{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VFXTKHBSLGXUFSYC2RDFL3UGRH","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":"bba921f50d5e84d55077284897c8afb21a7f503fd3a01a530a5656557a8dbf00","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-02T16:08:32Z","title_canon_sha256":"873081c57c5f3bf9af97abed5378b2a501fdeb89fb18e83f81c162703abddee7"},"schema_version":"1.0","source":{"id":"1410.0598","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0598","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0598v3","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0598","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"VFXTKHBSLGXU","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VFXTKHBSLGXUFSYC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VFXTKHBS","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:d396fa7346b1660b281fe19a53730bf9040554d12d56989ecb4698abea08f7ef","target":"graph","created_at":"2026-05-18T01:58:27Z","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 $L^p$ lower bounds for Coulomb energy for radially symmetric functions in $\\dot H^s(\\R^3)$ with $\\frac 12 <s<\\frac{3}{2}$. In case $\\frac 12 <s \\leq 1$ we show that the lower bounds are sharp.","authors_text":"Jacopo Bellazzini, Marco Ghimenti, Tohru Ozawa","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-02T16:08:32Z","title":"Sharp lower bounds for Coulomb energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0598","kind":"arxiv","version":3},"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:fec348076fbe1779a3a21b11a4552314e8db73b776b0e7a54539ff9f1eb602f4","target":"record","created_at":"2026-05-18T01:58:27Z","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":"bba921f50d5e84d55077284897c8afb21a7f503fd3a01a530a5656557a8dbf00","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-02T16:08:32Z","title_canon_sha256":"873081c57c5f3bf9af97abed5378b2a501fdeb89fb18e83f81c162703abddee7"},"schema_version":"1.0","source":{"id":"1410.0598","kind":"arxiv","version":3}},"canonical_sha256":"a96f351c3259af42cb02d44655ee8689df487b8d23ec64a4e8ff860cb63e2797","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a96f351c3259af42cb02d44655ee8689df487b8d23ec64a4e8ff860cb63e2797","first_computed_at":"2026-05-18T01:58:27.178437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:27.178437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0exs5MMJWuhF+IfWF8TMgwmHnMPH6/0UJjSNBn4GWghxSqg6oxVCj790qN98E7EMtEvDDa0WP4D8ntrg79kCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:27.178883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0598","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fec348076fbe1779a3a21b11a4552314e8db73b776b0e7a54539ff9f1eb602f4","sha256:d396fa7346b1660b281fe19a53730bf9040554d12d56989ecb4698abea08f7ef"],"state_sha256":"ee2a772511946fb4aa7de792047c1795491f73443ef3d92faa10bccf970d866e"}