{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WIII6TFDJ7NWBYFEA2UQH7J3KM","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":"71dbcc05ee14f858d401c32fca5d8cca81795048e63a1501e17583a5d8b31326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-01T18:00:02Z","title_canon_sha256":"5128578646fc324a58efe5b962f4b3dbe661ef5707268af058f7e6dff08cddc8"},"schema_version":"1.0","source":{"id":"2606.02707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02707","created_at":"2026-06-03T00:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02707v1","created_at":"2026-06-03T00:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02707","created_at":"2026-06-03T00:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"WIII6TFDJ7NW","created_at":"2026-06-03T00:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"WIII6TFDJ7NWBYFE","created_at":"2026-06-03T00:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"WIII6TFD","created_at":"2026-06-03T00:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:07b7adf89cd362513ac61c7deb53b167267f5e0232203596b5b7e6652305b3a7","target":"graph","created_at":"2026-06-03T00:05:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.02707/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is known that the saddle describing the contribution of supersymmetric black holes to the index of four-dimensional superconformal field theories is degenerate. This degeneracy is a consequence of the one-form symmetry of the theory, and can also be seen as a specific logarithmic correction to the saddle-point action. We discuss the gravitational realization of the one-form symmetry and of the index saddle degeneracy in different holographic setups. In order to illustrate the spontaneous breaking of the one-form symmetry at infinite volume, we employ a gravitational realization of the Cardy","authors_text":"Davide Cassani, Gianmarco Esposto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-01T18:00:02Z","title":"Gravitational index, black hole saddle degeneracy, and one-form symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02707","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":"sha256:6497c874b72aac36ef60df7e9db8882ed29d0dbc23e804bd5323d039b912f22b","target":"record","created_at":"2026-06-03T00:05:07Z","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":"71dbcc05ee14f858d401c32fca5d8cca81795048e63a1501e17583a5d8b31326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-06-01T18:00:02Z","title_canon_sha256":"5128578646fc324a58efe5b962f4b3dbe661ef5707268af058f7e6dff08cddc8"},"schema_version":"1.0","source":{"id":"2606.02707","kind":"arxiv","version":1}},"canonical_sha256":"b2108f4ca34fdb60e0a406a903fd3b53078503c16b8044ef8042e756e8fa4bf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2108f4ca34fdb60e0a406a903fd3b53078503c16b8044ef8042e756e8fa4bf1","first_computed_at":"2026-06-03T00:05:07.490161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T00:05:07.490161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Bljg4QKVuSVAtEWegNwJ4hYxHa2FJedMpHWcMBom81k6PobsJ4k034B8RmWiSpte2TCnZNDIM0TvX1nMhizDg==","signature_status":"signed_v1","signed_at":"2026-06-03T00:05:07.490623Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6497c874b72aac36ef60df7e9db8882ed29d0dbc23e804bd5323d039b912f22b","sha256:07b7adf89cd362513ac61c7deb53b167267f5e0232203596b5b7e6652305b3a7"],"state_sha256":"66373b5714267c345f0a0aabeb6431b51d67b09fc36925a7b70d0f21326eae69"}