{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IU2LRO2LP5QKSRXU5QY6JSI5EC","short_pith_number":"pith:IU2LRO2L","canonical_record":{"source":{"id":"1009.1601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-08T18:04:31Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"1b829e1d115d240b5259538a968156260d3b446bf181fde02ad991ef88ead42a","abstract_canon_sha256":"2eff73e0483387aba17fdee73dfae8b8c03b1abd4c78effd2dc149bba6d6e27b"},"schema_version":"1.0"},"canonical_sha256":"4534b8bb4b7f60a946f4ec31e4c91d208e73dca0d5864c9fda02f50a64bd8c50","source":{"kind":"arxiv","id":"1009.1601","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1601","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1601v1","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1601","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"IU2LRO2LP5QK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IU2LRO2LP5QKSRXU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IU2LRO2L","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IU2LRO2LP5QKSRXU5QY6JSI5EC","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-08T18:04:31Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"1b829e1d115d240b5259538a968156260d3b446bf181fde02ad991ef88ead42a","abstract_canon_sha256":"2eff73e0483387aba17fdee73dfae8b8c03b1abd4c78effd2dc149bba6d6e27b"},"schema_version":"1.0"},"canonical_sha256":"4534b8bb4b7f60a946f4ec31e4c91d208e73dca0d5864c9fda02f50a64bd8c50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:14.417772Z","signature_b64":"qqmIj9lTcIi40FcvJby6K/VnWzOTSTGfDXZicP5ECxfErNuo5qkEElafQPS0OdsWASJvcHQnbFxeogw0JH8QAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4534b8bb4b7f60a946f4ec31e4c91d208e73dca0d5864c9fda02f50a64bd8c50","last_reissued_at":"2026-05-18T04:41:14.417307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:14.417307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1601","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":"2026-05-18T04:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VuO4qoqi3zcg7Qr/VnjnQffax7Azw7rqnYQKjtfQKkfhOujwGPSiBvUDO8X3QU1A6I9yfRTT3i0X+Nooo3AfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:24.864930Z"},"content_sha256":"fec3ad9543e0eeba1033746c8cbfe8ac2ccf46002fa82ff4a42906495fa2560c","schema_version":"1.0","event_id":"sha256:fec3ad9543e0eeba1033746c8cbfe8ac2ccf46002fa82ff4a42906495fa2560c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IU2LRO2LP5QKSRXU5QY6JSI5EC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality Relations for the Classical Ground States of Soft-Matter Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Chase E. Zachary, Frank H. Stillinger, Salvatore Torquato","submitted_at":"2010-09-08T18:04:31Z","abstract_excerpt":"Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that can be applied to ordered and disordered classical ground states. These duality relations link the energy of configurations associated with a real-space potential to the corresponding energy of the dual (Fourier-transformed) potential. We apply the duality relations by demonstrating how information about the classical ground states of short-ranged potentials c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1601","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":"2026-05-18T04:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/jQk5VJ04mUxXl8UpIjjGrX7ss7cRk0e3Okmv2SzLvhMV6ktkLJEemdLoZWlJ+GwpxxdKY+mHlvseqlrYH6iDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:24.865283Z"},"content_sha256":"1edcaa2f28f20c8c0dc5f9537b4b1e9613463d59f6f13febfc9f0f6bd5cfdedc","schema_version":"1.0","event_id":"sha256:1edcaa2f28f20c8c0dc5f9537b4b1e9613463d59f6f13febfc9f0f6bd5cfdedc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/bundle.json","state_url":"https://pith.science/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/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":"2026-05-26T11:04:24Z","links":{"resolver":"https://pith.science/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC","bundle":"https://pith.science/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/bundle.json","state":"https://pith.science/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IU2LRO2LP5QKSRXU5QY6JSI5EC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IU2LRO2LP5QKSRXU5QY6JSI5EC","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":"2eff73e0483387aba17fdee73dfae8b8c03b1abd4c78effd2dc149bba6d6e27b","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-08T18:04:31Z","title_canon_sha256":"1b829e1d115d240b5259538a968156260d3b446bf181fde02ad991ef88ead42a"},"schema_version":"1.0","source":{"id":"1009.1601","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1601","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1601v1","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1601","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"IU2LRO2LP5QK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IU2LRO2LP5QKSRXU","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IU2LRO2L","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:1edcaa2f28f20c8c0dc5f9537b4b1e9613463d59f6f13febfc9f0f6bd5cfdedc","target":"graph","created_at":"2026-05-18T04:41:14Z","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":"Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that can be applied to ordered and disordered classical ground states. These duality relations link the energy of configurations associated with a real-space potential to the corresponding energy of the dual (Fourier-transformed) potential. We apply the duality relations by demonstrating how information about the classical ground states of short-ranged potentials c","authors_text":"Chase E. Zachary, Frank H. Stillinger, Salvatore Torquato","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-08T18:04:31Z","title":"Duality Relations for the Classical Ground States of Soft-Matter Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1601","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:fec3ad9543e0eeba1033746c8cbfe8ac2ccf46002fa82ff4a42906495fa2560c","target":"record","created_at":"2026-05-18T04:41:14Z","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":"2eff73e0483387aba17fdee73dfae8b8c03b1abd4c78effd2dc149bba6d6e27b","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-08T18:04:31Z","title_canon_sha256":"1b829e1d115d240b5259538a968156260d3b446bf181fde02ad991ef88ead42a"},"schema_version":"1.0","source":{"id":"1009.1601","kind":"arxiv","version":1}},"canonical_sha256":"4534b8bb4b7f60a946f4ec31e4c91d208e73dca0d5864c9fda02f50a64bd8c50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4534b8bb4b7f60a946f4ec31e4c91d208e73dca0d5864c9fda02f50a64bd8c50","first_computed_at":"2026-05-18T04:41:14.417307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:14.417307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqmIj9lTcIi40FcvJby6K/VnWzOTSTGfDXZicP5ECxfErNuo5qkEElafQPS0OdsWASJvcHQnbFxeogw0JH8QAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:14.417772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1601","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fec3ad9543e0eeba1033746c8cbfe8ac2ccf46002fa82ff4a42906495fa2560c","sha256:1edcaa2f28f20c8c0dc5f9537b4b1e9613463d59f6f13febfc9f0f6bd5cfdedc"],"state_sha256":"9a535ed314048dd8e62ed0ce9102b55112e9e0ab24abe4f4830071092861b6c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wae5+5mEZzTArUXJRz5ZCt6R4ZyYuKehp78OaU6g0L4rUbLmFJ7mlHN3Kp8DBR/yLVVHs7ncSoMgBN94UVkrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:04:24.867770Z","bundle_sha256":"cd1bcf1bfecea0b2aeaf3ad0624775dcd23d6ec5611425db84208fc26ab786bc"}}