{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7BGS5A3M6TKF4CO3EORMF6VH4P","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":"2eb6f1273552e66df10e2d417ce552c16f2b94afd052da4ae18890a7d56400f8","cross_cats_sorted":["astro-ph.HE","gr-qc","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-01-23T21:02:36Z","title_canon_sha256":"167ee21917f35502ceddc22f6c729fbe1c0bcfc977b2c5a6e4dac4e46cf65b38"},"schema_version":"1.0","source":{"id":"1201.4865","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4865","created_at":"2026-05-18T03:50:12Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4865v4","created_at":"2026-05-18T03:50:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4865","created_at":"2026-05-18T03:50:12Z"},{"alias_kind":"pith_short_12","alias_value":"7BGS5A3M6TKF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7BGS5A3M6TKF4CO3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7BGS5A3M","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7ea85388d5f029e75653b8a821e8a3d608ca72331559450da052e54203ba85c8","target":"graph","created_at":"2026-05-18T03:50:12Z","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 study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the ","authors_text":"Noburo Shiba","cross_cats":["astro-ph.HE","gr-qc","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-01-23T21:02:36Z","title":"Entanglement Entropy of Two Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4865","kind":"arxiv","version":4},"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":"sha256:3f3ea21b9043a0aca4f59fd3bfaffb13263aa06266aac2440315ea82227e6a6a","target":"record","created_at":"2026-05-18T03:50:12Z","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":"2eb6f1273552e66df10e2d417ce552c16f2b94afd052da4ae18890a7d56400f8","cross_cats_sorted":["astro-ph.HE","gr-qc","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-01-23T21:02:36Z","title_canon_sha256":"167ee21917f35502ceddc22f6c729fbe1c0bcfc977b2c5a6e4dac4e46cf65b38"},"schema_version":"1.0","source":{"id":"1201.4865","kind":"arxiv","version":4}},"canonical_sha256":"f84d2e836cf4d45e09db23a2c2faa7e3c4190b1bf460979e49f33fd41a429a2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f84d2e836cf4d45e09db23a2c2faa7e3c4190b1bf460979e49f33fd41a429a2b","first_computed_at":"2026-05-18T03:50:12.193440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:12.193440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6dLcvXL4hZ6OIBcqUIyctodgg22iWlBVCrcch0UsplZZDFf/iRB5HV4yzWATlRRMar8acLTRMstgnmwNhPC0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:12.194250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4865","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f3ea21b9043a0aca4f59fd3bfaffb13263aa06266aac2440315ea82227e6a6a","sha256:7ea85388d5f029e75653b8a821e8a3d608ca72331559450da052e54203ba85c8"],"state_sha256":"dba85391b9e9fee49a1c2994dcc08fb8767309121b0107d27b2a54d9dc261d01"}