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:52:08.023962Z"},"content_sha256":"c505d2a3c0e29f6787163a667d546f8063f9bdebc6e0bb0c6d56d3c0113f1529","schema_version":"1.0","event_id":"sha256:c505d2a3c0e29f6787163a667d546f8063f9bdebc6e0bb0c6d56d3c0113f1529"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OGXVBI3MNGGGRLXAKX5KDVDVSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volumes of generalized Chan-Robbins-Yuen polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jang Soo Kim, Karola M\\'esz\\'aros, Sylvie Corteel","submitted_at":"2017-04-10T04:00:36Z","abstract_excerpt":"The normalized volume of the Chan-Robbins-Yuen polytope ($CRY_n$) is the product of consecutive Catalan numbers. The polytope $CRY_n$ has captivated combinatorial audiences for over a decade, as there is no combinatorial proof for its volume formula. In their quest to understand $CRY_n$ better, the third author and Morales introduced two natural generalizations of it and conjectured that their volumes are certain powers of $2$ multiplied by a product of consecutive Catalan numbers. Zeilberger proved one of these conjectures. In this paper we present proofs of both conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02701","kind":"arxiv","version":1},"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":"2026-05-18T00:46:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KiT62SJuN9Pr4E1dzuoffkDmJl772dG+0cARCoUS5fD5+5qh1tyj/39lGwJ0toUQ9vlhVqSieG7fh1FLcLg1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:52:08.024422Z"},"content_sha256":"e95139eb9f64a5dc20fbf0cdf7bc26c56f24131af45a4b350012175371212998","schema_version":"1.0","event_id":"sha256:e95139eb9f64a5dc20fbf0cdf7bc26c56f24131af45a4b350012175371212998"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/bundle.json","state_url":"https://pith.science/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/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":"2026-05-26T15:52:08Z","links":{"resolver":"https://pith.science/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU","bundle":"https://pith.science/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/bundle.json","state":"https://pith.science/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGXVBI3MNGGGRLXAKX5KDVDVSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OGXVBI3MNGGGRLXAKX5KDVDVSU","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":"9443885438a52083bbd307881a1bd1ce9c3400cda52d4c8d22de289148c8d23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-10T04:00:36Z","title_canon_sha256":"0ffb840c9693b9b7fe72e30838725e7d567bb0735f65085724d78b9cd9e9af74"},"schema_version":"1.0","source":{"id":"1704.02701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02701","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02701v1","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02701","created_at":"2026-05-18T00:46:44Z"},{"alias_kind":"pith_short_12","alias_value":"OGXVBI3MNGGG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OGXVBI3MNGGGRLXA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OGXVBI3M","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:e95139eb9f64a5dc20fbf0cdf7bc26c56f24131af45a4b350012175371212998","target":"graph","created_at":"2026-05-18T00:46:44Z","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":"The normalized volume of the Chan-Robbins-Yuen polytope ($CRY_n$) is the product of consecutive Catalan numbers. The polytope $CRY_n$ has captivated combinatorial audiences for over a decade, as there is no combinatorial proof for its volume formula. In their quest to understand $CRY_n$ better, the third author and Morales introduced two natural generalizations of it and conjectured that their volumes are certain powers of $2$ multiplied by a product of consecutive Catalan numbers. Zeilberger proved one of these conjectures. In this paper we present proofs of both conjectures.","authors_text":"Jang Soo Kim, Karola M\\'esz\\'aros, Sylvie Corteel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-10T04:00:36Z","title":"Volumes of generalized Chan-Robbins-Yuen polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02701","kind":"arxiv","version":1},"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:c505d2a3c0e29f6787163a667d546f8063f9bdebc6e0bb0c6d56d3c0113f1529","target":"record","created_at":"2026-05-18T00:46:44Z","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":"9443885438a52083bbd307881a1bd1ce9c3400cda52d4c8d22de289148c8d23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-10T04:00:36Z","title_canon_sha256":"0ffb840c9693b9b7fe72e30838725e7d567bb0735f65085724d78b9cd9e9af74"},"schema_version":"1.0","source":{"id":"1704.02701","kind":"arxiv","version":1}},"canonical_sha256":"71af50a36c698c68aee055faa1d4759511c72e77e3a567773b997a117cc06021","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71af50a36c698c68aee055faa1d4759511c72e77e3a567773b997a117cc06021","first_computed_at":"2026-05-18T00:46:44.677152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:44.677152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l5/Rg/F9GIrJD3eEG4rHOI7DQZ08TrtoNFQqzUT5/pOvB8xRXvraOy3w1MHpOAJ7LqY1zSUcX3qFY6hzPZ1qBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:44.677786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c505d2a3c0e29f6787163a667d546f8063f9bdebc6e0bb0c6d56d3c0113f1529","sha256:e95139eb9f64a5dc20fbf0cdf7bc26c56f24131af45a4b350012175371212998"],"state_sha256":"4036c7fbb73bd49af3e722598836fa10a1d595db5937b7440736ffb0409eaf63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQCBkcXMYE7AH+s9kHGjeqWBoZU48TOSoXbZmYqdBW61nDmg7lVilSEyH0Jz3DToWaGKWDwrQ3oXtgCS3dBpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:52:08.027263Z","bundle_sha256":"494e4f653d920bb7a3549f92767bdf8071f3b7342b73110595e9ab2fe5cb876a"}}