{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:EESN2P6F6FEPV337N5W6HVV4RT","short_pith_number":"pith:EESN2P6F","schema_version":"1.0","canonical_sha256":"2124dd3fc5f148faef7f6f6de3d6bc8cf6b88897bfa5c8519df41264ab0e19ad","source":{"kind":"arxiv","id":"2210.06669","version":3},"attestation_state":"computed","paper":{"title":"Tensor Renormalization Group at Low Temperatures: Discontinuity Fixed Point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Slava Rychkov, Tom Kennedy","submitted_at":"2022-10-13T01:54:55Z","abstract_excerpt":"We continue our study of rigorous renormalization group (RG) maps for tensor networks that was begun in arXiv:2107.11464. In this paper we construct a rigorous RG map for 2D tensor networks whose domain includes tensors that represent the 2D Ising model at low temperatures with a magnetic field $h$. We prove that the RG map has two stable fixed points, corresponding to the two ground states, and one unstable fixed point which is an example of a discontinuity fixed point. For the Ising model at low temperatures the RG map flows to one of the stable fixed points if $h \\neq 0$, and to the discont"},"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":"2210.06669","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-13T01:54:55Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"b0dbe937b89238cae18ad248b66ce6e11b4a7e07d9d04154a1c3cf1e791d4ab8","abstract_canon_sha256":"e48c65569dc8d897e3657048f51a32b2feb102e112bfd83a1897723b9971b93a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:45:48.166702Z","signature_b64":"Kta2P/91ogfdvuxJZJrA+ayIcK8Vr2YOcxtUioWh4iUYEQ9/HLgndDsEOsY3+Q8pUCHbbPgfb6Q1hI57aK64BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2124dd3fc5f148faef7f6f6de3d6bc8cf6b88897bfa5c8519df41264ab0e19ad","last_reissued_at":"2026-07-05T06:45:48.166139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:45:48.166139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor Renormalization Group at Low Temperatures: Discontinuity Fixed Point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Slava Rychkov, Tom Kennedy","submitted_at":"2022-10-13T01:54:55Z","abstract_excerpt":"We continue our study of rigorous renormalization group (RG) maps for tensor networks that was begun in arXiv:2107.11464. In this paper we construct a rigorous RG map for 2D tensor networks whose domain includes tensors that represent the 2D Ising model at low temperatures with a magnetic field $h$. We prove that the RG map has two stable fixed points, corresponding to the two ground states, and one unstable fixed point which is an example of a discontinuity fixed point. For the Ising model at low temperatures the RG map flows to one of the stable fixed points if $h \\neq 0$, and to the discont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06669","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/2210.06669/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":"2210.06669","created_at":"2026-07-05T06:45:48.166197+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.06669v3","created_at":"2026-07-05T06:45:48.166197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06669","created_at":"2026-07-05T06:45:48.166197+00:00"},{"alias_kind":"pith_short_12","alias_value":"EESN2P6F6FEP","created_at":"2026-07-05T06:45:48.166197+00:00"},{"alias_kind":"pith_short_16","alias_value":"EESN2P6F6FEPV337","created_at":"2026-07-05T06:45:48.166197+00:00"},{"alias_kind":"pith_short_8","alias_value":"EESN2P6F","created_at":"2026-07-05T06:45:48.166197+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08568","citing_title":"Renormalization flows for 1D mixed states and a quantum Goursat lemma","ref_index":34,"is_internal_anchor":true},{"citing_arxiv_id":"2604.15749","citing_title":"Extracting conformal data from finite-size tensor-network flow in critical two-dimensional classical models","ref_index":143,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT","json":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT.json","graph_json":"https://pith.science/api/pith-number/EESN2P6F6FEPV337N5W6HVV4RT/graph.json","events_json":"https://pith.science/api/pith-number/EESN2P6F6FEPV337N5W6HVV4RT/events.json","paper":"https://pith.science/paper/EESN2P6F"},"agent_actions":{"view_html":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT","download_json":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT.json","view_paper":"https://pith.science/paper/EESN2P6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.06669&json=true","fetch_graph":"https://pith.science/api/pith-number/EESN2P6F6FEPV337N5W6HVV4RT/graph.json","fetch_events":"https://pith.science/api/pith-number/EESN2P6F6FEPV337N5W6HVV4RT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT/action/storage_attestation","attest_author":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT/action/author_attestation","sign_citation":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT/action/citation_signature","submit_replication":"https://pith.science/pith/EESN2P6F6FEPV337N5W6HVV4RT/action/replication_record"}},"created_at":"2026-07-05T06:45:48.166197+00:00","updated_at":"2026-07-05T06:45:48.166197+00:00"}