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Here we defined the initial transformation on theN= 2 model, written in the eigenbasis of the ˆσz-operators, as: ˆU2 = 1 2   1 1 1 1 1−1−1 1 1 1−1−1 1−1 1−1 ","work_id":"b22226b0-c6aa-4ba2-bcb0-4bdb15178943","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"H. A. Kramers and G. H. Wannier, Statistics of the two- dimensional ferromagnet. part i, Physical Review60, 252 (1941)","work_id":"2136fa0d-e5e7-47c0-8de7-b12a1c38611f","year":1941},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"J. M. Kosterlitz and D. J. Thouless, Ordering, metasta- bility and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics6, 1181 (1973)","work_id":"1346dc2f-26c4-4cfc-a4d7-81abef6efb4e","year":1973},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Fradkin, Disorder operators and their descendants, Journal of Statistical Physics167, 427–461 (2017)","work_id":"9a03fbb3-f54f-49e6-8381-4d90accf6309","year":2017}],"snapshot_sha256":"7df817dd24647ce0bca7cf349aefee838bc12d281bcdc4c9b873bccebdb4f54f"},"source":{"id":"2605.13363","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T20:00:26.614748Z","id":"23d91e28-51f0-4be0-83ab-8240efc368a9","model_set":{"reader":"grok-4.3"},"one_line_summary":"Open-boundary transverse-field Ising model admits exact invertible duality, invertible critical symmetry, and spontaneous duality breaking from differing physical sensitivities to local perturbations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Open boundaries make the transverse-field Ising duality exact and invertible.","strongest_claim":"the exact duality necessitates the presence of an anomalous edge degree of freedom, thus realizing a duality rather than topology based bulk-boundary correspondence... the spontaneous breakdown of a global symmetry in terms of the original model can equivalently be described as spontaneously breaking a local symmetry in the dual system... we term this emergent distinction due to arbitrarily small environmental influences spontaneous duality breaking.","weakest_assumption":"That adjusting to open boundary conditions produces a unique invertible duality operator without additional hidden assumptions on the operator algebra or the physical embedding, and that the differing sensitivities to local perturbations are sufficient to explain the apparent violation of Elitzur's theorem without further dynamical details."}},"verdict_id":"23d91e28-51f0-4be0-83ab-8240efc368a9"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9d1de6ed170758493c8585315143043fa0cd2ee89b82ae65115926de83d89868","target":"record","created_at":"2026-05-18T02:44:48Z","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":"cc6bf18b4418d80e320b11ea748a9b17165bcdc34388dae8a022cc62a30a2aa7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-05-13T11:24:09Z","title_canon_sha256":"1f15232d2023f6d3008e20b5ecaa618a26f7d434532502c64479dcbf45bc634c"},"schema_version":"1.0","source":{"id":"2605.13363","kind":"arxiv","version":1}},"canonical_sha256":"db80b1a8617be4b964eb9f2bac1bfd9f12949b3b06ffd2723a8db8515d2ac1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db80b1a8617be4b964eb9f2bac1bfd9f12949b3b06ffd2723a8db8515d2ac1ac","first_computed_at":"2026-05-18T02:44:48.113102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.113102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vD9WI9SuUgRqUOgi/VNNtY6GqZlyb9d3BbE11FIZkQebRg63Ue9OsCq12fD23dzDW9Ebe5ZeGAXcja0h7xXxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.113567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13363","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:bfd0492894fa03014d105bc91480a3c70f1a93d7e97cff7071916b8b09be1f62","sha256:c61f7d12ca884d8086aedb2bf7f5749727ba491a69a401b3f6307235417c9db3"]}],"invalid_events":[],"applied_event_ids":["sha256:9d1de6ed170758493c8585315143043fa0cd2ee89b82ae65115926de83d89868","sha256:d92cfe0b7ec7255d3ecbdc1f014e8ee3ff77ff3d940bc7490d87c9e90746e714"],"state_sha256":"6b5d07a15b68fc15d9c31b879810193736f232c4a0aaefdcc9bd7bdfcd24e0b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygIqh3fP/pn6GLQscP0cERhZ4F4FVxJURT3HWTiZ9LxSYqU+hbfkAmCDGXnSfhhs/plu5IaUT/aynFqHPRKaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T13:28:54.318560Z","bundle_sha256":"29c849b4fb28b5684f7630bd3d4842a960d00ce186bbf65ccfaf1be1d4675a68"}}