{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZQ46ADPBFOIZGIPFNHKRS3MABO","short_pith_number":"pith:ZQ46ADPB","canonical_record":{"source":{"id":"0901.2064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-14T16:58:55Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"901377d74dd81025353ba112a0bdff214d94cbe00010b556520bd9b1a8d189d1","abstract_canon_sha256":"fcfae24afbd5fbbe31ce3b398faeca604e70633fece24b09bb05b88304cd2e76"},"schema_version":"1.0"},"canonical_sha256":"cc39e00de12b919321e569d5196d800ba8039880df37b482066390fa9bda584f","source":{"kind":"arxiv","id":"0901.2064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.2064","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"0901.2064v1","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2064","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ46ADPBFOIZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ46ADPBFOIZGIPF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ46ADPB","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZQ46ADPBFOIZGIPFNHKRS3MABO","target":"record","payload":{"canonical_record":{"source":{"id":"0901.2064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-14T16:58:55Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"901377d74dd81025353ba112a0bdff214d94cbe00010b556520bd9b1a8d189d1","abstract_canon_sha256":"fcfae24afbd5fbbe31ce3b398faeca604e70633fece24b09bb05b88304cd2e76"},"schema_version":"1.0"},"canonical_sha256":"cc39e00de12b919321e569d5196d800ba8039880df37b482066390fa9bda584f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:57.454954Z","signature_b64":"WsKtnXboReqFgF8rU9sXGE6C41uh0oSvtqtZfMhnHG9tcvFA6t0faB/vzUSIbM5XHuv0TYjhP9Aj0rHLTzGeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc39e00de12b919321e569d5196d800ba8039880df37b482066390fa9bda584f","last_reissued_at":"2026-05-18T02:14:57.454409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:57.454409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.2064","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":"2026-05-18T02:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+U/+F5U7nVmcXvZANAVj5sdpsBM7BG36DuaV/CZCFn9+cSvFjt9U7hWvx6v5+nbRS67yLgAxqitYuKHtQ8AjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:51:50.607990Z"},"content_sha256":"49bd5ad21533fdfc6f06c4b32b903b6ce378436ef97061260e69592b41e4d6da","schema_version":"1.0","event_id":"sha256:49bd5ad21533fdfc6f06c4b32b903b6ce378436ef97061260e69592b41e4d6da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZQ46ADPBFOIZGIPFNHKRS3MABO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The smooth cut-off Hierarchical Reference Theory of fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Alberto Parola, Davide Pini, Luciano Reatto","submitted_at":"2009-01-14T16:58:55Z","abstract_excerpt":"We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation. A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT. Then, the theory is applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self consistent Ornstein-Zernike approximation is discussed. The asymptotic properties, close to the critical point are investigated and compared to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2064","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":"2026-05-18T02:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6yZKUetKI1bLynDPKiZjQzeNXxTdlrFhURF/kcpA2bxj4NRcJP16NeFCQkzpSRCqJcTW6Rd8J2IOUpxhvZfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:51:50.608355Z"},"content_sha256":"9c9497c74f6877738b2dd026b503a6e962a51a486750411b32a92fa4583da43d","schema_version":"1.0","event_id":"sha256:9c9497c74f6877738b2dd026b503a6e962a51a486750411b32a92fa4583da43d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/bundle.json","state_url":"https://pith.science/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/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":"2026-06-02T16:51:50Z","links":{"resolver":"https://pith.science/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO","bundle":"https://pith.science/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/bundle.json","state":"https://pith.science/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQ46ADPBFOIZGIPFNHKRS3MABO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZQ46ADPBFOIZGIPFNHKRS3MABO","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":"fcfae24afbd5fbbe31ce3b398faeca604e70633fece24b09bb05b88304cd2e76","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-14T16:58:55Z","title_canon_sha256":"901377d74dd81025353ba112a0bdff214d94cbe00010b556520bd9b1a8d189d1"},"schema_version":"1.0","source":{"id":"0901.2064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.2064","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"0901.2064v1","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2064","created_at":"2026-05-18T02:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZQ46ADPBFOIZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZQ46ADPBFOIZGIPF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZQ46ADPB","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:9c9497c74f6877738b2dd026b503a6e962a51a486750411b32a92fa4583da43d","target":"graph","created_at":"2026-05-18T02:14:57Z","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":"We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation. A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT. Then, the theory is applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self consistent Ornstein-Zernike approximation is discussed. The asymptotic properties, close to the critical point are investigated and compared to t","authors_text":"Alberto Parola, Davide Pini, Luciano Reatto","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-14T16:58:55Z","title":"The smooth cut-off Hierarchical Reference Theory of fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2064","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":"sha256:49bd5ad21533fdfc6f06c4b32b903b6ce378436ef97061260e69592b41e4d6da","target":"record","created_at":"2026-05-18T02:14:57Z","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":"fcfae24afbd5fbbe31ce3b398faeca604e70633fece24b09bb05b88304cd2e76","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2009-01-14T16:58:55Z","title_canon_sha256":"901377d74dd81025353ba112a0bdff214d94cbe00010b556520bd9b1a8d189d1"},"schema_version":"1.0","source":{"id":"0901.2064","kind":"arxiv","version":1}},"canonical_sha256":"cc39e00de12b919321e569d5196d800ba8039880df37b482066390fa9bda584f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc39e00de12b919321e569d5196d800ba8039880df37b482066390fa9bda584f","first_computed_at":"2026-05-18T02:14:57.454409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:57.454409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WsKtnXboReqFgF8rU9sXGE6C41uh0oSvtqtZfMhnHG9tcvFA6t0faB/vzUSIbM5XHuv0TYjhP9Aj0rHLTzGeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:57.454954Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.2064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49bd5ad21533fdfc6f06c4b32b903b6ce378436ef97061260e69592b41e4d6da","sha256:9c9497c74f6877738b2dd026b503a6e962a51a486750411b32a92fa4583da43d"],"state_sha256":"80144c2ccd7bef2f36229f2b805151a1f3a0302ca2340fa64c7d34a6e6069039"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psh0n3J4xlia1gvnNeZ17SZMsq5hhACULEhVvRE2tdBVrY3AdjNbdxsnnKOPKJn5lv59JEfjIKv8NFR2tKcDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:51:50.610287Z","bundle_sha256":"c414f687e944aa4da4d811a43cfe96e2755e03fb432f533c89cb37b648017bbf"}}