{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:U4M25KKF7BZEMQAH7FODYPZR7S","short_pith_number":"pith:U4M25KKF","canonical_record":{"source":{"id":"2112.09122","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-12-16T18:59:00Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"7a131784554a68c6a61010e03cfeae43521871db920fe4a975df80e83d3d9e76","abstract_canon_sha256":"4e81bada64648d4d4ae9efb1dd87ed5deb21729dc7eb27cb9f1fe259d619e91e"},"schema_version":"1.0"},"canonical_sha256":"a719aea945f872464007f95c3c3f31fca4e805ddb23462d4faf2136b8d8b5d70","source":{"kind":"arxiv","id":"2112.09122","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.09122","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"2112.09122v3","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.09122","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"U4M25KKF7BZE","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_16","alias_value":"U4M25KKF7BZEMQAH","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_8","alias_value":"U4M25KKF","created_at":"2026-07-05T05:06:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:U4M25KKF7BZEMQAH7FODYPZR7S","target":"record","payload":{"canonical_record":{"source":{"id":"2112.09122","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-12-16T18:59:00Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"7a131784554a68c6a61010e03cfeae43521871db920fe4a975df80e83d3d9e76","abstract_canon_sha256":"4e81bada64648d4d4ae9efb1dd87ed5deb21729dc7eb27cb9f1fe259d619e91e"},"schema_version":"1.0"},"canonical_sha256":"a719aea945f872464007f95c3c3f31fca4e805ddb23462d4faf2136b8d8b5d70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:53.806143Z","signature_b64":"SqvFZ9oqBbPOZfkCSHEHfsUppabvVLkW1wyBfd5YxwDDkvaMOP8Z9oxFLtHGIFgvWfQwEYovgmRf8zWbnqHRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a719aea945f872464007f95c3c3f31fca4e805ddb23462d4faf2136b8d8b5d70","last_reissued_at":"2026-07-05T05:06:53.805645Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:53.805645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.09122","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LNjvLPnztvhrBYC553874tf/XIMi5dieCtu2xv8B/JzOoG+/JN/7a0aXmAsI+dZUR7d+64ReI6w0h/0wbGVBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:37:01.418031Z"},"content_sha256":"b65e81f369f0f1a367562f0525a04f2b584b97f13d393acda134d25639f1fc86","schema_version":"1.0","event_id":"sha256:b65e81f369f0f1a367562f0525a04f2b584b97f13d393acda134d25639f1fc86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:U4M25KKF7BZEMQAH7FODYPZR7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflected entropy in random tensor networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Chris Akers, Pratik Rath, Simon Lin, Thomas Faulkner","submitted_at":"2021-12-16T18:59:00Z","abstract_excerpt":"In holographic theories, the reflected entropy has been shown to be dual to the area of the entanglement wedge cross section. We study the same problem in random tensor networks demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.09122","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/2112.09122/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0pEgfhrjwWoApHNqpD5nh2NoxvICOa3iS205ABNlkmtk+9B+KRAl0gpbCNAXN1YMMMrZQNSeQOcDDxqH413Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:37:01.418745Z"},"content_sha256":"3312276e64483b8804024913f3306e8195ba0dbb4f75ed802cbd0b353ad3d9bb","schema_version":"1.0","event_id":"sha256:3312276e64483b8804024913f3306e8195ba0dbb4f75ed802cbd0b353ad3d9bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4M25KKF7BZEMQAH7FODYPZR7S/bundle.json","state_url":"https://pith.science/pith/U4M25KKF7BZEMQAH7FODYPZR7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4M25KKF7BZEMQAH7FODYPZR7S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T02:37:01Z","links":{"resolver":"https://pith.science/pith/U4M25KKF7BZEMQAH7FODYPZR7S","bundle":"https://pith.science/pith/U4M25KKF7BZEMQAH7FODYPZR7S/bundle.json","state":"https://pith.science/pith/U4M25KKF7BZEMQAH7FODYPZR7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4M25KKF7BZEMQAH7FODYPZR7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:U4M25KKF7BZEMQAH7FODYPZR7S","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":"4e81bada64648d4d4ae9efb1dd87ed5deb21729dc7eb27cb9f1fe259d619e91e","cross_cats_sorted":["gr-qc","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-12-16T18:59:00Z","title_canon_sha256":"7a131784554a68c6a61010e03cfeae43521871db920fe4a975df80e83d3d9e76"},"schema_version":"1.0","source":{"id":"2112.09122","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.09122","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"2112.09122v3","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.09122","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"U4M25KKF7BZE","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_16","alias_value":"U4M25KKF7BZEMQAH","created_at":"2026-07-05T05:06:53Z"},{"alias_kind":"pith_short_8","alias_value":"U4M25KKF","created_at":"2026-07-05T05:06:53Z"}],"graph_snapshots":[{"event_id":"sha256:3312276e64483b8804024913f3306e8195ba0dbb4f75ed802cbd0b353ad3d9bb","target":"graph","created_at":"2026-07-05T05:06:53Z","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/2112.09122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In holographic theories, the reflected entropy has been shown to be dual to the area of the entanglement wedge cross section. We study the same problem in random tensor networks demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computi","authors_text":"Chris Akers, Pratik Rath, Simon Lin, Thomas Faulkner","cross_cats":["gr-qc","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-12-16T18:59:00Z","title":"Reflected entropy in random tensor networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.09122","kind":"arxiv","version":3},"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:b65e81f369f0f1a367562f0525a04f2b584b97f13d393acda134d25639f1fc86","target":"record","created_at":"2026-07-05T05:06:53Z","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":"4e81bada64648d4d4ae9efb1dd87ed5deb21729dc7eb27cb9f1fe259d619e91e","cross_cats_sorted":["gr-qc","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-12-16T18:59:00Z","title_canon_sha256":"7a131784554a68c6a61010e03cfeae43521871db920fe4a975df80e83d3d9e76"},"schema_version":"1.0","source":{"id":"2112.09122","kind":"arxiv","version":3}},"canonical_sha256":"a719aea945f872464007f95c3c3f31fca4e805ddb23462d4faf2136b8d8b5d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a719aea945f872464007f95c3c3f31fca4e805ddb23462d4faf2136b8d8b5d70","first_computed_at":"2026-07-05T05:06:53.805645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:53.805645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SqvFZ9oqBbPOZfkCSHEHfsUppabvVLkW1wyBfd5YxwDDkvaMOP8Z9oxFLtHGIFgvWfQwEYovgmRf8zWbnqHRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:53.806143Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.09122","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b65e81f369f0f1a367562f0525a04f2b584b97f13d393acda134d25639f1fc86","sha256:3312276e64483b8804024913f3306e8195ba0dbb4f75ed802cbd0b353ad3d9bb"],"state_sha256":"ea81cde7ff15f83993b85a276d1c7573c2bee48946c5faf527c2f2c8b85dc1df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jL3OsbLilLc6xw6vRhuB3m+afWBKAGifonxMywGVJqroSe6VFQw7JwVlwjpZfZF9VAq3bLEAK/1dF5IwYoERAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:37:01.423266Z","bundle_sha256":"8c0435f5aa3963a4c6f4eb74d8b3d11b9840521d77c466794717f28364109fe7"}}