{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:KZ4Q56NZBR52JIMHP54KRAQRWW","short_pith_number":"pith:KZ4Q56NZ","canonical_record":{"source":{"id":"math/9801059","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1998-01-13T05:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"be12586fe80041c7f5087e338ee378c9a17d87210fa1ab0e276e3901ed4c3a43","abstract_canon_sha256":"af6a7c2703cced0cf6f05f50c75a5b5f272e8139a8c719c747b4c7e3fdb6052c"},"schema_version":"1.0"},"canonical_sha256":"56790ef9b90c7ba4a1877f78a88211b59e35a0ebaa669029f656df2e80cbf4e1","source":{"kind":"arxiv","id":"math/9801059","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9801059","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/9801059v3","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801059","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"KZ4Q56NZBR52","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_16","alias_value":"KZ4Q56NZBR52JIMH","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_8","alias_value":"KZ4Q56NZ","created_at":"2026-07-04T14:40:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:KZ4Q56NZBR52JIMHP54KRAQRWW","target":"record","payload":{"canonical_record":{"source":{"id":"math/9801059","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1998-01-13T05:16:02Z","cross_cats_sorted":[],"title_canon_sha256":"be12586fe80041c7f5087e338ee378c9a17d87210fa1ab0e276e3901ed4c3a43","abstract_canon_sha256":"af6a7c2703cced0cf6f05f50c75a5b5f272e8139a8c719c747b4c7e3fdb6052c"},"schema_version":"1.0"},"canonical_sha256":"56790ef9b90c7ba4a1877f78a88211b59e35a0ebaa669029f656df2e80cbf4e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:25.126231Z","signature_b64":"/Xa+CS4fTcgN7nhUArU5L1KFI/E9OWey8Y/wfthe+WkyW4WMjNTdHFR5jDNjjnVlnlX5N/vW3LD5e6BZxVoECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56790ef9b90c7ba4a1877f78a88211b59e35a0ebaa669029f656df2e80cbf4e1","last_reissued_at":"2026-07-04T14:40:25.125811Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:25.125811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9801059","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":"2026-07-04T14:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9adZX8eS4PF1w+89f7zfwcJjNKOTf0BLwdAyw2lC7RdCKOB4MczpHNEY+mzcO/Y8U3ZuznKlRVuAbRqHIm1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:40:39.066858Z"},"content_sha256":"d581ea79d46b80ba32ed8366901fcb57e283c4e765c883d4cfc276b32ed72123","schema_version":"1.0","event_id":"sha256:d581ea79d46b80ba32ed8366901fcb57e283c4e765c883d4cfc276b32ed72123"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:KZ4Q56NZBR52JIMHP54KRAQRWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The shape of a typical boxed plane partition","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Cohn, James Propp, Michael Larsen","submitted_at":"1998-01-13T05:16:02Z","abstract_excerpt":"Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams fit inside the box). Equivalently, we describe the distribution of the three different orientations of lozenges in a random lozenge tiling of a large hexagon. We prove a generalization of the classical formula of MacMahon for the number of plane partitions in a box; for each of the possible ways in which the tilings of a region can behave when restricted to c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801059","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/math/9801059/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":"2026-07-04T14:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XKsVshlfMmA9wAAgHdEuNoPd4przt+Noa9A5SDUTgBl4VrEPA7ua8fw/yrLdPYEsXD8GZLRJ+aL8Ngazk0IhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:40:39.067650Z"},"content_sha256":"9410ef14c8d45cf7febcb5d92e14b1a710586b533de6b7fa30524c6231f08e12","schema_version":"1.0","event_id":"sha256:9410ef14c8d45cf7febcb5d92e14b1a710586b533de6b7fa30524c6231f08e12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/bundle.json","state_url":"https://pith.science/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/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":"2026-08-16T13:40:39Z","links":{"resolver":"https://pith.science/pith/KZ4Q56NZBR52JIMHP54KRAQRWW","bundle":"https://pith.science/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/bundle.json","state":"https://pith.science/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZ4Q56NZBR52JIMHP54KRAQRWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:KZ4Q56NZBR52JIMHP54KRAQRWW","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":"af6a7c2703cced0cf6f05f50c75a5b5f272e8139a8c719c747b4c7e3fdb6052c","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1998-01-13T05:16:02Z","title_canon_sha256":"be12586fe80041c7f5087e338ee378c9a17d87210fa1ab0e276e3901ed4c3a43"},"schema_version":"1.0","source":{"id":"math/9801059","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9801059","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/9801059v3","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801059","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"KZ4Q56NZBR52","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_16","alias_value":"KZ4Q56NZBR52JIMH","created_at":"2026-07-04T14:40:25Z"},{"alias_kind":"pith_short_8","alias_value":"KZ4Q56NZ","created_at":"2026-07-04T14:40:25Z"}],"graph_snapshots":[{"event_id":"sha256:9410ef14c8d45cf7febcb5d92e14b1a710586b533de6b7fa30524c6231f08e12","target":"graph","created_at":"2026-07-04T14:40:25Z","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/math/9801059/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams fit inside the box). Equivalently, we describe the distribution of the three different orientations of lozenges in a random lozenge tiling of a large hexagon. We prove a generalization of the classical formula of MacMahon for the number of plane partitions in a box; for each of the possible ways in which the tilings of a region can behave when restricted to c","authors_text":"Henry Cohn, James Propp, Michael Larsen","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"1998-01-13T05:16:02Z","title":"The shape of a typical boxed plane partition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801059","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:d581ea79d46b80ba32ed8366901fcb57e283c4e765c883d4cfc276b32ed72123","target":"record","created_at":"2026-07-04T14:40:25Z","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":"af6a7c2703cced0cf6f05f50c75a5b5f272e8139a8c719c747b4c7e3fdb6052c","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1998-01-13T05:16:02Z","title_canon_sha256":"be12586fe80041c7f5087e338ee378c9a17d87210fa1ab0e276e3901ed4c3a43"},"schema_version":"1.0","source":{"id":"math/9801059","kind":"arxiv","version":3}},"canonical_sha256":"56790ef9b90c7ba4a1877f78a88211b59e35a0ebaa669029f656df2e80cbf4e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56790ef9b90c7ba4a1877f78a88211b59e35a0ebaa669029f656df2e80cbf4e1","first_computed_at":"2026-07-04T14:40:25.125811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:25.125811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Xa+CS4fTcgN7nhUArU5L1KFI/E9OWey8Y/wfthe+WkyW4WMjNTdHFR5jDNjjnVlnlX5N/vW3LD5e6BZxVoECg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:25.126231Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9801059","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d581ea79d46b80ba32ed8366901fcb57e283c4e765c883d4cfc276b32ed72123","sha256:9410ef14c8d45cf7febcb5d92e14b1a710586b533de6b7fa30524c6231f08e12"],"state_sha256":"e25e63dcb42134a2b2de166c8c0a49fa7641f3388e59427135e0e3f3aafb8dfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INyDGxdhuAohwOZAeBdkwxVV0eN8nqps+253JxnoGtXnrsx5XWGXd8WHFgXeZO/N/dOxRlbUFTYB/GrzQDRgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:40:39.072775Z","bundle_sha256":"1309e16aa20e64c0bcdbe5a5c1ac8b367d2c95fdbd26f9d28a1d683337cda583"}}