{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FRI5F2X3G3KWJANZTSTLATWY56","short_pith_number":"pith:FRI5F2X3","canonical_record":{"source":{"id":"0905.0679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-05T19:48:34Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"46217b3479fbdf1070b8e349101b8ab3d83c75cf6a1d1950e116f87c90aa02f7","abstract_canon_sha256":"0597afc6ecc0ae8a1dc837be169303aadb4b617e7b711cdac2c49a1b9ce7b395"},"schema_version":"1.0"},"canonical_sha256":"2c51d2eafb36d56481b99ca6b04ed8efb7a95f4f1dc150ccc7c9e1d7c5e847c6","source":{"kind":"arxiv","id":"0905.0679","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0679","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0679v2","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0679","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"FRI5F2X3G3KW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FRI5F2X3G3KWJANZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FRI5F2X3","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FRI5F2X3G3KWJANZTSTLATWY56","target":"record","payload":{"canonical_record":{"source":{"id":"0905.0679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-05T19:48:34Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"46217b3479fbdf1070b8e349101b8ab3d83c75cf6a1d1950e116f87c90aa02f7","abstract_canon_sha256":"0597afc6ecc0ae8a1dc837be169303aadb4b617e7b711cdac2c49a1b9ce7b395"},"schema_version":"1.0"},"canonical_sha256":"2c51d2eafb36d56481b99ca6b04ed8efb7a95f4f1dc150ccc7c9e1d7c5e847c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:17.142245Z","signature_b64":"ptYOpuFrJtegfiWBKplQi+5+0Zyxrb06sJz+M56A+29IFXtoBNVbJp04vh+ZSLYWwF07j/2+/1K7my3Bc71dDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c51d2eafb36d56481b99ca6b04ed8efb7a95f4f1dc150ccc7c9e1d7c5e847c6","last_reissued_at":"2026-05-18T04:15:17.141344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:17.141344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.0679","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":"2026-05-18T04:15:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VepvwUxomeGbf/qalHzumOUdjeMiAcYIbuWBehGNwy77BijCHghNe+n7euDoU6ld8lEN78DTR4vhhXx2NMlZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:49:26.433787Z"},"content_sha256":"418bdfe3ffe6fa2bf1da169638baa578da9dc31ce5c3d43d2730eb1dfc532a8f","schema_version":"1.0","event_id":"sha256:418bdfe3ffe6fa2bf1da169638baa578da9dc31ce5c3d43d2730eb1dfc532a8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FRI5F2X3G3KWJANZTSTLATWY56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"q-Distributions on boxed plane partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alexei Borodin, Eric M. Rains, Vadim Gorin","submitted_at":"2009-05-05T19:48:34Z","abstract_excerpt":"We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of these weights that are related to orthogonal polynomials; they form three two-dimensional families. For distributions from these families we prove two types of results.\n  First, we construct explicit Markov chains that preserve these distributions. In particular, this leads to a relatively simple exact sampling algorithm.\n  Second, we consider a limit when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0679","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":"2026-05-18T04:15:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IyQjRgldVVVliZM+E51PkOr8KORwQ8VDcvUzs8UkV8Dgxv8p7F7Cy5OuRXxzktSXQn3Ew3AbkHWtZfVKj0vKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:49:26.434481Z"},"content_sha256":"c3007629cc946bb0283a120857cd7644c1a4a6697973f8886558295ac0873f7c","schema_version":"1.0","event_id":"sha256:c3007629cc946bb0283a120857cd7644c1a4a6697973f8886558295ac0873f7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRI5F2X3G3KWJANZTSTLATWY56/bundle.json","state_url":"https://pith.science/pith/FRI5F2X3G3KWJANZTSTLATWY56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRI5F2X3G3KWJANZTSTLATWY56/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":"2026-06-07T18:49:26Z","links":{"resolver":"https://pith.science/pith/FRI5F2X3G3KWJANZTSTLATWY56","bundle":"https://pith.science/pith/FRI5F2X3G3KWJANZTSTLATWY56/bundle.json","state":"https://pith.science/pith/FRI5F2X3G3KWJANZTSTLATWY56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRI5F2X3G3KWJANZTSTLATWY56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FRI5F2X3G3KWJANZTSTLATWY56","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":"0597afc6ecc0ae8a1dc837be169303aadb4b617e7b711cdac2c49a1b9ce7b395","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-05T19:48:34Z","title_canon_sha256":"46217b3479fbdf1070b8e349101b8ab3d83c75cf6a1d1950e116f87c90aa02f7"},"schema_version":"1.0","source":{"id":"0905.0679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0679","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0679v2","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0679","created_at":"2026-05-18T04:15:17Z"},{"alias_kind":"pith_short_12","alias_value":"FRI5F2X3G3KW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FRI5F2X3G3KWJANZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FRI5F2X3","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:c3007629cc946bb0283a120857cd7644c1a4a6697973f8886558295ac0873f7c","target":"graph","created_at":"2026-05-18T04:15:17Z","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 introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of these weights that are related to orthogonal polynomials; they form three two-dimensional families. For distributions from these families we prove two types of results.\n  First, we construct explicit Markov chains that preserve these distributions. In particular, this leads to a relatively simple exact sampling algorithm.\n  Second, we consider a limit when ","authors_text":"Alexei Borodin, Eric M. Rains, Vadim Gorin","cross_cats":["math.CO","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-05T19:48:34Z","title":"q-Distributions on boxed plane partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0679","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":"sha256:418bdfe3ffe6fa2bf1da169638baa578da9dc31ce5c3d43d2730eb1dfc532a8f","target":"record","created_at":"2026-05-18T04:15:17Z","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":"0597afc6ecc0ae8a1dc837be169303aadb4b617e7b711cdac2c49a1b9ce7b395","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-05-05T19:48:34Z","title_canon_sha256":"46217b3479fbdf1070b8e349101b8ab3d83c75cf6a1d1950e116f87c90aa02f7"},"schema_version":"1.0","source":{"id":"0905.0679","kind":"arxiv","version":2}},"canonical_sha256":"2c51d2eafb36d56481b99ca6b04ed8efb7a95f4f1dc150ccc7c9e1d7c5e847c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c51d2eafb36d56481b99ca6b04ed8efb7a95f4f1dc150ccc7c9e1d7c5e847c6","first_computed_at":"2026-05-18T04:15:17.141344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:17.141344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptYOpuFrJtegfiWBKplQi+5+0Zyxrb06sJz+M56A+29IFXtoBNVbJp04vh+ZSLYWwF07j/2+/1K7my3Bc71dDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:17.142245Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:418bdfe3ffe6fa2bf1da169638baa578da9dc31ce5c3d43d2730eb1dfc532a8f","sha256:c3007629cc946bb0283a120857cd7644c1a4a6697973f8886558295ac0873f7c"],"state_sha256":"cb1348288b9698266a24f4324bfb62cfcd3c010e8456c193ab6d95c7bdadcdf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+yThQaazA7LqCegngzXTwQRmcUzh6FVrmZQAEO2XkH8grKYnxozfy8z1hqSgd1JHJ+y8BCv5xZIEgJeY4x7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:49:26.438169Z","bundle_sha256":"60fb3a02666373382ad1e9881c1de671dfd8a37d6ba8ddf3eccba2f9cb871d84"}}