{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QE4A33GOA2HW37WDIZO5Z3HUTN","short_pith_number":"pith:QE4A33GO","canonical_record":{"source":{"id":"2412.13561","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-18T07:22:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7bd99e8f482bf8e1d1596d4ddc34b30b11cdc570314af755771d8f047303e140","abstract_canon_sha256":"e4d8e8e508a6a2dfb403e55f323521d33618934a26f3eb7610a172fd330f0951"},"schema_version":"1.0"},"canonical_sha256":"81380decce068f6dfec3465ddcecf49b474648609246ebe73e96884d5c120d69","source":{"kind":"arxiv","id":"2412.13561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.13561","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2412.13561v1","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13561","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"QE4A33GOA2HW","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"QE4A33GOA2HW37WD","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"QE4A33GO","created_at":"2026-07-05T10:05:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QE4A33GOA2HW37WDIZO5Z3HUTN","target":"record","payload":{"canonical_record":{"source":{"id":"2412.13561","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-18T07:22:38Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7bd99e8f482bf8e1d1596d4ddc34b30b11cdc570314af755771d8f047303e140","abstract_canon_sha256":"e4d8e8e508a6a2dfb403e55f323521d33618934a26f3eb7610a172fd330f0951"},"schema_version":"1.0"},"canonical_sha256":"81380decce068f6dfec3465ddcecf49b474648609246ebe73e96884d5c120d69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:05:47.392763Z","signature_b64":"Gl+e0oE+xd8jCjJ5i2KWpIg3eKs/eIgWme9fAJg0TSEY0A6OHIMbp+gwl6yr3zjoCf2M3gK9N2f1fejI6ZOnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81380decce068f6dfec3465ddcecf49b474648609246ebe73e96884d5c120d69","last_reissued_at":"2026-07-05T10:05:47.392232Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:05:47.392232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.13561","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":"2026-07-05T10:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6kO0QcNJCHkKQLDrCcXbq7Em74DHlbLsZTLcL1QnRS4Fa/d47w7UCSaEM+krcVhj0U8MImB05FwGPV0IupBhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:17:46.325391Z"},"content_sha256":"7cccd35c5459674694dfab2cf11c14195b89c917b280af5a71dbce7650fa687f","schema_version":"1.0","event_id":"sha256:7cccd35c5459674694dfab2cf11c14195b89c917b280af5a71dbce7650fa687f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QE4A33GOA2HW37WDIZO5Z3HUTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher rank elliptic partition functions and multisymmetric elliptic functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Allan John Gerrard, Kazumitsu Sakai, Kohei Motegi","submitted_at":"2024-12-18T07:22:38Z","abstract_excerpt":"We introduce and investigate a class of $\\mathfrak{gl}_{M+1}$ partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and determine the explicit forms, for each of the rational, trigonometric and elliptic versions. The resulting multisymmetric functions can be regarded as extensions of the rational, trigonometric and elliptic weight functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13561","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.13561/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":"2026-07-05T10:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufD831kQ54yrfPhtmiTKKkWaulHmjfkv3uH8plbJwwiPMPSC2MDcV9m0rkP97JVW0vltbjHUQkmQ3Tya460WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:17:46.325930Z"},"content_sha256":"ca010e91ed38a16b1d46c0722170502304cc0789cf5959f32fdcaaefed44bd24","schema_version":"1.0","event_id":"sha256:ca010e91ed38a16b1d46c0722170502304cc0789cf5959f32fdcaaefed44bd24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/bundle.json","state_url":"https://pith.science/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/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":"2026-08-21T00:17:46Z","links":{"resolver":"https://pith.science/pith/QE4A33GOA2HW37WDIZO5Z3HUTN","bundle":"https://pith.science/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/bundle.json","state":"https://pith.science/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QE4A33GOA2HW37WDIZO5Z3HUTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QE4A33GOA2HW37WDIZO5Z3HUTN","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":"e4d8e8e508a6a2dfb403e55f323521d33618934a26f3eb7610a172fd330f0951","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-18T07:22:38Z","title_canon_sha256":"7bd99e8f482bf8e1d1596d4ddc34b30b11cdc570314af755771d8f047303e140"},"schema_version":"1.0","source":{"id":"2412.13561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.13561","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2412.13561v1","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13561","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"QE4A33GOA2HW","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"QE4A33GOA2HW37WD","created_at":"2026-07-05T10:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"QE4A33GO","created_at":"2026-07-05T10:05:47Z"}],"graph_snapshots":[{"event_id":"sha256:ca010e91ed38a16b1d46c0722170502304cc0789cf5959f32fdcaaefed44bd24","target":"graph","created_at":"2026-07-05T10:05:47Z","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/2412.13561/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and investigate a class of $\\mathfrak{gl}_{M+1}$ partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and determine the explicit forms, for each of the rational, trigonometric and elliptic versions. The resulting multisymmetric functions can be regarded as extensions of the rational, trigonometric and elliptic weight functions.","authors_text":"Allan John Gerrard, Kazumitsu Sakai, Kohei Motegi","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-18T07:22:38Z","title":"Higher rank elliptic partition functions and multisymmetric elliptic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13561","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":"sha256:7cccd35c5459674694dfab2cf11c14195b89c917b280af5a71dbce7650fa687f","target":"record","created_at":"2026-07-05T10:05:47Z","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":"e4d8e8e508a6a2dfb403e55f323521d33618934a26f3eb7610a172fd330f0951","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-12-18T07:22:38Z","title_canon_sha256":"7bd99e8f482bf8e1d1596d4ddc34b30b11cdc570314af755771d8f047303e140"},"schema_version":"1.0","source":{"id":"2412.13561","kind":"arxiv","version":1}},"canonical_sha256":"81380decce068f6dfec3465ddcecf49b474648609246ebe73e96884d5c120d69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81380decce068f6dfec3465ddcecf49b474648609246ebe73e96884d5c120d69","first_computed_at":"2026-07-05T10:05:47.392232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:05:47.392232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gl+e0oE+xd8jCjJ5i2KWpIg3eKs/eIgWme9fAJg0TSEY0A6OHIMbp+gwl6yr3zjoCf2M3gK9N2f1fejI6ZOnAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:05:47.392763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.13561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cccd35c5459674694dfab2cf11c14195b89c917b280af5a71dbce7650fa687f","sha256:ca010e91ed38a16b1d46c0722170502304cc0789cf5959f32fdcaaefed44bd24"],"state_sha256":"330b4e46e9fd2e52a289b5dcf8a6f7857be59f73d078e428157b7612449c25d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t61fOmA3fGiDeCnE+Z9TIdXZB+mpuW/GJwnWzi3H0ZnE861lwIZPHz83cscMQT/8En69/ZLxfCtQyn21cmHLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T00:17:46.329548Z","bundle_sha256":"dd73fe876369fa077810aaa12ade1279e5b0a897e4be6b58fe7c74b33b118e92"}}