{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7G46GZAA2GL3G4SJQT7DXQTUTQ","short_pith_number":"pith:7G46GZAA","canonical_record":{"source":{"id":"1502.04393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-02-15T23:53:58Z","cross_cats_sorted":[],"title_canon_sha256":"c038fe8ef3d4e74c954c4878804932815c8866d094017a21ac4bf7435280d6b1","abstract_canon_sha256":"fb09889e30d208a344ae279a3f33dc052ac6b1c5a05ebc5be55b54d8547f2ac3"},"schema_version":"1.0"},"canonical_sha256":"f9b9e36400d197b3724984fe3bc2749c0dd05a3ff37943a6e9222cc3d579e8df","source":{"kind":"arxiv","id":"1502.04393","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04393","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04393v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04393","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"7G46GZAA2GL3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7G46GZAA2GL3G4SJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7G46GZAA","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7G46GZAA2GL3G4SJQT7DXQTUTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-02-15T23:53:58Z","cross_cats_sorted":[],"title_canon_sha256":"c038fe8ef3d4e74c954c4878804932815c8866d094017a21ac4bf7435280d6b1","abstract_canon_sha256":"fb09889e30d208a344ae279a3f33dc052ac6b1c5a05ebc5be55b54d8547f2ac3"},"schema_version":"1.0"},"canonical_sha256":"f9b9e36400d197b3724984fe3bc2749c0dd05a3ff37943a6e9222cc3d579e8df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.852369Z","signature_b64":"3U7L4KE2RL+A85k5WPzkmyaV3p4UBllp8hmpaVSrDPpOjHVtgqnkE575Lh/op0Knp3330EVyfD4D2ItX/blRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9b9e36400d197b3724984fe3bc2749c0dd05a3ff37943a6e9222cc3d579e8df","last_reissued_at":"2026-05-18T02:26:59.851847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.851847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04393","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VivC2z5QJC4zxv8hIBl21iNcxjcRCQlWEO7jm6/zY4vK2UE1RBeflZfExpLQxXBpBHG8ZFv/zXUcBYfzdFD8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:10:21.651498Z"},"content_sha256":"7f46c1d9d1a52ddf157ce493e5f47703e46cd26751253fad52e7997c870fdf54","schema_version":"1.0","event_id":"sha256:7f46c1d9d1a52ddf157ce493e5f47703e46cd26751253fad52e7997c870fdf54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7G46GZAA2GL3G4SJQT7DXQTUTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution Functionals 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":"2015-02-15T23:53:58Z","abstract_excerpt":"The current article completes our investigation of the hard-particle interaction by determining their distribution functionals. Beginning with a short review of the perturbation expansion of the free-energy functional, we derive two representations of the correlation functionals in rooted and unrooted Mayer diagrams, which are related by a functional derivative. This map allows to transfer the mathematical methods, developed previously for unrooted diagrams, to the current representation in rooted graphs. Translating then the Mayer to Ree-Hoover diagrams and determining their automorphism grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04393","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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gVrmSZyYxQCpQCpFdVQtMnKNV9Wa8UAj3qP/idtEObS7EXdzJ3VtZr6Y3x8Z3O4obp4xloEM8AgewDyWwwzAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:10:21.652083Z"},"content_sha256":"0348cb68d206d1b1e0cec4ca8515e258628c8fddfbad251e2ad2085f74d5436c","schema_version":"1.0","event_id":"sha256:0348cb68d206d1b1e0cec4ca8515e258628c8fddfbad251e2ad2085f74d5436c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/bundle.json","state_url":"https://pith.science/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/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":"2026-06-24T23:10:21Z","links":{"resolver":"https://pith.science/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ","bundle":"https://pith.science/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/bundle.json","state":"https://pith.science/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7G46GZAA2GL3G4SJQT7DXQTUTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7G46GZAA2GL3G4SJQT7DXQTUTQ","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":"fb09889e30d208a344ae279a3f33dc052ac6b1c5a05ebc5be55b54d8547f2ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-02-15T23:53:58Z","title_canon_sha256":"c038fe8ef3d4e74c954c4878804932815c8866d094017a21ac4bf7435280d6b1"},"schema_version":"1.0","source":{"id":"1502.04393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04393","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04393v1","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04393","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"7G46GZAA2GL3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7G46GZAA2GL3G4SJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7G46GZAA","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:0348cb68d206d1b1e0cec4ca8515e258628c8fddfbad251e2ad2085f74d5436c","target":"graph","created_at":"2026-05-18T02:26:59Z","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":"The current article completes our investigation of the hard-particle interaction by determining their distribution functionals. Beginning with a short review of the perturbation expansion of the free-energy functional, we derive two representations of the correlation functionals in rooted and unrooted Mayer diagrams, which are related by a functional derivative. This map allows to transfer the mathematical methods, developed previously for unrooted diagrams, to the current representation in rooted graphs. Translating then the Mayer to Ree-Hoover diagrams and determining their automorphism grou","authors_text":"Stephan Korden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-02-15T23:53:58Z","title":"Distribution Functionals for Hard Particles in N Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04393","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":"sha256:7f46c1d9d1a52ddf157ce493e5f47703e46cd26751253fad52e7997c870fdf54","target":"record","created_at":"2026-05-18T02:26:59Z","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":"fb09889e30d208a344ae279a3f33dc052ac6b1c5a05ebc5be55b54d8547f2ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-02-15T23:53:58Z","title_canon_sha256":"c038fe8ef3d4e74c954c4878804932815c8866d094017a21ac4bf7435280d6b1"},"schema_version":"1.0","source":{"id":"1502.04393","kind":"arxiv","version":1}},"canonical_sha256":"f9b9e36400d197b3724984fe3bc2749c0dd05a3ff37943a6e9222cc3d579e8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9b9e36400d197b3724984fe3bc2749c0dd05a3ff37943a6e9222cc3d579e8df","first_computed_at":"2026-05-18T02:26:59.851847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.851847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3U7L4KE2RL+A85k5WPzkmyaV3p4UBllp8hmpaVSrDPpOjHVtgqnkE575Lh/op0Knp3330EVyfD4D2ItX/blRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.852369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f46c1d9d1a52ddf157ce493e5f47703e46cd26751253fad52e7997c870fdf54","sha256:0348cb68d206d1b1e0cec4ca8515e258628c8fddfbad251e2ad2085f74d5436c"],"state_sha256":"40005e4ded4fcbdd92ca8935023a76b11469d8106f9ec8c2922399395c56f44a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wwkkuqeee5eMGJ9BHkdSJJYKz3EtGM5uCE96nV31C2mYbTrvfvaLfyznd7pa0TDV+pSLm1/obmLD9xj33FR0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:10:21.654368Z","bundle_sha256":"2b67586b605ec85cf874bd90905cbf612fcc60e0cb517b8f01bfd0bd557d5dba"}}