{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z6F52TWKDVG2Z5BSFJHFQUKBTP","short_pith_number":"pith:Z6F52TWK","canonical_record":{"source":{"id":"1103.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T23:08:14Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"fe0eb23cbb688fad074a3ac2781685130179892115265c6e5d4a6a453d946cb5","abstract_canon_sha256":"e1ce0e62d5d26ddc49aa07fef34c6bf0373805349b04ff3438df0a18171ff14d"},"schema_version":"1.0"},"canonical_sha256":"cf8bdd4eca1d4dacf4322a4e5851419bc6c06d1cfeaf047ee716a00f1bc4e311","source":{"kind":"arxiv","id":"1103.2162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2162","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2162v1","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2162","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z6F52TWKDVG2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6F52TWKDVG2Z5BS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6F52TWK","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z6F52TWKDVG2Z5BSFJHFQUKBTP","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T23:08:14Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"fe0eb23cbb688fad074a3ac2781685130179892115265c6e5d4a6a453d946cb5","abstract_canon_sha256":"e1ce0e62d5d26ddc49aa07fef34c6bf0373805349b04ff3438df0a18171ff14d"},"schema_version":"1.0"},"canonical_sha256":"cf8bdd4eca1d4dacf4322a4e5851419bc6c06d1cfeaf047ee716a00f1bc4e311","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:56.070271Z","signature_b64":"QV4KL1wsO0AnJGwd8VY979dIjV4OGKDtyGme6WYK5vqu0LEDkmw3U5o8B4E8d6L2AsxMda5OOwnllqLOF3JAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf8bdd4eca1d4dacf4322a4e5851419bc6c06d1cfeaf047ee716a00f1bc4e311","last_reissued_at":"2026-05-18T04:26:56.069563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:56.069563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2162","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":"2026-05-18T04:26:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"89DhX0+oqSa8q/2TcAYMGqJiC/GKfDmr5zvTADQ2VtaF5InFT+NXP9GYtMtd8BzOLMFWHwm5vz2/CR2hsxTaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:46.943858Z"},"content_sha256":"1ba62efa032407509a5fe8d8fba98380de74566b06dd8f09a1cc79f372083833","schema_version":"1.0","event_id":"sha256:1ba62efa032407509a5fe8d8fba98380de74566b06dd8f09a1cc79f372083833"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z6F52TWKDVG2Z5BSFJHFQUKBTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new estimate on the indirect Coulomb Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gonzalo Bley, Michael Loss, Rafael D. Benguria","submitted_at":"2011-03-10T23:08:14Z","abstract_excerpt":"We prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller constant, 1.45 < 1.68) but involving an additive kinetic energy term of the single particle density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2162","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":"2026-05-18T04:26:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/asXjjkKb5rXKayLiIUMwIa1KytwXX0VWWbfbVbTUpSjm85ejedsvt79x46TFNaq9XlgpkrbUkRBErKYZrcDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:24:46.944196Z"},"content_sha256":"ef7c787d505b903bc6fb03226a8fafc3e7a183e06823fdd4ec0e5f19ba434f8d","schema_version":"1.0","event_id":"sha256:ef7c787d505b903bc6fb03226a8fafc3e7a183e06823fdd4ec0e5f19ba434f8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/bundle.json","state_url":"https://pith.science/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/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":"2026-06-24T10:24:46Z","links":{"resolver":"https://pith.science/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP","bundle":"https://pith.science/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/bundle.json","state":"https://pith.science/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6F52TWKDVG2Z5BSFJHFQUKBTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z6F52TWKDVG2Z5BSFJHFQUKBTP","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":"e1ce0e62d5d26ddc49aa07fef34c6bf0373805349b04ff3438df0a18171ff14d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T23:08:14Z","title_canon_sha256":"fe0eb23cbb688fad074a3ac2781685130179892115265c6e5d4a6a453d946cb5"},"schema_version":"1.0","source":{"id":"1103.2162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2162","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2162v1","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2162","created_at":"2026-05-18T04:26:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z6F52TWKDVG2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6F52TWKDVG2Z5BS","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6F52TWK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:ef7c787d505b903bc6fb03226a8fafc3e7a183e06823fdd4ec0e5f19ba434f8d","target":"graph","created_at":"2026-05-18T04:26:56Z","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 prove a new lower bound on the indirect Coulomb energy in quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the classical Lieb--Oxford bound (with a smaller constant, 1.45 < 1.68) but involving an additive kinetic energy term of the single particle density.","authors_text":"Gonzalo Bley, Michael Loss, Rafael D. Benguria","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T23:08:14Z","title":"A new estimate on the indirect Coulomb Energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2162","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":"sha256:1ba62efa032407509a5fe8d8fba98380de74566b06dd8f09a1cc79f372083833","target":"record","created_at":"2026-05-18T04:26:56Z","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":"e1ce0e62d5d26ddc49aa07fef34c6bf0373805349b04ff3438df0a18171ff14d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-10T23:08:14Z","title_canon_sha256":"fe0eb23cbb688fad074a3ac2781685130179892115265c6e5d4a6a453d946cb5"},"schema_version":"1.0","source":{"id":"1103.2162","kind":"arxiv","version":1}},"canonical_sha256":"cf8bdd4eca1d4dacf4322a4e5851419bc6c06d1cfeaf047ee716a00f1bc4e311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8bdd4eca1d4dacf4322a4e5851419bc6c06d1cfeaf047ee716a00f1bc4e311","first_computed_at":"2026-05-18T04:26:56.069563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:56.069563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QV4KL1wsO0AnJGwd8VY979dIjV4OGKDtyGme6WYK5vqu0LEDkmw3U5o8B4E8d6L2AsxMda5OOwnllqLOF3JAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:56.070271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ba62efa032407509a5fe8d8fba98380de74566b06dd8f09a1cc79f372083833","sha256:ef7c787d505b903bc6fb03226a8fafc3e7a183e06823fdd4ec0e5f19ba434f8d"],"state_sha256":"0f8e7b9d4c7f3124431551c96c1c7a162c8ade26449cd05fc75aba64da533de9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JR5PHy+3syf4ZePqTIu17vROkvdNtZtiKVhvl0G1Y7IGWmGKp9F/2x85mKC05yPIu0Hj6HaCrmaqhsi/8xzcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:24:46.946247Z","bundle_sha256":"fc1bb19e659f070cd04607cd893eabbf8ba2bad0120e005361c9a6ae9d81d657"}}