{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YAOCFNDW5LZNQI6T46GOT2MGAX","short_pith_number":"pith:YAOCFNDW","canonical_record":{"source":{"id":"2204.01973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-05T03:56:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6301dbf83c080e9a1e86cd5e737161736e5558cd9a9ccb1aaed016f3599529fe","abstract_canon_sha256":"03c6746989fce621551e9b8ab3bb423bd3547f9315ebcbfbb17759792231ab5a"},"schema_version":"1.0"},"canonical_sha256":"c01c22b476eaf2d823d3e78ce9e98605dcbaf635e85083abf35cc3b4aaebc139","source":{"kind":"arxiv","id":"2204.01973","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.01973","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"2204.01973v3","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.01973","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"YAOCFNDW5LZN","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_16","alias_value":"YAOCFNDW5LZNQI6T","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_8","alias_value":"YAOCFNDW","created_at":"2026-07-05T04:38:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YAOCFNDW5LZNQI6T46GOT2MGAX","target":"record","payload":{"canonical_record":{"source":{"id":"2204.01973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-05T03:56:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6301dbf83c080e9a1e86cd5e737161736e5558cd9a9ccb1aaed016f3599529fe","abstract_canon_sha256":"03c6746989fce621551e9b8ab3bb423bd3547f9315ebcbfbb17759792231ab5a"},"schema_version":"1.0"},"canonical_sha256":"c01c22b476eaf2d823d3e78ce9e98605dcbaf635e85083abf35cc3b4aaebc139","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:24.443993Z","signature_b64":"YGKaT6uh/h8fNbU3gka+5Y+ZhNWNwcyLQMoVMyKpn47W3fOuHx87yUDI5BRSg4at4cYgPs46qfx4sRRKZ7LoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01c22b476eaf2d823d3e78ce9e98605dcbaf635e85083abf35cc3b4aaebc139","last_reissued_at":"2026-07-05T04:38:24.443653Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:24.443653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.01973","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":"2026-07-05T04:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ntbw4hzlKUokjm8hWNirAOwxQqE9fVI+R8pb9fhW3WgTKnNAvPojrKh++zW4zQOXIZKZSW95/OcLW6vtNT5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:50:01.634311Z"},"content_sha256":"25dc77867597dea5046d56bc24499e37de12339cf7adf96d7926d3518449261a","schema_version":"1.0","event_id":"sha256:25dc77867597dea5046d56bc24499e37de12339cf7adf96d7926d3518449261a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YAOCFNDW5LZNQI6T46GOT2MGAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"M2-branes and plane partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Tadashi Okazaki","submitted_at":"2022-04-05T03:56:39Z","abstract_excerpt":"There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry $\\mathbb{C}^2$ probed by a stack of $N$ M2-branes and plane partitions of trace $N$. We give combinatorial expressions of the indices which count the local operators parametrizing $\\mathbb{C}^2/\\mathbb{Z}_k$ probed by $N$ M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large $N$ limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.01973","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/2204.01973/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":"2026-07-05T04:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z9LfOjuu+25gnmKtaHjoiEcdlpi3RZm3SiytptHaXYtRGlhgARHi4yY3vjwHjZf2K4+vkzN2rdoc1GW2FfgZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:50:01.635111Z"},"content_sha256":"b8e0fcb8787fc7bae03c0b3cdd5bcbba6f077778e7ec19753a7d811ec6f07c9c","schema_version":"1.0","event_id":"sha256:b8e0fcb8787fc7bae03c0b3cdd5bcbba6f077778e7ec19753a7d811ec6f07c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/bundle.json","state_url":"https://pith.science/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/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":"2026-08-04T10:50:01Z","links":{"resolver":"https://pith.science/pith/YAOCFNDW5LZNQI6T46GOT2MGAX","bundle":"https://pith.science/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/bundle.json","state":"https://pith.science/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAOCFNDW5LZNQI6T46GOT2MGAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YAOCFNDW5LZNQI6T46GOT2MGAX","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":"03c6746989fce621551e9b8ab3bb423bd3547f9315ebcbfbb17759792231ab5a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-05T03:56:39Z","title_canon_sha256":"6301dbf83c080e9a1e86cd5e737161736e5558cd9a9ccb1aaed016f3599529fe"},"schema_version":"1.0","source":{"id":"2204.01973","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.01973","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"2204.01973v3","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.01973","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"YAOCFNDW5LZN","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_16","alias_value":"YAOCFNDW5LZNQI6T","created_at":"2026-07-05T04:38:24Z"},{"alias_kind":"pith_short_8","alias_value":"YAOCFNDW","created_at":"2026-07-05T04:38:24Z"}],"graph_snapshots":[{"event_id":"sha256:b8e0fcb8787fc7bae03c0b3cdd5bcbba6f077778e7ec19753a7d811ec6f07c9c","target":"graph","created_at":"2026-07-05T04:38:24Z","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/2204.01973/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry $\\mathbb{C}^2$ probed by a stack of $N$ M2-branes and plane partitions of trace $N$. We give combinatorial expressions of the indices which count the local operators parametrizing $\\mathbb{C}^2/\\mathbb{Z}_k$ probed by $N$ M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large $N$ limit.","authors_text":"Tadashi Okazaki","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-05T03:56:39Z","title":"M2-branes and plane partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.01973","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":"sha256:25dc77867597dea5046d56bc24499e37de12339cf7adf96d7926d3518449261a","target":"record","created_at":"2026-07-05T04:38:24Z","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":"03c6746989fce621551e9b8ab3bb423bd3547f9315ebcbfbb17759792231ab5a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-05T03:56:39Z","title_canon_sha256":"6301dbf83c080e9a1e86cd5e737161736e5558cd9a9ccb1aaed016f3599529fe"},"schema_version":"1.0","source":{"id":"2204.01973","kind":"arxiv","version":3}},"canonical_sha256":"c01c22b476eaf2d823d3e78ce9e98605dcbaf635e85083abf35cc3b4aaebc139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c01c22b476eaf2d823d3e78ce9e98605dcbaf635e85083abf35cc3b4aaebc139","first_computed_at":"2026-07-05T04:38:24.443653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:24.443653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YGKaT6uh/h8fNbU3gka+5Y+ZhNWNwcyLQMoVMyKpn47W3fOuHx87yUDI5BRSg4at4cYgPs46qfx4sRRKZ7LoBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:24.443993Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.01973","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25dc77867597dea5046d56bc24499e37de12339cf7adf96d7926d3518449261a","sha256:b8e0fcb8787fc7bae03c0b3cdd5bcbba6f077778e7ec19753a7d811ec6f07c9c"],"state_sha256":"401877bedab25e71e7e1c44e3f200c6d4230e28abc734202b2fef127bbd03f40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7Wf+cr+epPsZXp2LSrVlMwrsi2UABYvJBW7HF8WhCjeRN556bv17b3wK4np0lQ3hyBwpoQz0GWKGxBhtBYLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:50:01.640436Z","bundle_sha256":"82bd67b5d82a7712b8a00923cb781095dfbfa1d8be2cb4fbc0472ea1e26c829d"}}