{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:DSOGGBLUVSB4VNKCUW5N5Q5CQG","short_pith_number":"pith:DSOGGBLU","canonical_record":{"source":{"id":"2211.16045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-29T09:30:27Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"8ce380828b938497a0c1f5986eeeb33ed3b45fc9b35cc22ef8bbfe653fb8218e","abstract_canon_sha256":"d4c961d582f217eb2f69cf75abbf27a0c14d8bce924979560e2eaf02d0dc2074"},"schema_version":"1.0"},"canonical_sha256":"1c9c630574ac83cab542a5badec3a281b99e7155ecc81e4384f78b56f68a5b79","source":{"kind":"arxiv","id":"2211.16045","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16045","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16045v2","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16045","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"DSOGGBLUVSB4","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_16","alias_value":"DSOGGBLUVSB4VNKC","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_8","alias_value":"DSOGGBLU","created_at":"2026-07-05T07:48:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:DSOGGBLUVSB4VNKCUW5N5Q5CQG","target":"record","payload":{"canonical_record":{"source":{"id":"2211.16045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-29T09:30:27Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"8ce380828b938497a0c1f5986eeeb33ed3b45fc9b35cc22ef8bbfe653fb8218e","abstract_canon_sha256":"d4c961d582f217eb2f69cf75abbf27a0c14d8bce924979560e2eaf02d0dc2074"},"schema_version":"1.0"},"canonical_sha256":"1c9c630574ac83cab542a5badec3a281b99e7155ecc81e4384f78b56f68a5b79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:48:44.222655Z","signature_b64":"AwT1WY5IGi96yu54KKndeCbkalxjKr6I/u9Q2bk3HgZ4DpctyaTm7W5STr4TMy9EqmVqmraJ9LOs2mg+1OkuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c9c630574ac83cab542a5badec3a281b99e7155ecc81e4384f78b56f68a5b79","last_reissued_at":"2026-07-05T07:48:44.222265Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:48:44.222265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.16045","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znO6L2DMoUxS3lDumDwjjClSY5kXXjROMXzh7ZV1C9gHvbZLa/eMCSlNeufrLzZ8ni1bTXgoYWtDKh3iY2tAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T23:19:02.744987Z"},"content_sha256":"1e4cb583de3707c58a026611a42a332af73933bdd1437f487a6932be9fc9eb03","schema_version":"1.0","event_id":"sha256:1e4cb583de3707c58a026611a42a332af73933bdd1437f487a6932be9fc9eb03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:DSOGGBLUVSB4VNKCUW5N5Q5CQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fun with replicas: tripartitions in tensor networks and gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Freek Witteveen, Geoff Penington, Michael Walter","submitted_at":"2022-11-29T09:30:27Z","abstract_excerpt":"We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and is bounded from above by $\\log d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with $A$, $B$, and $C$. We argue that for holographic states with a fixed spatial geometry, $G(A:B:C)$ is similarly compu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16045","kind":"arxiv","version":2},"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/2211.16045/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":"2026-07-05T07:48:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZTVt5DYjaXw51WlzGgD6YEzfVTDppb2e3mFvpkCDIx15LXndR7YIMYBfWsUwzxHhLzJS4ipLxeZAYxCreBVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T23:19:02.745675Z"},"content_sha256":"ddca20d0e2dc2c99e8f9de8a480b3b245c277801028576f7b297baad0704681d","schema_version":"1.0","event_id":"sha256:ddca20d0e2dc2c99e8f9de8a480b3b245c277801028576f7b297baad0704681d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/bundle.json","state_url":"https://pith.science/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/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":"2026-08-19T23:19:02Z","links":{"resolver":"https://pith.science/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG","bundle":"https://pith.science/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/bundle.json","state":"https://pith.science/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSOGGBLUVSB4VNKCUW5N5Q5CQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:DSOGGBLUVSB4VNKCUW5N5Q5CQG","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":"d4c961d582f217eb2f69cf75abbf27a0c14d8bce924979560e2eaf02d0dc2074","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-29T09:30:27Z","title_canon_sha256":"8ce380828b938497a0c1f5986eeeb33ed3b45fc9b35cc22ef8bbfe653fb8218e"},"schema_version":"1.0","source":{"id":"2211.16045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16045","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16045v2","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16045","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_12","alias_value":"DSOGGBLUVSB4","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_16","alias_value":"DSOGGBLUVSB4VNKC","created_at":"2026-07-05T07:48:44Z"},{"alias_kind":"pith_short_8","alias_value":"DSOGGBLU","created_at":"2026-07-05T07:48:44Z"}],"graph_snapshots":[{"event_id":"sha256:ddca20d0e2dc2c99e8f9de8a480b3b245c277801028576f7b297baad0704681d","target":"graph","created_at":"2026-07-05T07:48:44Z","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/2211.16045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new correlation measure for tripartite pure states that we call $G(A:B:C)$. The quantity is symmetric with respect to the subsystems $A$, $B$, $C$, invariant under local unitaries, and is bounded from above by $\\log d_A d_B$. For random tensor network states, we prove that $G(A:B:C)$ is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with $A$, $B$, and $C$. We argue that for holographic states with a fixed spatial geometry, $G(A:B:C)$ is similarly compu","authors_text":"Freek Witteveen, Geoff Penington, Michael Walter","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-29T09:30:27Z","title":"Fun with replicas: tripartitions in tensor networks and gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16045","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":"sha256:1e4cb583de3707c58a026611a42a332af73933bdd1437f487a6932be9fc9eb03","target":"record","created_at":"2026-07-05T07:48:44Z","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":"d4c961d582f217eb2f69cf75abbf27a0c14d8bce924979560e2eaf02d0dc2074","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-11-29T09:30:27Z","title_canon_sha256":"8ce380828b938497a0c1f5986eeeb33ed3b45fc9b35cc22ef8bbfe653fb8218e"},"schema_version":"1.0","source":{"id":"2211.16045","kind":"arxiv","version":2}},"canonical_sha256":"1c9c630574ac83cab542a5badec3a281b99e7155ecc81e4384f78b56f68a5b79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c9c630574ac83cab542a5badec3a281b99e7155ecc81e4384f78b56f68a5b79","first_computed_at":"2026-07-05T07:48:44.222265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:48:44.222265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AwT1WY5IGi96yu54KKndeCbkalxjKr6I/u9Q2bk3HgZ4DpctyaTm7W5STr4TMy9EqmVqmraJ9LOs2mg+1OkuCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:48:44.222655Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.16045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e4cb583de3707c58a026611a42a332af73933bdd1437f487a6932be9fc9eb03","sha256:ddca20d0e2dc2c99e8f9de8a480b3b245c277801028576f7b297baad0704681d"],"state_sha256":"12eb607ed1254d35fbb033160f87018a1be0818e55c2064199501604a42af68a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/3F2BNu9NkFm8BoYw1S53ACVkJBxbYclIwa0uYZtrmyYuDoy0/Tee/SoJscWUbKt6R4fhGyU3sMzUNXe2DRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T23:19:02.751934Z","bundle_sha256":"a51dd9bde106919206e13e7749e223544ba473266c054c554b4edc6b32066ad9"}}