{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BZMTQDIECWBGAZKKAGECEUO35R","short_pith_number":"pith:BZMTQDIE","schema_version":"1.0","canonical_sha256":"0e59380d04158260654a01882251dbec52aef4f3db662c1a4b17316d6a3b8fcb","source":{"kind":"arxiv","id":"1911.12561","version":3},"attestation_state":"computed","paper":{"title":"Upper bound about cross-sections inside black holes and complexity growth rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Run-Qiu Yang","submitted_at":"2019-11-28T07:14:37Z","abstract_excerpt":"This paper studies cross-sections inside black holes and conjectures a universal inequality: in a static $(d+1)$-dimensional asymptotically planar/spherical Schwarzschild-AdS spacetime of given energy $E$ and AdS radius $\\ell_{\\text{AdS}}$, the ``size of cross-section'' inside black holes is bounded by $8\\pi E\\ell_{\\text{AdS}}/(d-1)$. To support this conjecture, it gives the proofs for cases with spherical/planar symmetries and some special cases without planar/spherical symmetries. As one corollary, it shows that the complexity growth rate in complexity-volume conjecture satisfies the upper b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1911.12561","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-11-28T07:14:37Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"e35bb5674b69c245e05529b81181a04e290cf3902322f40d6e24eb8f8e448983","abstract_canon_sha256":"e4e5fbd16c9bbd4511650b5087d9f60adc08fdc9acb9fd8c12510f65a31e6b36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:50:16.397799Z","signature_b64":"cTOFt02uhhQGJmG3O2YAAQYiLPRFAFa6KslhEwOvyC/uPZOt2rj78eYN0uhkkgw00PQ+JlZ7v802mmtIaGBTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e59380d04158260654a01882251dbec52aef4f3db662c1a4b17316d6a3b8fcb","last_reissued_at":"2026-07-05T01:50:16.397344Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:50:16.397344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bound about cross-sections inside black holes and complexity growth rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Run-Qiu Yang","submitted_at":"2019-11-28T07:14:37Z","abstract_excerpt":"This paper studies cross-sections inside black holes and conjectures a universal inequality: in a static $(d+1)$-dimensional asymptotically planar/spherical Schwarzschild-AdS spacetime of given energy $E$ and AdS radius $\\ell_{\\text{AdS}}$, the ``size of cross-section'' inside black holes is bounded by $8\\pi E\\ell_{\\text{AdS}}/(d-1)$. To support this conjecture, it gives the proofs for cases with spherical/planar symmetries and some special cases without planar/spherical symmetries. As one corollary, it shows that the complexity growth rate in complexity-volume conjecture satisfies the upper b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.12561","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.12561/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1911.12561","created_at":"2026-07-05T01:50:16.397393+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.12561v3","created_at":"2026-07-05T01:50:16.397393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.12561","created_at":"2026-07-05T01:50:16.397393+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZMTQDIECWBG","created_at":"2026-07-05T01:50:16.397393+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZMTQDIECWBGAZKK","created_at":"2026-07-05T01:50:16.397393+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZMTQDIE","created_at":"2026-07-05T01:50:16.397393+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21079","citing_title":"Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents","ref_index":44,"is_internal_anchor":false},{"citing_arxiv_id":"2606.21079","citing_title":"Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents","ref_index":52,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R","json":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R.json","graph_json":"https://pith.science/api/pith-number/BZMTQDIECWBGAZKKAGECEUO35R/graph.json","events_json":"https://pith.science/api/pith-number/BZMTQDIECWBGAZKKAGECEUO35R/events.json","paper":"https://pith.science/paper/BZMTQDIE"},"agent_actions":{"view_html":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R","download_json":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R.json","view_paper":"https://pith.science/paper/BZMTQDIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.12561&json=true","fetch_graph":"https://pith.science/api/pith-number/BZMTQDIECWBGAZKKAGECEUO35R/graph.json","fetch_events":"https://pith.science/api/pith-number/BZMTQDIECWBGAZKKAGECEUO35R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R/action/storage_attestation","attest_author":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R/action/author_attestation","sign_citation":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R/action/citation_signature","submit_replication":"https://pith.science/pith/BZMTQDIECWBGAZKKAGECEUO35R/action/replication_record"}},"created_at":"2026-07-05T01:50:16.397393+00:00","updated_at":"2026-07-05T01:50:16.397393+00:00"}