{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L4FTGASSC5OLOITAFCEI7KGSZ4","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":"f475bf00e889e1265e6a910764e758779b828fa9a393654632f94a0663f8a884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-05-12T14:45:06Z","title_canon_sha256":"78f6d4061ec94ea1d848dcf352624cfe793c50784cdb516d10399fc065563b0a"},"schema_version":"1.0","source":{"id":"1105.2490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2490","created_at":"2026-05-18T03:23:34Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2490v2","created_at":"2026-05-18T03:23:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2490","created_at":"2026-05-18T03:23:34Z"},{"alias_kind":"pith_short_12","alias_value":"L4FTGASSC5OL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L4FTGASSC5OLOITA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L4FTGASS","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:1c2afcee80ad94ea949b7b14dd2d7dd035101237f5dd1288a57e7a0b71d5981e","target":"graph","created_at":"2026-05-18T03:23:34Z","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 analyse the physical implications of adding a topological density term $\\theta Tr(F\\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\\theta$, contrary to what would be expected for a true topological density. The topological nature of the $\\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\\theta$. The results o","authors_text":"Fabrizio Canfora, Jorge Zanelli, Luigi Rosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-05-12T14:45:06Z","title":"Theta term in a bounded region"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2490","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":"sha256:934127f0d72029e327e3f039b6c6885e2f9755afbd990620d40b900c667925e3","target":"record","created_at":"2026-05-18T03:23:34Z","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":"f475bf00e889e1265e6a910764e758779b828fa9a393654632f94a0663f8a884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-05-12T14:45:06Z","title_canon_sha256":"78f6d4061ec94ea1d848dcf352624cfe793c50784cdb516d10399fc065563b0a"},"schema_version":"1.0","source":{"id":"1105.2490","kind":"arxiv","version":2}},"canonical_sha256":"5f0b330252175cb7226028888fa8d2cf3f088a6fd8ee24eaa3cb236b6c3df928","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f0b330252175cb7226028888fa8d2cf3f088a6fd8ee24eaa3cb236b6c3df928","first_computed_at":"2026-05-18T03:23:34.184517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:34.184517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ae30urTvLw+Q8sf1jDCWii6tRdu7n6RkEZPkk5DJYnT9Zrder+W18fdvtQZufXSi0iWdjZdNoOpMJU56i6saAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:34.185336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:934127f0d72029e327e3f039b6c6885e2f9755afbd990620d40b900c667925e3","sha256:1c2afcee80ad94ea949b7b14dd2d7dd035101237f5dd1288a57e7a0b71d5981e"],"state_sha256":"03b6bc6da853dbc06f0b184d37a0ec8d6f36877330c3e4ee593398b28110f881"}