{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b77fa0fedb96ef9a6ab303c70d659d1833f41c1963486f07bbdae67782a9159c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["25c94828b16686eb5314eae282467cf6037f489af84a46eb4789f6c67b1cbcdc","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"d36584234bcd1b260ae86c1abfd776e119a8b6aaa45f8652d0841fa6683d3d93","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"amo.dipolar-supersolids.superfluid-fraction-2d","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"In a supersolid only part of the matter flows freely (the superfluid fraction). It has been measured in a chain of droplets, but not in a two-dimensional crystal where it can depend on direction.","posed_since":"","precise":"For a 2D triangular or honeycomb supersolid of Dy-164 or Er-166, measure the superfluid fraction tensor $f_{s},ij$ (via Josephson oscillations, moment of inertia or sound speeds) as a function of density contrast, and compare with Leggett's upper and lower bounds computed from the measured density profile. Answer: $f_{s},ij$ versus contrast with errors.","problem_ref":"25c94828b16686eb5314eae282467cf6037f489af84a46eb4789f6c67b1cbcdc","references":"","settled_by":"A 2D measurement of $f_s$ along two lattice directions compared with Leggett bounds from in-situ imaging.","status_note":"A 2024 Josephson-effect measurement in a one-dimensional droplet array found a sub-unity fraction consistent with the Leggett bound (Biagioni et al., Nature 2024; arXiv:2311.04757).","title":"Superfluid fraction tensor of a two-dimensional dipolar supersolid","topic_ref":null},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d5b65295ca33df6dcc766c5b0d78a5227356ba38e3738ee242cbe960a1077b86","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"3ac9c333a1b017a5dc5e06cf0ee1ab03d9d413bb830120a8b9463942d2fc5cb0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"4Y9nkhmWSBC0UpJqXXq1ohM65I9l-1xw7mupn7BbK5g2zpl7cPD-NxBZx728CUTO0LL_3nPD8LXd9P7bMWb3BA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIOsnDM6GwF6XcXgbPDuGrA9nUE7uDASCouUY5QtL8XLDxIDrBqkdJ9qKXMlmX8vICFEaIhHbDZomZyqlTqUQCzT-ACPAg9necGwn21qls2nOeyvSjv9e1lSztDijMOfPN8zC0h0QI8SCQ_ytVHoU6tfRMR9WEwI27g4BXZXhWUXKTEa_mX-5E4gjxIIouEol0lj_xk9v-0ic-Pz1gwSTrDzT7cYsohXuXgQnnCPEghRsSZ0yO7DTwD6cxQtKBRyPKEJyUh9jNT-Aduof8v-oI8CDYGANngbAZlUaRwqdhopuTGG41Ekahw4_TQIsmOLJyWQjwICSrAzGHuYDGyrjmPwKi3YvsiKDdzLRmzYH0IeCfveIRCPAgIekMa_m1u51-PW-hSRA4fgflQ3E8UENgESx95L7LlxYI8SDYW1nvfhAbf15fxYweLGiGtYK21xyRv_zJHX5DdVcU4wjxIJdQdDsL3v2lA7qZb8kMJtOgaTQmbgchdPcS5lYJqDLnCPAgkPXX-naXR0fRIdS-sEDlzYmtMvSCNH42ESUF0QXb6NUI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIwL4XrDZ-0IpYigua-tyM64wqd0uqRilnI0aoHuu2bPDxIMCiqPYSs0F2cdtAb5SxAU8WrD4R05Yiviog31ROYWgECPEgxA6_S-7YPYweQObu4y2q1uoBPLtz-Y5gbQMcgaAViSYI8CAG_4oIQkhy8poENiILbtGdwzPS-8SxIrfg2ARc85-H5gjwILIHsTvwpLTWFH8s8CfgBQaeZ0aNcUCbhaIC3sLlh6lOCPEg9cZ4bWec0wYRDcfPfz7trax2EvZrXFvlW4DnBgCYoQkI8CB3zhe-btw0HGuUJxoSvBHmqljX2i_xtKv9PisvVpjr8gjxIGSBYk34U9ro0Avf9MJgik6rywdM4recJQsShrUyoVGJCPEgraRI2npokG3tsYuZYconfMt0ARYLxAQQuCOiQUqeUM8I8SDArwsGYVuomKH_DJiJGziPwECn7skqn20TGM58Ezco0wjwIIgwugvlgSNOmTWMhquqetKjeLf0x7d1a1MH4KU52JbFCPAg3mczMYDKOd7Nhf3ojA9ZvuTsN66Y1NnyYTp9j8GKQNwI8SCvAiiN-Hrv7IEejd8wdUihoozu5KOvpoBFJ0vg3UnGAQj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"2216","tree_size":"3804","proof":["b6b74f4c468c3057d4540fd1207c44f1d03157513c53a9db10e6113e577b5ced","f25accf62e4f58c9cb725ecece3f7db4fd3642794a5f9f027eb370970353e008","4d4546e13f10379fb9b7da79090a13e69f7121c5feb35e2a0b866d17e1865395","0b3beefb87893fbf3fec6ba3c15abaa5a7342eb9dbd411c44acfb6bbf91731ff","8702cd8ac833e36da61c8d2b13f558865dada019fdeb78350b50f8e9d7c5fbaa","161d8bf433ae645616c7c6a125497d03efce949a5dc7960e323b3e24ca5621f3","6a6dd27141672b28efa1ee62891bc3591ef1954d1d4256adbabec756be6e0a64","9761eb0f4689d6e5f28934059787de8a9f8da3f799c91405afdf99769db5c00d","9f197ad4a050ba9a768c42080a12af180f8a85b30776c547c433648f943b3824","453fe2db8b5276d732edac85634e8be036b4709a91a2584f32a4b9edcc8ca9de","325287f5a43e4f3ad4072ec4bd53d43c50c1393021a056122e9cb0fad83b868f","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\nd1c6b659ba39ceda3b36cd1650837c63380dc8e5b9fdca64b4cffc97801761f2\n2216\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIMfPYG8nrZkts0hVU7K2ew9sxrlkgiZMucL9fZ6L18pAikB+mjEmipxfcwx7O20VUUu4YrS/agK/HadWuewuHgA=\n"},"orcid_key_evidence":[],"attesting":null}