{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IEXTEUFKOGQZA7G2PVFXYLNZAI","short_pith_number":"pith:IEXTEUFK","canonical_record":{"source":{"id":"1804.09737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-25T18:16:47Z","cross_cats_sorted":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"title_canon_sha256":"b4f29d7a8365887dec1cea1b7c439191ab0ae790d3427bd8eaad2c3e87735e54","abstract_canon_sha256":"02fcd414af3af8f048b4307adca8165c2ae15c71212b2501dee1f51fe4d2bb19"},"schema_version":"1.0"},"canonical_sha256":"412f3250aa71a1907cda7d4b7c2db9020e2adf133a3602cb66fcfb3b9dc05964","source":{"kind":"arxiv","id":"1804.09737","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09737","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09737v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09737","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"IEXTEUFKOGQZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IEXTEUFKOGQZA7G2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IEXTEUFK","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IEXTEUFKOGQZA7G2PVFXYLNZAI","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-25T18:16:47Z","cross_cats_sorted":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"title_canon_sha256":"b4f29d7a8365887dec1cea1b7c439191ab0ae790d3427bd8eaad2c3e87735e54","abstract_canon_sha256":"02fcd414af3af8f048b4307adca8165c2ae15c71212b2501dee1f51fe4d2bb19"},"schema_version":"1.0"},"canonical_sha256":"412f3250aa71a1907cda7d4b7c2db9020e2adf133a3602cb66fcfb3b9dc05964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:59.603519Z","signature_b64":"Zoo3DXdBgNWQhYN9bxPdhgqtV/TnfTZOgJ9m3YY/cP9TArDyB8NGc5O3KjZsPmC8U5zaF2xj0fYFr8ieJyhWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"412f3250aa71a1907cda7d4b7c2db9020e2adf133a3602cb66fcfb3b9dc05964","last_reissued_at":"2026-05-17T23:44:59.602812Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:59.602812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09737","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhYjkVURdwZrESBTD3EVV1dZ+qIRMvqNZr935fP1my59hjfC+dU4Efhi6+J445UURkB/b3kCkcZysHZ1j0yqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:30:17.751024Z"},"content_sha256":"a33b4cc5228eeb483ac21e926b25a5a1b667e0a1f65dafb7e6dc9317f6d9d9dc","schema_version":"1.0","event_id":"sha256:a33b4cc5228eeb483ac21e926b25a5a1b667e0a1f65dafb7e6dc9317f6d9d9dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IEXTEUFKOGQZA7G2PVFXYLNZAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergent statistical mechanics of entanglement in random unitary circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam Nahum, Tianci Zhou","submitted_at":"2018-04-25T18:16:47Z","abstract_excerpt":"We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary circuits. We demonstrate explicitly the emergence of a `minimal membrane' governing entanglement growth, which in 1+1D is a directed random walk in spacetime (or a variant thereof). Using the replica trick to handle the logarithm in the definition of the $n$th R\\'enyi entropy $S_n$, we map the calculation of the entanglement after a quench to a problem of intera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09737","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":""},"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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QODO3XB90TPJElwTqH845j62BIaqaubyqF8lVhd7Njem8XVFTkQsK5AyeEoypWkN0GmQruwpQa05XRdGSW6YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T23:30:17.751747Z"},"content_sha256":"1ecc95d2104f83931bae28b32e1c8c67576435e6f522b268638af990cbc5557c","schema_version":"1.0","event_id":"sha256:1ecc95d2104f83931bae28b32e1c8c67576435e6f522b268638af990cbc5557c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/bundle.json","state_url":"https://pith.science/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/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":"2026-05-19T23:30:17Z","links":{"resolver":"https://pith.science/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI","bundle":"https://pith.science/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/bundle.json","state":"https://pith.science/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEXTEUFKOGQZA7G2PVFXYLNZAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IEXTEUFKOGQZA7G2PVFXYLNZAI","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":"02fcd414af3af8f048b4307adca8165c2ae15c71212b2501dee1f51fe4d2bb19","cross_cats_sorted":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-25T18:16:47Z","title_canon_sha256":"b4f29d7a8365887dec1cea1b7c439191ab0ae790d3427bd8eaad2c3e87735e54"},"schema_version":"1.0","source":{"id":"1804.09737","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09737","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09737v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09737","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"IEXTEUFKOGQZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IEXTEUFKOGQZA7G2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IEXTEUFK","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:1ecc95d2104f83931bae28b32e1c8c67576435e6f522b268638af990cbc5557c","target":"graph","created_at":"2026-05-17T23:44:59Z","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":"We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary circuits. We demonstrate explicitly the emergence of a `minimal membrane' governing entanglement growth, which in 1+1D is a directed random walk in spacetime (or a variant thereof). Using the replica trick to handle the logarithm in the definition of the $n$th R\\'enyi entropy $S_n$, we map the calculation of the entanglement after a quench to a problem of intera","authors_text":"Adam Nahum, Tianci Zhou","cross_cats":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-25T18:16:47Z","title":"Emergent statistical mechanics of entanglement in random unitary circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09737","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:a33b4cc5228eeb483ac21e926b25a5a1b667e0a1f65dafb7e6dc9317f6d9d9dc","target":"record","created_at":"2026-05-17T23:44:59Z","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":"02fcd414af3af8f048b4307adca8165c2ae15c71212b2501dee1f51fe4d2bb19","cross_cats_sorted":["cond-mat.str-el","hep-th","nlin.CD","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-25T18:16:47Z","title_canon_sha256":"b4f29d7a8365887dec1cea1b7c439191ab0ae790d3427bd8eaad2c3e87735e54"},"schema_version":"1.0","source":{"id":"1804.09737","kind":"arxiv","version":2}},"canonical_sha256":"412f3250aa71a1907cda7d4b7c2db9020e2adf133a3602cb66fcfb3b9dc05964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"412f3250aa71a1907cda7d4b7c2db9020e2adf133a3602cb66fcfb3b9dc05964","first_computed_at":"2026-05-17T23:44:59.602812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:59.602812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zoo3DXdBgNWQhYN9bxPdhgqtV/TnfTZOgJ9m3YY/cP9TArDyB8NGc5O3KjZsPmC8U5zaF2xj0fYFr8ieJyhWBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:59.603519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09737","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a33b4cc5228eeb483ac21e926b25a5a1b667e0a1f65dafb7e6dc9317f6d9d9dc","sha256:1ecc95d2104f83931bae28b32e1c8c67576435e6f522b268638af990cbc5557c"],"state_sha256":"0550ac64d562735f741a545b309e91351d0e0f4d330e602d814617ee4a5e587f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7+mJ4PCqrzVSEKJ36vn5otaQduCYc2fvXhvV1TI/eC5/SIYug9yLoXWYetkIEPZ+76AzT2rXtWkUshrtk+VBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T23:30:17.755461Z","bundle_sha256":"604416fa9ab7957ba82e1e6e3e3ae9157abe627d2698b2d67da61461acefba22"}}