{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:4JXYYE7RHDVPBCXX27ZMWXC7ZD","short_pith_number":"pith:4JXYYE7R","schema_version":"1.0","canonical_sha256":"e26f8c13f138eaf08af7d7f2cb5c5fc8cc3f7a5b3a8ac5b7ff0b5e682a4692c1","source":{"kind":"arxiv","id":"2103.06873","version":3},"attestation_state":"computed","paper":{"title":"Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cond-mat.str-el","hep-th"],"primary_cat":"quant-ph","authors_text":"Matteo Ippoliti, Tibor Rakovszky, Vedika Khemani","submitted_at":"2021-03-11T18:57:29Z","abstract_excerpt":"The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size -- from logarithmic to extensive to \\emph{fractal}. We show how these outcomes in non-unitary circuits (that are \"spacetime-dual\" to"},"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":"2103.06873","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2021-03-11T18:57:29Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cond-mat.str-el","hep-th"],"title_canon_sha256":"7a78f57a8c83113dd5f61e27e5c0f5487d1ea63f5c7c399d3c4e309cc9b6e6f9","abstract_canon_sha256":"b9c1c052371dfb3f0cecc3577600dd79b3529eb015c5833e9440e39f61a514ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:17:14.050634Z","signature_b64":"hBNP8qNEZzf1enaShgTpwlHG2bwEYpfz1jmqECZkR2BBjM+f38+axRzhCS+yp+2vcF46BxHq1UcUwU0kd8dBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26f8c13f138eaf08af7d7f2cb5c5fc8cc3f7a5b3a8ac5b7ff0b5e682a4692c1","last_reissued_at":"2026-07-05T04:17:14.050270Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:17:14.050270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cond-mat.str-el","hep-th"],"primary_cat":"quant-ph","authors_text":"Matteo Ippoliti, Tibor Rakovszky, Vedika Khemani","submitted_at":"2021-03-11T18:57:29Z","abstract_excerpt":"The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size -- from logarithmic to extensive to \\emph{fractal}. We show how these outcomes in non-unitary circuits (that are \"spacetime-dual\" to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.06873","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/2103.06873/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":"2103.06873","created_at":"2026-07-05T04:17:14.050327+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.06873v3","created_at":"2026-07-05T04:17:14.050327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.06873","created_at":"2026-07-05T04:17:14.050327+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JXYYE7RHDVP","created_at":"2026-07-05T04:17:14.050327+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JXYYE7RHDVPBCXX","created_at":"2026-07-05T04:17:14.050327+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JXYYE7R","created_at":"2026-07-05T04:17:14.050327+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.08356","citing_title":"Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD","json":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD.json","graph_json":"https://pith.science/api/pith-number/4JXYYE7RHDVPBCXX27ZMWXC7ZD/graph.json","events_json":"https://pith.science/api/pith-number/4JXYYE7RHDVPBCXX27ZMWXC7ZD/events.json","paper":"https://pith.science/paper/4JXYYE7R"},"agent_actions":{"view_html":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD","download_json":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD.json","view_paper":"https://pith.science/paper/4JXYYE7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.06873&json=true","fetch_graph":"https://pith.science/api/pith-number/4JXYYE7RHDVPBCXX27ZMWXC7ZD/graph.json","fetch_events":"https://pith.science/api/pith-number/4JXYYE7RHDVPBCXX27ZMWXC7ZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD/action/storage_attestation","attest_author":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD/action/author_attestation","sign_citation":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD/action/citation_signature","submit_replication":"https://pith.science/pith/4JXYYE7RHDVPBCXX27ZMWXC7ZD/action/replication_record"}},"created_at":"2026-07-05T04:17:14.050327+00:00","updated_at":"2026-07-05T04:17:14.050327+00:00"}