{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UE6BHRMUYITXSX3IQFDMVBBQIP","short_pith_number":"pith:UE6BHRMU","canonical_record":{"source":{"id":"1601.01694","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-01-07T21:00:25Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"title_canon_sha256":"eff02a3a003170570925cfed5fad736cdfb15b0d82c0c733c5a780bd8de976ca","abstract_canon_sha256":"259421d74e1afefdce34905c1422bfc9bf600da12834622c80d409ca939c4a43"},"schema_version":"1.0"},"canonical_sha256":"a13c13c594c227795f688146ca843043cf8d4641a341b5f887d6b6cdc1b4f37a","source":{"kind":"arxiv","id":"1601.01694","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01694","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01694v3","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01694","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"UE6BHRMUYITX","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UE6BHRMUYITXSX3I","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UE6BHRMU","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UE6BHRMUYITXSX3IQFDMVBBQIP","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01694","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-01-07T21:00:25Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"title_canon_sha256":"eff02a3a003170570925cfed5fad736cdfb15b0d82c0c733c5a780bd8de976ca","abstract_canon_sha256":"259421d74e1afefdce34905c1422bfc9bf600da12834622c80d409ca939c4a43"},"schema_version":"1.0"},"canonical_sha256":"a13c13c594c227795f688146ca843043cf8d4641a341b5f887d6b6cdc1b4f37a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:12.581810Z","signature_b64":"9ykvTB0OT+DFqcMijk2v7IMlcpdEvs9P8Gz3rjb+P+BeJQUUpoIen2+IXIZtaC1+ELIeBsjq5uh8ppgCA4KECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a13c13c594c227795f688146ca843043cf8d4641a341b5f887d6b6cdc1b4f37a","last_reissued_at":"2026-05-18T01:00:12.581129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:12.581129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01694","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":"2026-05-18T01:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvmNNcQV1YcZUk7ocwYFeFMvJZ2PkW8p0Kko1BMpgAvkqrS5hsPf3Erp6qcU3AAbbZNs0DkaoKfTEgrtgxwZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T13:41:50.446912Z"},"content_sha256":"c984103447576c70d551f906136cba16bd8eb546078aea1402b919675a90b0fe","schema_version":"1.0","event_id":"sha256:c984103447576c70d551f906136cba16bd8eb546078aea1402b919675a90b0fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UE6BHRMUYITXSX3IQFDMVBBQIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holographic duality from random tensor networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Michael Walter, Nathaniel Thomas, Patrick Hayden, Sepehr Nezami, Xiao-Liang Qi, Zhao Yang","submitted_at":"2016-01-07T21:00:25Z","abstract_excerpt":"Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01694","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":""},"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":"2026-05-18T01:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLoLJMsfD6IHknQVlB6u6J++oJuMkiEZNwC0dnRawGB8bR04Hysj0/91xtcJvfA1Y2L8E0aKAkjPaqlCdvGgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T13:41:50.447254Z"},"content_sha256":"abfc168436b2e67325dc388df3bb20a6aa25cffb8b10135a73b548b05e86d636","schema_version":"1.0","event_id":"sha256:abfc168436b2e67325dc388df3bb20a6aa25cffb8b10135a73b548b05e86d636"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/bundle.json","state_url":"https://pith.science/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/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":"2026-07-13T13:41:50Z","links":{"resolver":"https://pith.science/pith/UE6BHRMUYITXSX3IQFDMVBBQIP","bundle":"https://pith.science/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/bundle.json","state":"https://pith.science/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UE6BHRMUYITXSX3IQFDMVBBQIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UE6BHRMUYITXSX3IQFDMVBBQIP","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":"259421d74e1afefdce34905c1422bfc9bf600da12834622c80d409ca939c4a43","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-01-07T21:00:25Z","title_canon_sha256":"eff02a3a003170570925cfed5fad736cdfb15b0d82c0c733c5a780bd8de976ca"},"schema_version":"1.0","source":{"id":"1601.01694","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01694","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01694v3","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01694","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"UE6BHRMUYITX","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UE6BHRMUYITXSX3I","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UE6BHRMU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:abfc168436b2e67325dc388df3bb20a6aa25cffb8b10135a73b548b05e86d636","target":"graph","created_at":"2026-05-18T01:00:12Z","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"},"paper":{"abstract_excerpt":"Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show th","authors_text":"Michael Walter, Nathaniel Thomas, Patrick Hayden, Sepehr Nezami, Xiao-Liang Qi, Zhao Yang","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-01-07T21:00:25Z","title":"Holographic duality from random tensor networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01694","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:c984103447576c70d551f906136cba16bd8eb546078aea1402b919675a90b0fe","target":"record","created_at":"2026-05-18T01:00:12Z","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":"259421d74e1afefdce34905c1422bfc9bf600da12834622c80d409ca939c4a43","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-01-07T21:00:25Z","title_canon_sha256":"eff02a3a003170570925cfed5fad736cdfb15b0d82c0c733c5a780bd8de976ca"},"schema_version":"1.0","source":{"id":"1601.01694","kind":"arxiv","version":3}},"canonical_sha256":"a13c13c594c227795f688146ca843043cf8d4641a341b5f887d6b6cdc1b4f37a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a13c13c594c227795f688146ca843043cf8d4641a341b5f887d6b6cdc1b4f37a","first_computed_at":"2026-05-18T01:00:12.581129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:12.581129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ykvTB0OT+DFqcMijk2v7IMlcpdEvs9P8Gz3rjb+P+BeJQUUpoIen2+IXIZtaC1+ELIeBsjq5uh8ppgCA4KECA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:12.581810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01694","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c984103447576c70d551f906136cba16bd8eb546078aea1402b919675a90b0fe","sha256:abfc168436b2e67325dc388df3bb20a6aa25cffb8b10135a73b548b05e86d636"],"state_sha256":"03ed255d9040cb56bd904811692d69d134dd992876a833e09b500869f685a7cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRbX5/OgYSz0WSxmpVSf1IvFxeU7OSG2INWg7RWQqcxk6vgqm82pnf7QckIYc+mx1z1drGRFQ7uQHp+K3q6sBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T13:41:50.449106Z","bundle_sha256":"d028ecb8c69ef039e0b9ff1e39882f1a8cb0a0cfe8a047d7020275bfb33b06ab"}}