{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CXMS3R76RB7F5TZ33EZKC64257","short_pith_number":"pith:CXMS3R76","schema_version":"1.0","canonical_sha256":"15d92dc7fe887e5ecf3bd932a17b9aefd948c21fc2a62954b2e028ee11bb3ab9","source":{"kind":"arxiv","id":"2208.10507","version":1},"attestation_state":"computed","paper":{"title":"Covariant bit threads","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Matthew Headrick, Veronika E. Hubeny","submitted_at":"2022-08-22T18:00:01Z","abstract_excerpt":"We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize th"},"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":"2208.10507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-08-22T18:00:01Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"eb932f4da0b36518076e7585935482b82be8495964d5eee63b4d898bd80b523a","abstract_canon_sha256":"643bf387d261cfff39c147f4a1fa352f1a1f8f3a3c48a24cbf886f5ed7a29256"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:38:50.707195Z","signature_b64":"4JEym9sFtS3SuMojtDEisA2pySLB3ADzzoJWcb648SI3VBXeCyN+aKlMt8RdT/jHdp26t52UeXojtxnXRNEKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15d92dc7fe887e5ecf3bd932a17b9aefd948c21fc2a62954b2e028ee11bb3ab9","last_reissued_at":"2026-07-05T08:38:50.706759Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:38:50.706759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covariant bit threads","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Matthew Headrick, Veronika E. Hubeny","submitted_at":"2022-08-22T18:00:01Z","abstract_excerpt":"We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10507","kind":"arxiv","version":1},"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/2208.10507/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":"2208.10507","created_at":"2026-07-05T08:38:50.706820+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.10507v1","created_at":"2026-07-05T08:38:50.706820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10507","created_at":"2026-07-05T08:38:50.706820+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXMS3R76RB7F","created_at":"2026-07-05T08:38:50.706820+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXMS3R76RB7F5TZ3","created_at":"2026-07-05T08:38:50.706820+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXMS3R76","created_at":"2026-07-05T08:38:50.706820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30466","citing_title":"Holography and Kinematic Space for Gravitational Sub-regions in AdS","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2510.22601","citing_title":"Quantum Bit Threads and the Entropohedron","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2601.19979","citing_title":"Exploring the holographic entropy cone via reinforcement learning","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257","json":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257.json","graph_json":"https://pith.science/api/pith-number/CXMS3R76RB7F5TZ33EZKC64257/graph.json","events_json":"https://pith.science/api/pith-number/CXMS3R76RB7F5TZ33EZKC64257/events.json","paper":"https://pith.science/paper/CXMS3R76"},"agent_actions":{"view_html":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257","download_json":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257.json","view_paper":"https://pith.science/paper/CXMS3R76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.10507&json=true","fetch_graph":"https://pith.science/api/pith-number/CXMS3R76RB7F5TZ33EZKC64257/graph.json","fetch_events":"https://pith.science/api/pith-number/CXMS3R76RB7F5TZ33EZKC64257/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257/action/storage_attestation","attest_author":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257/action/author_attestation","sign_citation":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257/action/citation_signature","submit_replication":"https://pith.science/pith/CXMS3R76RB7F5TZ33EZKC64257/action/replication_record"}},"created_at":"2026-07-05T08:38:50.706820+00:00","updated_at":"2026-07-05T08:38:50.706820+00:00"}