{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PJ33HQ7ZG2WHV3HMXF6JEWOSJG","short_pith_number":"pith:PJ33HQ7Z","canonical_record":{"source":{"id":"2606.23039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-22T08:47:27Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"682ad2a8b1d0a14a128054d078298c6bf9169e3e0f7a3a8fcef43f958ea21c43","abstract_canon_sha256":"b3d836423b4db39dd20b3de01532853b193dc350c99ee27c2df2c975a6cc757a"},"schema_version":"1.0"},"canonical_sha256":"7a77b3c3f936ac7aececb97c9259d249b660f8174e95e24259f15d447d54e755","source":{"kind":"arxiv","id":"2606.23039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23039","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23039v1","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23039","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"PJ33HQ7ZG2WH","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_16","alias_value":"PJ33HQ7ZG2WHV3HM","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_8","alias_value":"PJ33HQ7Z","created_at":"2026-06-23T03:14:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PJ33HQ7ZG2WHV3HMXF6JEWOSJG","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-22T08:47:27Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"682ad2a8b1d0a14a128054d078298c6bf9169e3e0f7a3a8fcef43f958ea21c43","abstract_canon_sha256":"b3d836423b4db39dd20b3de01532853b193dc350c99ee27c2df2c975a6cc757a"},"schema_version":"1.0"},"canonical_sha256":"7a77b3c3f936ac7aececb97c9259d249b660f8174e95e24259f15d447d54e755","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:07.410069Z","signature_b64":"1Z/gfPdi3PJmXlFx4scOAd65hSLd7W+B1ftkt0Znfkp5jYMk199dY4t2+66vM7CvQYpsYLl/3aUnZpiUXMsIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a77b3c3f936ac7aececb97c9259d249b660f8174e95e24259f15d447d54e755","last_reissued_at":"2026-06-23T03:14:07.409688Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:07.409688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23039","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":"2026-06-23T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rwk0w3FRLxclDiVEedD7XO3olMhUGYKY7JoGZ3NkLz9L26OtpElniVVtMwGEWy2SXLlzfymfCkNETtp9DbW/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:51:45.412248Z"},"content_sha256":"d851ba198fed269618555f68ab86e67b983e07bdf68d5c7bb2ae2663f1256114","schema_version":"1.0","event_id":"sha256:d851ba198fed269618555f68ab86e67b983e07bdf68d5c7bb2ae2663f1256114"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PJ33HQ7ZG2WHV3HMXF6JEWOSJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Physics of Planar Carroll Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Fei Huang, Lo\\\"ic Marsot","submitted_at":"2026-06-22T08:47:27Z","abstract_excerpt":"In this article, we define and study the statistical physics of planar Carrollian systems. While it has been shown recently that, for general dimensions, the Carroll limit of Poincar\\'e statistical physics typically does not converge, we show that thanks to the central extensions of the Carroll algebra in the plane, and by considering systems with angular momentum, there exists a well defined notion of planar Carrollian statistical physics.\n  Using Souriau's geometric thermodynamics, we compute the partition function for particles on a uniformly rotating disc, and show that rotation is inevita"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23039","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/2606.23039/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":"2026-06-23T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz8D3JCD28U7qxHNuhhShMB2rGjMB8Jg12EmZ3WoubrygImUQl9mi/czbkLdBgQ78V6IOti6luEHAr/xkPcwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:51:45.412635Z"},"content_sha256":"5ab20505094d57a373d3ea76e31cd30df2b0f4d114e62a0b24d24ceb512fb35f","schema_version":"1.0","event_id":"sha256:5ab20505094d57a373d3ea76e31cd30df2b0f4d114e62a0b24d24ceb512fb35f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/bundle.json","state_url":"https://pith.science/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/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":"2026-06-30T09:51:45Z","links":{"resolver":"https://pith.science/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG","bundle":"https://pith.science/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/bundle.json","state":"https://pith.science/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJ33HQ7ZG2WHV3HMXF6JEWOSJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PJ33HQ7ZG2WHV3HMXF6JEWOSJG","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":"b3d836423b4db39dd20b3de01532853b193dc350c99ee27c2df2c975a6cc757a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-22T08:47:27Z","title_canon_sha256":"682ad2a8b1d0a14a128054d078298c6bf9169e3e0f7a3a8fcef43f958ea21c43"},"schema_version":"1.0","source":{"id":"2606.23039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23039","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23039v1","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23039","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"PJ33HQ7ZG2WH","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_16","alias_value":"PJ33HQ7ZG2WHV3HM","created_at":"2026-06-23T03:14:07Z"},{"alias_kind":"pith_short_8","alias_value":"PJ33HQ7Z","created_at":"2026-06-23T03:14:07Z"}],"graph_snapshots":[{"event_id":"sha256:5ab20505094d57a373d3ea76e31cd30df2b0f4d114e62a0b24d24ceb512fb35f","target":"graph","created_at":"2026-06-23T03:14:07Z","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/2606.23039/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we define and study the statistical physics of planar Carrollian systems. While it has been shown recently that, for general dimensions, the Carroll limit of Poincar\\'e statistical physics typically does not converge, we show that thanks to the central extensions of the Carroll algebra in the plane, and by considering systems with angular momentum, there exists a well defined notion of planar Carrollian statistical physics.\n  Using Souriau's geometric thermodynamics, we compute the partition function for particles on a uniformly rotating disc, and show that rotation is inevita","authors_text":"Fei Huang, Lo\\\"ic Marsot","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-22T08:47:27Z","title":"Statistical Physics of Planar Carroll Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23039","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:d851ba198fed269618555f68ab86e67b983e07bdf68d5c7bb2ae2663f1256114","target":"record","created_at":"2026-06-23T03:14:07Z","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":"b3d836423b4db39dd20b3de01532853b193dc350c99ee27c2df2c975a6cc757a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-06-22T08:47:27Z","title_canon_sha256":"682ad2a8b1d0a14a128054d078298c6bf9169e3e0f7a3a8fcef43f958ea21c43"},"schema_version":"1.0","source":{"id":"2606.23039","kind":"arxiv","version":1}},"canonical_sha256":"7a77b3c3f936ac7aececb97c9259d249b660f8174e95e24259f15d447d54e755","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a77b3c3f936ac7aececb97c9259d249b660f8174e95e24259f15d447d54e755","first_computed_at":"2026-06-23T03:14:07.409688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:07.409688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Z/gfPdi3PJmXlFx4scOAd65hSLd7W+B1ftkt0Znfkp5jYMk199dY4t2+66vM7CvQYpsYLl/3aUnZpiUXMsIDw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:07.410069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d851ba198fed269618555f68ab86e67b983e07bdf68d5c7bb2ae2663f1256114","sha256:5ab20505094d57a373d3ea76e31cd30df2b0f4d114e62a0b24d24ceb512fb35f"],"state_sha256":"549ce33f596f9fb65d3ae0c796066eb456b35bf0aa280419662dac7a20ad9980"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2cRYj45GPYA2Gl+DvoMFnaGkO5XG8jHNXnsqNwKXkx5qu/AhG3YWN1LKq/ow8VqQo1KJRqz9sD4YA2Ex9B2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T09:51:45.414554Z","bundle_sha256":"90245fd89b999c98459acb1ac5d216415075f83b37c861072c2068b39985c0f3"}}