{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BKR3CDV3ZI4PMTGYR7YUVBZTJL","short_pith_number":"pith:BKR3CDV3","canonical_record":{"source":{"id":"2606.22123","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2026-06-20T16:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"335a26cb3f619e96b6808c79fcf0301f83ba2604453e7e16aa34721c338bdffd","abstract_canon_sha256":"d5c22c5e9a88b05a925c7cf633eab276dfd617ebcc0f94857e4d4435e3098c5d"},"schema_version":"1.0"},"canonical_sha256":"0aa3b10ebbca38f64cd88ff14a87334af09bc6a3330540f820586a2363210af9","source":{"kind":"arxiv","id":"2606.22123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22123","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22123v1","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22123","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_12","alias_value":"BKR3CDV3ZI4P","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_16","alias_value":"BKR3CDV3ZI4PMTGY","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_8","alias_value":"BKR3CDV3","created_at":"2026-06-23T02:13:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BKR3CDV3ZI4PMTGYR7YUVBZTJL","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22123","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2026-06-20T16:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"335a26cb3f619e96b6808c79fcf0301f83ba2604453e7e16aa34721c338bdffd","abstract_canon_sha256":"d5c22c5e9a88b05a925c7cf633eab276dfd617ebcc0f94857e4d4435e3098c5d"},"schema_version":"1.0"},"canonical_sha256":"0aa3b10ebbca38f64cd88ff14a87334af09bc6a3330540f820586a2363210af9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:28.893346Z","signature_b64":"acrdqbymVztm8nKR9axrRDo+Pr2bLVAFqCX0Zn4tWKi8hKdBLHJXAPvVPGXgXOI7EFwTAm0Fc/MWyAt9x+BfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aa3b10ebbca38f64cd88ff14a87334af09bc6a3330540f820586a2363210af9","last_reissued_at":"2026-06-23T02:13:28.892919Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:28.892919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22123","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":"2026-06-23T02:13:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pr9Pb6KggfIF686lMukNn+3XSCETy8xB1kmBSDPJYocpOdft0shTdHOC/Yi1uPf+lSs4C2v9OF2Q1hlquYmbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:46:06.459944Z"},"content_sha256":"8604b21cd5674cbbe34862af49bb3a13ad3f5c3c8804bc58691cd02980286873","schema_version":"1.0","event_id":"sha256:8604b21cd5674cbbe34862af49bb3a13ad3f5c3c8804bc58691cd02980286873"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BKR3CDV3ZI4PMTGYR7YUVBZTJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enhanced approach to calculation of cluster integrals for lattice models of matter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"M. V. Ushcats, S. Yu. Ushcats","submitted_at":"2026-06-20T16:05:01Z","abstract_excerpt":"The study is devoted to enhancing the existing techniques of calculating Mayer's expansion cluster integrals for lattice models of matter. Two important optimizations are proposed: simplifying the calculation of the integrand at each integration point and reducing the number of such integration points due to eliminating physically identical configurations. Based on those optimizations, new data on high-order cluster integrals are obtained for a number of 2D and 3D lattice models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22123","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/2606.22123/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":"2026-06-23T02:13:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qet9JdtkzFqkSdaC+G4ZHXUK+iYMSwgb6zh10FYbJ5vs0Hx9Z6yMaQFhzh1BcLb0b4Ud6je5CPfcGJOZICvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:46:06.460313Z"},"content_sha256":"247fb70633fe62fd4590e7a6e5628a905cf0db2d9aa982a0ccb0597dd3010ca5","schema_version":"1.0","event_id":"sha256:247fb70633fe62fd4590e7a6e5628a905cf0db2d9aa982a0ccb0597dd3010ca5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/bundle.json","state_url":"https://pith.science/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/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":"2026-06-29T20:46:06Z","links":{"resolver":"https://pith.science/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL","bundle":"https://pith.science/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/bundle.json","state":"https://pith.science/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BKR3CDV3ZI4PMTGYR7YUVBZTJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BKR3CDV3ZI4PMTGYR7YUVBZTJL","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":"d5c22c5e9a88b05a925c7cf633eab276dfd617ebcc0f94857e4d4435e3098c5d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2026-06-20T16:05:01Z","title_canon_sha256":"335a26cb3f619e96b6808c79fcf0301f83ba2604453e7e16aa34721c338bdffd"},"schema_version":"1.0","source":{"id":"2606.22123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22123","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22123v1","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22123","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_12","alias_value":"BKR3CDV3ZI4P","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_16","alias_value":"BKR3CDV3ZI4PMTGY","created_at":"2026-06-23T02:13:28Z"},{"alias_kind":"pith_short_8","alias_value":"BKR3CDV3","created_at":"2026-06-23T02:13:28Z"}],"graph_snapshots":[{"event_id":"sha256:247fb70633fe62fd4590e7a6e5628a905cf0db2d9aa982a0ccb0597dd3010ca5","target":"graph","created_at":"2026-06-23T02:13:28Z","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/2606.22123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The study is devoted to enhancing the existing techniques of calculating Mayer's expansion cluster integrals for lattice models of matter. Two important optimizations are proposed: simplifying the calculation of the integrand at each integration point and reducing the number of such integration points due to eliminating physically identical configurations. Based on those optimizations, new data on high-order cluster integrals are obtained for a number of 2D and 3D lattice models.","authors_text":"M. V. Ushcats, S. Yu. Ushcats","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2026-06-20T16:05:01Z","title":"Enhanced approach to calculation of cluster integrals for lattice models of matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22123","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":"sha256:8604b21cd5674cbbe34862af49bb3a13ad3f5c3c8804bc58691cd02980286873","target":"record","created_at":"2026-06-23T02:13:28Z","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":"d5c22c5e9a88b05a925c7cf633eab276dfd617ebcc0f94857e4d4435e3098c5d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2026-06-20T16:05:01Z","title_canon_sha256":"335a26cb3f619e96b6808c79fcf0301f83ba2604453e7e16aa34721c338bdffd"},"schema_version":"1.0","source":{"id":"2606.22123","kind":"arxiv","version":1}},"canonical_sha256":"0aa3b10ebbca38f64cd88ff14a87334af09bc6a3330540f820586a2363210af9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aa3b10ebbca38f64cd88ff14a87334af09bc6a3330540f820586a2363210af9","first_computed_at":"2026-06-23T02:13:28.892919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:28.892919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"acrdqbymVztm8nKR9axrRDo+Pr2bLVAFqCX0Zn4tWKi8hKdBLHJXAPvVPGXgXOI7EFwTAm0Fc/MWyAt9x+BfAw==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:28.893346Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8604b21cd5674cbbe34862af49bb3a13ad3f5c3c8804bc58691cd02980286873","sha256:247fb70633fe62fd4590e7a6e5628a905cf0db2d9aa982a0ccb0597dd3010ca5"],"state_sha256":"488c8f93f4625495da3abef4d34252865a3eee8133471bf12df16fa2572fe83d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7exqFgsJy+CgDG8hYgr78Est7gjqBdMpilYwSBjytDL8ZieT6ETtXu9hJeJJ3g+s72vArsccloXfnmLFDzsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T20:46:06.462256Z","bundle_sha256":"3bae2e0d94ccc283ecc6a8c0346d185223eb3ca6830247b63ac795d4307a1ece"}}