{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NVTUXOZZL7YOOHLXBMJ634FWS5","short_pith_number":"pith:NVTUXOZZ","canonical_record":{"source":{"id":"2307.01052","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2023-07-03T14:32:37Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"f48bb604d61755bcb9b094b393793e2c24b212a4e03cd6309730575e3d56154e","abstract_canon_sha256":"7c352e2c1b5d64fbe36790d0ec2d12b1935a3b510907a44d64f53cffc43a9b95"},"schema_version":"1.0"},"canonical_sha256":"6d674bbb395ff0e71d770b13edf0b6976d59c12a571eab64c8ff44719c874ae3","source":{"kind":"arxiv","id":"2307.01052","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.01052","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"2307.01052v2","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.01052","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"NVTUXOZZL7YO","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"NVTUXOZZL7YOOHLX","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"NVTUXOZZ","created_at":"2026-07-05T06:33:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NVTUXOZZL7YOOHLXBMJ634FWS5","target":"record","payload":{"canonical_record":{"source":{"id":"2307.01052","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2023-07-03T14:32:37Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"f48bb604d61755bcb9b094b393793e2c24b212a4e03cd6309730575e3d56154e","abstract_canon_sha256":"7c352e2c1b5d64fbe36790d0ec2d12b1935a3b510907a44d64f53cffc43a9b95"},"schema_version":"1.0"},"canonical_sha256":"6d674bbb395ff0e71d770b13edf0b6976d59c12a571eab64c8ff44719c874ae3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:46.885192Z","signature_b64":"wTOfwaH0kZHZNnTvqPUm/yCQ8fT2AnwVgdu5hvHoxC8V0o0/qUn6ftyVf9OFUC59XLDS/FBpMjRTMnYjKfRJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d674bbb395ff0e71d770b13edf0b6976d59c12a571eab64c8ff44719c874ae3","last_reissued_at":"2026-07-05T06:33:46.884758Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:46.884758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.01052","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":"2026-07-05T06:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ddHiEdHhHhXkB5vcUK2O9KGmM+8DGR0nIVCvjO9E5fReN0Q9JBEo0+8Ga98ScviDWUzbn6afPt8eD/n4OPG2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:09:51.747309Z"},"content_sha256":"6888027a41c650e6c40e126e30d4393640eb14d2b30e3a5a259cb64589ae704b","schema_version":"1.0","event_id":"sha256:6888027a41c650e6c40e126e30d4393640eb14d2b30e3a5a259cb64589ae704b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NVTUXOZZL7YOOHLXBMJ634FWS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Theorems and Phase Transitions in the Tensor Curie-Weiss Potts Model","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Sanchayan Bhowal, Somabha Mukherjee","submitted_at":"2023-07-03T14:32:37Z","abstract_excerpt":"In this paper, we derive results about the limiting distribution of the empirical magnetization vector and the maximum likelihood (ML) estimates of the natural parameters in the tensor Curie-Weiss Potts model. Our results reveal surprisingly new phase transition phenomena including the existence of a smooth curve in the interior of the parameter plane on which the magnetization vector and the ML estimates have mixture limiting distributions, the latter comprising of both continuous and discrete components, and a surprising superefficiency phenomenon of the ML estimates, which stipulates an $N^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.01052","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.01052/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":"2026-07-05T06:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7eaussBhCfOAhprkywiB456Ub10Vi1t8GCv+mf6jnVuhHhHIywU1mPLzb7eGgFpqfP7Oo7E2JxHsTnUuaZrsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:09:51.747702Z"},"content_sha256":"95d8c4e2c0a0e9b6130e8d5b1b0fe46e6cc512176939c767b57d0c81098bdb7d","schema_version":"1.0","event_id":"sha256:95d8c4e2c0a0e9b6130e8d5b1b0fe46e6cc512176939c767b57d0c81098bdb7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/bundle.json","state_url":"https://pith.science/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/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":"2026-08-13T07:09:51Z","links":{"resolver":"https://pith.science/pith/NVTUXOZZL7YOOHLXBMJ634FWS5","bundle":"https://pith.science/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/bundle.json","state":"https://pith.science/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVTUXOZZL7YOOHLXBMJ634FWS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NVTUXOZZL7YOOHLXBMJ634FWS5","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":"7c352e2c1b5d64fbe36790d0ec2d12b1935a3b510907a44d64f53cffc43a9b95","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2023-07-03T14:32:37Z","title_canon_sha256":"f48bb604d61755bcb9b094b393793e2c24b212a4e03cd6309730575e3d56154e"},"schema_version":"1.0","source":{"id":"2307.01052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.01052","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"2307.01052v2","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.01052","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"NVTUXOZZL7YO","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"NVTUXOZZL7YOOHLX","created_at":"2026-07-05T06:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"NVTUXOZZ","created_at":"2026-07-05T06:33:46Z"}],"graph_snapshots":[{"event_id":"sha256:95d8c4e2c0a0e9b6130e8d5b1b0fe46e6cc512176939c767b57d0c81098bdb7d","target":"graph","created_at":"2026-07-05T06:33:46Z","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/2307.01052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive results about the limiting distribution of the empirical magnetization vector and the maximum likelihood (ML) estimates of the natural parameters in the tensor Curie-Weiss Potts model. Our results reveal surprisingly new phase transition phenomena including the existence of a smooth curve in the interior of the parameter plane on which the magnetization vector and the ML estimates have mixture limiting distributions, the latter comprising of both continuous and discrete components, and a surprising superefficiency phenomenon of the ML estimates, which stipulates an $N^","authors_text":"Sanchayan Bhowal, Somabha Mukherjee","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2023-07-03T14:32:37Z","title":"Limit Theorems and Phase Transitions in the Tensor Curie-Weiss Potts Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.01052","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":"sha256:6888027a41c650e6c40e126e30d4393640eb14d2b30e3a5a259cb64589ae704b","target":"record","created_at":"2026-07-05T06:33:46Z","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":"7c352e2c1b5d64fbe36790d0ec2d12b1935a3b510907a44d64f53cffc43a9b95","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2023-07-03T14:32:37Z","title_canon_sha256":"f48bb604d61755bcb9b094b393793e2c24b212a4e03cd6309730575e3d56154e"},"schema_version":"1.0","source":{"id":"2307.01052","kind":"arxiv","version":2}},"canonical_sha256":"6d674bbb395ff0e71d770b13edf0b6976d59c12a571eab64c8ff44719c874ae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d674bbb395ff0e71d770b13edf0b6976d59c12a571eab64c8ff44719c874ae3","first_computed_at":"2026-07-05T06:33:46.884758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:46.884758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wTOfwaH0kZHZNnTvqPUm/yCQ8fT2AnwVgdu5hvHoxC8V0o0/qUn6ftyVf9OFUC59XLDS/FBpMjRTMnYjKfRJDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:46.885192Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.01052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6888027a41c650e6c40e126e30d4393640eb14d2b30e3a5a259cb64589ae704b","sha256:95d8c4e2c0a0e9b6130e8d5b1b0fe46e6cc512176939c767b57d0c81098bdb7d"],"state_sha256":"416332b3547479c231fabc833dbb6a6e4d944c52952190c609a3893770a7ce0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdCOeg25+oYrVshLpG9tq3Co9EL1lkvzzNxmiU3IsjqnKqk9BacoWQX1OWQM7USX3NnC8jSyDQxYYDrUuvTtDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T07:09:51.750809Z","bundle_sha256":"baf2c3a56eea607e4ed41490ac408c85a20605a4260455aa5aabd61baf287682"}}