{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NGTDPESUXED77EVLF6YFTS3VLD","short_pith_number":"pith:NGTDPESU","canonical_record":{"source":{"id":"1904.02754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T19:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"f0d743c623f45e37099df442caf305cde78bd52e48f3cd2ba912237cf9ddb5b1","abstract_canon_sha256":"ef12d72eebd0ecde219b9f212044b188c6c201740a58f3c6036569fa33706396"},"schema_version":"1.0"},"canonical_sha256":"69a6379254b907ff92ab2fb059cb7558f2a94ddd1808c231f3e1811a4124b26a","source":{"kind":"arxiv","id":"1904.02754","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02754","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02754v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02754","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"NGTDPESUXED7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NGTDPESUXED77EVL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NGTDPESU","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NGTDPESUXED77EVLF6YFTS3VLD","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T19:10:01Z","cross_cats_sorted":[],"title_canon_sha256":"f0d743c623f45e37099df442caf305cde78bd52e48f3cd2ba912237cf9ddb5b1","abstract_canon_sha256":"ef12d72eebd0ecde219b9f212044b188c6c201740a58f3c6036569fa33706396"},"schema_version":"1.0"},"canonical_sha256":"69a6379254b907ff92ab2fb059cb7558f2a94ddd1808c231f3e1811a4124b26a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:19.783217Z","signature_b64":"UK4PGPZlohNmmUgI7JUbUf4BwPxNSNAUh3PLxhwkSKtXui7qOtq0NY8L+a67FbU6ydW6V/1d6RaobfaUOT6uDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69a6379254b907ff92ab2fb059cb7558f2a94ddd1808c231f3e1811a4124b26a","last_reissued_at":"2026-05-17T23:49:19.782637Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:19.782637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02754","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gG+hlzDj5zKeJU7Ra1q052E8UNSbFrUJCgkDmk/F0l6M8ZgOYY7iJW1EK2rnff6E6DUnlDlgX1dM5ZrEk1cJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:17:59.556171Z"},"content_sha256":"47fff9dcfc8440b67130b1e07134dcdb22e9fbeb512636b53e4430facd47855d","schema_version":"1.0","event_id":"sha256:47fff9dcfc8440b67130b1e07134dcdb22e9fbeb512636b53e4430facd47855d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NGTDPESUXED77EVLF6YFTS3VLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minuscule reverse plane partitions via quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Garver, Hugh Thomas, Rebecca Patrias","submitted_at":"2019-04-04T19:10:01Z","abstract_excerpt":"The Hillman--Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape $\\lambda$ and reverse plane partitions of $\\lambda$. We use the tools of quiver representations to generalize Hillman--Grassl in type $A$ and to define an analogue in all minuscule types. This is an extended abstract prepared for FPSAC 2019 based on arXiv:1812.08345, emphasizing its combinatorial aspects."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02754","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZv/EyfHZOgAHsZ8hyI1AdxZoAHXJ23rcZ+eWsk19VxWKqIjIF0F8hE+8SruRE6k7VXThLgZDjQtIP9z2pPBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:17:59.556753Z"},"content_sha256":"335d62a213b97af0ce223bea11754127ec4ea9e8b6caca45e9b522e240077694","schema_version":"1.0","event_id":"sha256:335d62a213b97af0ce223bea11754127ec4ea9e8b6caca45e9b522e240077694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGTDPESUXED77EVLF6YFTS3VLD/bundle.json","state_url":"https://pith.science/pith/NGTDPESUXED77EVLF6YFTS3VLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGTDPESUXED77EVLF6YFTS3VLD/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":"2026-06-04T22:17:59Z","links":{"resolver":"https://pith.science/pith/NGTDPESUXED77EVLF6YFTS3VLD","bundle":"https://pith.science/pith/NGTDPESUXED77EVLF6YFTS3VLD/bundle.json","state":"https://pith.science/pith/NGTDPESUXED77EVLF6YFTS3VLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGTDPESUXED77EVLF6YFTS3VLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NGTDPESUXED77EVLF6YFTS3VLD","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":"ef12d72eebd0ecde219b9f212044b188c6c201740a58f3c6036569fa33706396","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T19:10:01Z","title_canon_sha256":"f0d743c623f45e37099df442caf305cde78bd52e48f3cd2ba912237cf9ddb5b1"},"schema_version":"1.0","source":{"id":"1904.02754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02754","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02754v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02754","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"NGTDPESUXED7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NGTDPESUXED77EVL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NGTDPESU","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:335d62a213b97af0ce223bea11754127ec4ea9e8b6caca45e9b522e240077694","target":"graph","created_at":"2026-05-17T23:49:19Z","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 Hillman--Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape $\\lambda$ and reverse plane partitions of $\\lambda$. We use the tools of quiver representations to generalize Hillman--Grassl in type $A$ and to define an analogue in all minuscule types. This is an extended abstract prepared for FPSAC 2019 based on arXiv:1812.08345, emphasizing its combinatorial aspects.","authors_text":"Alexander Garver, Hugh Thomas, Rebecca Patrias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T19:10:01Z","title":"Minuscule reverse plane partitions via quiver representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02754","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":"sha256:47fff9dcfc8440b67130b1e07134dcdb22e9fbeb512636b53e4430facd47855d","target":"record","created_at":"2026-05-17T23:49:19Z","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":"ef12d72eebd0ecde219b9f212044b188c6c201740a58f3c6036569fa33706396","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T19:10:01Z","title_canon_sha256":"f0d743c623f45e37099df442caf305cde78bd52e48f3cd2ba912237cf9ddb5b1"},"schema_version":"1.0","source":{"id":"1904.02754","kind":"arxiv","version":1}},"canonical_sha256":"69a6379254b907ff92ab2fb059cb7558f2a94ddd1808c231f3e1811a4124b26a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69a6379254b907ff92ab2fb059cb7558f2a94ddd1808c231f3e1811a4124b26a","first_computed_at":"2026-05-17T23:49:19.782637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:19.782637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UK4PGPZlohNmmUgI7JUbUf4BwPxNSNAUh3PLxhwkSKtXui7qOtq0NY8L+a67FbU6ydW6V/1d6RaobfaUOT6uDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:19.783217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47fff9dcfc8440b67130b1e07134dcdb22e9fbeb512636b53e4430facd47855d","sha256:335d62a213b97af0ce223bea11754127ec4ea9e8b6caca45e9b522e240077694"],"state_sha256":"e7689f54e554fffe4be4f05f905e8441c979700b08cc6985069475915e48e22e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRrceiGW6JrvCXKvwugA74E9aVkw5/ccJFZVexT+pG6leYawlnG8XBSTGpfwVxJpg3Wkx3kdgWoAt0luHlgWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:17:59.559782Z","bundle_sha256":"284b33de7a08fee1c36c8f97be2cd8609a698a0d15ba57d08fd84583f896b274"}}