{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:SVF3MKBBDYQORHJY6VJZ2YQNGX","short_pith_number":"pith:SVF3MKBB","canonical_record":{"source":{"id":"2312.12398","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T18:33:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c67e434b0278194924017bc22f58616ac94b543db82d48dafe432428c3dbb1e4","abstract_canon_sha256":"5d085e2b912c394cf6ba858dd9b96c9d4e6a52430924a8630c0d43f5c0e8fca7"},"schema_version":"1.0"},"canonical_sha256":"954bb628211e20e89d38f5539d620d35f019aaf4d7028ea85fd5bc3bf358fb02","source":{"kind":"arxiv","id":"2312.12398","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12398","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12398v3","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12398","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"SVF3MKBBDYQO","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_16","alias_value":"SVF3MKBBDYQORHJY","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_8","alias_value":"SVF3MKBB","created_at":"2026-07-05T08:39:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:SVF3MKBBDYQORHJY6VJZ2YQNGX","target":"record","payload":{"canonical_record":{"source":{"id":"2312.12398","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T18:33:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c67e434b0278194924017bc22f58616ac94b543db82d48dafe432428c3dbb1e4","abstract_canon_sha256":"5d085e2b912c394cf6ba858dd9b96c9d4e6a52430924a8630c0d43f5c0e8fca7"},"schema_version":"1.0"},"canonical_sha256":"954bb628211e20e89d38f5539d620d35f019aaf4d7028ea85fd5bc3bf358fb02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:29.879130Z","signature_b64":"7KkS/WXt6v4EXv4C98bII+6kD3UFVPn7oVtgPD6dE8sI7wRZZtjwQNDSZvY7oHiDzBtx6KOHjpom9kVS6UHlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"954bb628211e20e89d38f5539d620d35f019aaf4d7028ea85fd5bc3bf358fb02","last_reissued_at":"2026-07-05T08:39:29.878683Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:29.878683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.12398","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":"2026-07-05T08:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6RcGNXlgAYFNKlbyNmMzMIa61ZogLJcSryS9+pEvc/2A1uM1d24tsCUofA+qytD73ryyGvEmTy8qprKnLTvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T06:03:30.793727Z"},"content_sha256":"8869e48e6ec7baaef0265d0128ba121dc63013b7b9a745f85ac31366c9ce3d30","schema_version":"1.0","event_id":"sha256:8869e48e6ec7baaef0265d0128ba121dc63013b7b9a745f85ac31366c9ce3d30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:SVF3MKBBDYQORHJY6VJZ2YQNGX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauged permutation invariant matrix quantum mechanics: Partition functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"hep-th","authors_text":"Denjoe O'Connor, Sanjaye Ramgoolam","submitted_at":"2023-12-19T18:33:31Z","abstract_excerpt":"The Hilbert spaces of matrix quantum mechanical systems with $N \\times N$ matrix degrees of freedom $ X $ have been analysed recently in terms of $S_N$ symmetric group elements $U$ acting as $X \\rightarrow U X U^T $. Solvable models have been constructed uncovering partition algebras as hidden symmetries of these systems. The solvable models include an 11-dimensional space of matrix harmonic oscillators, the simplest of which is the standard matrix harmonic oscillator with $U(N)$ symmetry. The permutation symmetry is realised as gauge symmetry in a path integral formulation in a companion pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12398","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/2312.12398/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":"2026-07-05T08:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPeuRDDSXRsO6pnDomgtCXjgjA9PAX7Z7vJyb3b8QIE9vc+O0d8C3lrTWpRJX6RJW6HKaw1wQpcsu2SlDV7LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T06:03:30.794238Z"},"content_sha256":"b80dcf18ac34e8465e3723c08836a271181b449f34060399d62b28c873862567","schema_version":"1.0","event_id":"sha256:b80dcf18ac34e8465e3723c08836a271181b449f34060399d62b28c873862567"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/bundle.json","state_url":"https://pith.science/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/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":"2026-08-18T06:03:30Z","links":{"resolver":"https://pith.science/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX","bundle":"https://pith.science/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/bundle.json","state":"https://pith.science/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVF3MKBBDYQORHJY6VJZ2YQNGX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SVF3MKBBDYQORHJY6VJZ2YQNGX","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":"5d085e2b912c394cf6ba858dd9b96c9d4e6a52430924a8630c0d43f5c0e8fca7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T18:33:31Z","title_canon_sha256":"c67e434b0278194924017bc22f58616ac94b543db82d48dafe432428c3dbb1e4"},"schema_version":"1.0","source":{"id":"2312.12398","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.12398","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"2312.12398v3","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12398","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"SVF3MKBBDYQO","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_16","alias_value":"SVF3MKBBDYQORHJY","created_at":"2026-07-05T08:39:29Z"},{"alias_kind":"pith_short_8","alias_value":"SVF3MKBB","created_at":"2026-07-05T08:39:29Z"}],"graph_snapshots":[{"event_id":"sha256:b80dcf18ac34e8465e3723c08836a271181b449f34060399d62b28c873862567","target":"graph","created_at":"2026-07-05T08:39:29Z","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/2312.12398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Hilbert spaces of matrix quantum mechanical systems with $N \\times N$ matrix degrees of freedom $ X $ have been analysed recently in terms of $S_N$ symmetric group elements $U$ acting as $X \\rightarrow U X U^T $. Solvable models have been constructed uncovering partition algebras as hidden symmetries of these systems. The solvable models include an 11-dimensional space of matrix harmonic oscillators, the simplest of which is the standard matrix harmonic oscillator with $U(N)$ symmetry. The permutation symmetry is realised as gauge symmetry in a path integral formulation in a companion pape","authors_text":"Denjoe O'Connor, Sanjaye Ramgoolam","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T18:33:31Z","title":"Gauged permutation invariant matrix quantum mechanics: Partition functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12398","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":"sha256:8869e48e6ec7baaef0265d0128ba121dc63013b7b9a745f85ac31366c9ce3d30","target":"record","created_at":"2026-07-05T08:39:29Z","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":"5d085e2b912c394cf6ba858dd9b96c9d4e6a52430924a8630c0d43f5c0e8fca7","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-19T18:33:31Z","title_canon_sha256":"c67e434b0278194924017bc22f58616ac94b543db82d48dafe432428c3dbb1e4"},"schema_version":"1.0","source":{"id":"2312.12398","kind":"arxiv","version":3}},"canonical_sha256":"954bb628211e20e89d38f5539d620d35f019aaf4d7028ea85fd5bc3bf358fb02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"954bb628211e20e89d38f5539d620d35f019aaf4d7028ea85fd5bc3bf358fb02","first_computed_at":"2026-07-05T08:39:29.878683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:29.878683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KkS/WXt6v4EXv4C98bII+6kD3UFVPn7oVtgPD6dE8sI7wRZZtjwQNDSZvY7oHiDzBtx6KOHjpom9kVS6UHlDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:29.879130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.12398","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8869e48e6ec7baaef0265d0128ba121dc63013b7b9a745f85ac31366c9ce3d30","sha256:b80dcf18ac34e8465e3723c08836a271181b449f34060399d62b28c873862567"],"state_sha256":"ec2f2e75c89b8c865e2cde7760ef1326b9993e73d12ad6ad060460e531522740"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BSXrNY9BGUZqu9wVaWvlMwBfHcK4XWittB0Qg1hnbwzbCafSxmf7hHiVLQbOocqwDjNxK7U6mugO+/0teXEEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T06:03:30.798113Z","bundle_sha256":"892ac26d9e853e8846c335c06b0d85cd4b06f36c50908b058950e6497446aebd"}}