{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N63RAUKIEKHNXFNPIQMWL3HAZZ","short_pith_number":"pith:N63RAUKI","canonical_record":{"source":{"id":"1403.2054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-03-09T13:15:18Z","cross_cats_sorted":[],"title_canon_sha256":"2fa534abf89cff336c4ff0ee3da77ed516c86c030889ddeff1a9e20ef921b584","abstract_canon_sha256":"45d03f7ee315303f5451eb3745f6d29d80e2d64d182c80d9907f163dfe9f5dd2"},"schema_version":"1.0"},"canonical_sha256":"6fb7105148228edb95af441965ece0ce7923509f4f1309eeb2f542e8b8cad5c1","source":{"kind":"arxiv","id":"1403.2054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2054","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2054v1","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2054","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"N63RAUKIEKHN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N63RAUKIEKHNXFNP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N63RAUKI","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N63RAUKIEKHNXFNPIQMWL3HAZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-03-09T13:15:18Z","cross_cats_sorted":[],"title_canon_sha256":"2fa534abf89cff336c4ff0ee3da77ed516c86c030889ddeff1a9e20ef921b584","abstract_canon_sha256":"45d03f7ee315303f5451eb3745f6d29d80e2d64d182c80d9907f163dfe9f5dd2"},"schema_version":"1.0"},"canonical_sha256":"6fb7105148228edb95af441965ece0ce7923509f4f1309eeb2f542e8b8cad5c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:11.414529Z","signature_b64":"aCudCOSz/osZYnEbIWcLveKiFsiqewlfS5iAX8qFfuZcj2j86fBfxXbtTfeGHmlkF7p3wmncoqsLsIqRx9Y8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fb7105148228edb95af441965ece0ce7923509f4f1309eeb2f542e8b8cad5c1","last_reissued_at":"2026-05-18T02:04:11.413846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:11.413846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2054","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":"2026-05-18T02:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eEFZhhcz4LlkmZq2/GsY3MSb/2RmP6oM9yZzeuQc9mwgyV7TLAkyMkg1ggI0wLXXzIB10kAAS+infs+InJFxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:33:24.030673Z"},"content_sha256":"d8dd1e832a116e36d417c4f1b37d0ebc4469a6080d84766b497e799fe608c95c","schema_version":"1.0","event_id":"sha256:d8dd1e832a116e36d417c4f1b37d0ebc4469a6080d84766b497e799fe608c95c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N63RAUKIEKHNXFNPIQMWL3HAZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density Functional Theory for Hard Particles in N Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Stephan Korden","submitted_at":"2014-03-09T13:15:18Z","abstract_excerpt":"Recently it has been shown that the heuristic Rosenfeld functional derives from the virial expansion for particles which overlap in one center. Here, we generalize this approach to any number of intersections. Starting from the virial expansion in Ree-Hoover diagrams, it is shown in the first part that each intersection pattern defines exactly one infinite class of diagrams. Determining their automorphism groups, we sum over all its elements and derive a generic functional. The second part proves that this functional factorizes into a convolute of integral kernels for each intersection center."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2054","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":""},"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":"2026-05-18T02:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJVqbDN/bIYIo3Lp7mI69reUbOOd6qnPiVMXDwz3pP4Bu/4/Z+CENZecVAn8YEJtvxIbUwF8P9qrqPwss1IRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:33:24.031016Z"},"content_sha256":"ded661c1fdc48f8559962a19f25b72a521ac7424216d44dc7a2b76c0b21f2c62","schema_version":"1.0","event_id":"sha256:ded661c1fdc48f8559962a19f25b72a521ac7424216d44dc7a2b76c0b21f2c62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/bundle.json","state_url":"https://pith.science/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/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":"2026-06-24T21:33:24Z","links":{"resolver":"https://pith.science/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ","bundle":"https://pith.science/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/bundle.json","state":"https://pith.science/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N63RAUKIEKHNXFNPIQMWL3HAZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N63RAUKIEKHNXFNPIQMWL3HAZZ","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":"45d03f7ee315303f5451eb3745f6d29d80e2d64d182c80d9907f163dfe9f5dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-03-09T13:15:18Z","title_canon_sha256":"2fa534abf89cff336c4ff0ee3da77ed516c86c030889ddeff1a9e20ef921b584"},"schema_version":"1.0","source":{"id":"1403.2054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2054","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2054v1","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2054","created_at":"2026-05-18T02:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"N63RAUKIEKHN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N63RAUKIEKHNXFNP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N63RAUKI","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ded661c1fdc48f8559962a19f25b72a521ac7424216d44dc7a2b76c0b21f2c62","target":"graph","created_at":"2026-05-18T02:04:11Z","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"},"paper":{"abstract_excerpt":"Recently it has been shown that the heuristic Rosenfeld functional derives from the virial expansion for particles which overlap in one center. Here, we generalize this approach to any number of intersections. Starting from the virial expansion in Ree-Hoover diagrams, it is shown in the first part that each intersection pattern defines exactly one infinite class of diagrams. Determining their automorphism groups, we sum over all its elements and derive a generic functional. The second part proves that this functional factorizes into a convolute of integral kernels for each intersection center.","authors_text":"Stephan Korden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-03-09T13:15:18Z","title":"Density Functional Theory for Hard Particles in N Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2054","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:d8dd1e832a116e36d417c4f1b37d0ebc4469a6080d84766b497e799fe608c95c","target":"record","created_at":"2026-05-18T02:04:11Z","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":"45d03f7ee315303f5451eb3745f6d29d80e2d64d182c80d9907f163dfe9f5dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-03-09T13:15:18Z","title_canon_sha256":"2fa534abf89cff336c4ff0ee3da77ed516c86c030889ddeff1a9e20ef921b584"},"schema_version":"1.0","source":{"id":"1403.2054","kind":"arxiv","version":1}},"canonical_sha256":"6fb7105148228edb95af441965ece0ce7923509f4f1309eeb2f542e8b8cad5c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fb7105148228edb95af441965ece0ce7923509f4f1309eeb2f542e8b8cad5c1","first_computed_at":"2026-05-18T02:04:11.413846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:11.413846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aCudCOSz/osZYnEbIWcLveKiFsiqewlfS5iAX8qFfuZcj2j86fBfxXbtTfeGHmlkF7p3wmncoqsLsIqRx9Y8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:11.414529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8dd1e832a116e36d417c4f1b37d0ebc4469a6080d84766b497e799fe608c95c","sha256:ded661c1fdc48f8559962a19f25b72a521ac7424216d44dc7a2b76c0b21f2c62"],"state_sha256":"0658f7554b350d9dc16cae35b2a59ea3703001f5a2e360445e36fbf9bccd7a52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yDy+/rr42tauUhG8rz1VpyNskxjAuX79I7ihn221xgpx4hArqJXFobe+h9tFu3AtWt5c5BUzftLskUPQlth9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:33:24.033019Z","bundle_sha256":"d7d96b999879ce73110d80a57a022af0d30f8dc7b4ef40dc8d8eae90e7e7c1c9"}}