{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:WN2FTA6CJIVAWXTX2GJP3GTBVJ","short_pith_number":"pith:WN2FTA6C","canonical_record":{"source":{"id":"2210.07785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-14T13:14:36Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"855212d0c6fe51aa7d9026246684b0979d6dba5715bcec08edd5cccab6451840","abstract_canon_sha256":"d6ac76cd65dbc1aabb8c90eb44f5dfc465572235918de629a5e093fb25d21120"},"schema_version":"1.0"},"canonical_sha256":"b3745983c24a2a0b5e77d192fd9a61aa54bbd9429712ed74953a15390a5ef9c4","source":{"kind":"arxiv","id":"2210.07785","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.07785","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"2210.07785v2","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.07785","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"WN2FTA6CJIVA","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"WN2FTA6CJIVAWXTX","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"WN2FTA6C","created_at":"2026-07-05T05:55:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:WN2FTA6CJIVAWXTX2GJP3GTBVJ","target":"record","payload":{"canonical_record":{"source":{"id":"2210.07785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-14T13:14:36Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"855212d0c6fe51aa7d9026246684b0979d6dba5715bcec08edd5cccab6451840","abstract_canon_sha256":"d6ac76cd65dbc1aabb8c90eb44f5dfc465572235918de629a5e093fb25d21120"},"schema_version":"1.0"},"canonical_sha256":"b3745983c24a2a0b5e77d192fd9a61aa54bbd9429712ed74953a15390a5ef9c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:55:42.432332Z","signature_b64":"1QgFPrFFWbIFuTKHRcBrsqzVGy/LrXnwkuJf3zvyM1rV9VtjX17vm55IDNvHpe3in2c/1yB2LMPBH7bIAeZMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3745983c24a2a0b5e77d192fd9a61aa54bbd9429712ed74953a15390a5ef9c4","last_reissued_at":"2026-07-05T05:55:42.431923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:55:42.431923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.07785","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQBLvLA0NDgA7Mt6rqSaJo23foK2k4zW5oLuKNQn/YvQH8gzahokWQsug/ddf0xvfpfR3iGcy/XT/FayUdULDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:09:17.117872Z"},"content_sha256":"caa1307f3d2f264b121396c2734f7f046ffa7193c9359f33a2d15e95ede36964","schema_version":"1.0","event_id":"sha256:caa1307f3d2f264b121396c2734f7f046ffa7193c9359f33a2d15e95ede36964"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:WN2FTA6CJIVAWXTX2GJP3GTBVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical Density Functional Theory: Representability and Universal Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Mathieu Lewin, Michal Jex, Peter S. Madsen","submitted_at":"2022-10-14T13:14:36Z","abstract_excerpt":"We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which decays fast enough at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.07785","kind":"arxiv","version":2},"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/2210.07785/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":"2026-07-05T05:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gk7g1QXb+GFh8acoWhB9U+Z51rbRr00x/zRqLL+H0Eedc4O6/ZURSqxWJNBUniyNggKo7ctZKC9f8y3FiAfFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:09:17.118367Z"},"content_sha256":"03cce8ed671730d27bce45a3b3d33c783e2c602e9a9c77b7a668e735deaccae7","schema_version":"1.0","event_id":"sha256:03cce8ed671730d27bce45a3b3d33c783e2c602e9a9c77b7a668e735deaccae7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/bundle.json","state_url":"https://pith.science/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/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":"2026-08-04T09:09:17Z","links":{"resolver":"https://pith.science/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ","bundle":"https://pith.science/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/bundle.json","state":"https://pith.science/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WN2FTA6CJIVAWXTX2GJP3GTBVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WN2FTA6CJIVAWXTX2GJP3GTBVJ","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":"d6ac76cd65dbc1aabb8c90eb44f5dfc465572235918de629a5e093fb25d21120","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-14T13:14:36Z","title_canon_sha256":"855212d0c6fe51aa7d9026246684b0979d6dba5715bcec08edd5cccab6451840"},"schema_version":"1.0","source":{"id":"2210.07785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.07785","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"2210.07785v2","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.07785","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"WN2FTA6CJIVA","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"WN2FTA6CJIVAWXTX","created_at":"2026-07-05T05:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"WN2FTA6C","created_at":"2026-07-05T05:55:42Z"}],"graph_snapshots":[{"event_id":"sha256:03cce8ed671730d27bce45a3b3d33c783e2c602e9a9c77b7a668e735deaccae7","target":"graph","created_at":"2026-07-05T05:55:42Z","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/2210.07785/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which decays fast enough at infinity.","authors_text":"Mathieu Lewin, Michal Jex, Peter S. Madsen","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-14T13:14:36Z","title":"Classical Density Functional Theory: Representability and Universal Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.07785","kind":"arxiv","version":2},"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:caa1307f3d2f264b121396c2734f7f046ffa7193c9359f33a2d15e95ede36964","target":"record","created_at":"2026-07-05T05:55:42Z","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":"d6ac76cd65dbc1aabb8c90eb44f5dfc465572235918de629a5e093fb25d21120","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-14T13:14:36Z","title_canon_sha256":"855212d0c6fe51aa7d9026246684b0979d6dba5715bcec08edd5cccab6451840"},"schema_version":"1.0","source":{"id":"2210.07785","kind":"arxiv","version":2}},"canonical_sha256":"b3745983c24a2a0b5e77d192fd9a61aa54bbd9429712ed74953a15390a5ef9c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3745983c24a2a0b5e77d192fd9a61aa54bbd9429712ed74953a15390a5ef9c4","first_computed_at":"2026-07-05T05:55:42.431923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:55:42.431923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1QgFPrFFWbIFuTKHRcBrsqzVGy/LrXnwkuJf3zvyM1rV9VtjX17vm55IDNvHpe3in2c/1yB2LMPBH7bIAeZMCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:55:42.432332Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.07785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa1307f3d2f264b121396c2734f7f046ffa7193c9359f33a2d15e95ede36964","sha256:03cce8ed671730d27bce45a3b3d33c783e2c602e9a9c77b7a668e735deaccae7"],"state_sha256":"6d5c9fe923bb97e9c7f87b18a20f48d4133152e40e32192559b78c5f25399fe4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5qUpfLGTbpX4hGZQkiDFwHuyTtQzuiEFqq3JjU8qQWKx+MSdxczZOGNihDcsVDNL6SaTPJyLgXD9YVuMOUMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:09:17.122919Z","bundle_sha256":"ce37013860a8c395836b56dfa5f25b8633e7570ef2436588e2c0dcd68abd43f4"}}