{"as_of":"2026-08-16T13:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5cdad0dfef480aa4e200b45c05599f4481cdf24d50aeefb3a4eceae338565a11","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T02:51:57.365240Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.14232/citation-record","integrity":"/paper/2607.14232/integrity","json":"/paper/2607.14232/citation-record.json","paper":"/paper/2607.14232"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:53.719642Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:53.719642Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:178977f1cef9fc16224cf2cb0eaae76569ff8ba0aeb79d91c3ce3db1bf342ece","observation_id":"a9d073fc-a916-4c64-b5d9-de83bb455e57","resolution":{"observed_at":"2026-08-02T02:51:53.719642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:53.892372Z","title":"von Klitzing, The quantized Hall effect, Rev","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:53.892372Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:b6050ed673e1dff6f6f5f4250908d7544737565102e82fdf643bc4999cb1e140","observation_id":"50fcb893-342d-4c9d-ab50-04405df467a9","resolution":{"observed_at":"2026-08-02T02:51:53.892372Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.056166Z","title":"Chang, C","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.056166Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:2e8450766f741140b2cef349f0574e94ee2bf40d3404b6e8522a167bf1000fd8","observation_id":"86a4786a-8990-4b37-ba9e-a1ccd1e0ec07","resolution":{"observed_at":"2026-08-02T02:51:54.056166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.214864Z","title":"Qi and S.C","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.214864Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:a6ef2b772acf72df21cfa7ca87c6b38063ae57e01983ce643a5cd254aff00c1a","observation_id":"09828cd9-a294-48d2-9eb8-cc70f533ae01","resolution":{"observed_at":"2026-08-02T02:51:54.214864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.298820Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.298820Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:d974b3949dd8b7122fa5ab05c2bdc77bc343190f307aafb61faa2b68f49121ff","observation_id":"080d3928-789c-42b6-823e-28f7dd349de1","resolution":{"observed_at":"2026-08-02T02:51:54.298820Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.383910Z","title":"Zheng, et al., Quasi-1D Coulomb Drag in the Nonlinear Regime, Phys","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.383910Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:d7922f6bd9b9da814af14cb92b790b1b3d964b3f21c75962b550f7ced272ac1d","observation_id":"18f4e99d-6b66-4457-89bd-583856a83e07","resolution":{"observed_at":"2026-08-02T02:51:54.383910Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.442062Z","title":"Zheng, et al., Quasi-one-dimensional Coulomb drag between spin-polarized quantum wires, Phys","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.442062Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:719c585f2ccdb6e3ae30f56f5d2704e150a76446ff0275ca8f853532c506558b","observation_id":"1fd9afc0-b840-426e-ae48-165e0745da69","resolution":{"observed_at":"2026-08-02T02:51:54.442062Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.594503Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.594503Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:aae7fb0ad0548777a62c4f2476a357164197aa3e3f634e312a72837e005a4764","observation_id":"664c8316-03b6-4131-aad2-725b8d086138","resolution":{"observed_at":"2026-08-02T02:51:54.594503Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.731589Z","title":"Hamada, E","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.731589Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:5354ecbb43c7f2120f2b7e9d035d77eb9807de9dbffe514e88d5ab3927e5cf07","observation_id":"bcb5d863-27b3-4428-a459-7e2ec1b5b734","resolution":{"observed_at":"2026-08-02T02:51:54.731589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.901681Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.901681Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:126685e2f371edc7531bd067bf47d68f9640e6f76c6e5c37515877abf118e2e5","observation_id":"500b2b42-cf1f-4271-96c2-f8d875a4682a","resolution":{"observed_at":"2026-08-02T02:51:54.901681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:54.992996Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:54.992996Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:d32a78475cd008689ecdca943778bce8eaf7734ebf58c78556ec8cc7fbc5041a","observation_id":"94d399f8-7a55-41f0-9012-e1d2cff0af79","resolution":{"observed_at":"2026-08-02T02:51:54.992996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.134336Z","title":"Brzezicki and T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.134336Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:fbf0ecca6e00050eb79fcbbdcb6d0b9e6a6d655d0992e10ecb18a6b4106279c9","observation_id":"efe87a68-d29a-4eee-bd11-714c3d39a413","resolution":{"observed_at":"2026-08-02T02:51:55.134336Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.237486Z","title":"McCann, Catalog of noninteracting tight-binding models with two energy bands in one dimension, Phys","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.237486Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:d048f337cc6a355192cf21984a62bbf68efe7b89adf9fa59fa552264ef6f5c60","observation_id":"8676c04a-fb46-41d7-a353-7af099a2f30d","resolution":{"observed_at":"2026-08-02T02:51:55.237486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.365966Z","title":"Cayssol and J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.365966Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:286c02c8585e08350a5a51e45650139d993e246ac61c05a7c3a90197b5fcc060","observation_id":"ac7f0464-b926-40c3-b39a-c06dc7432403","resolution":{"observed_at":"2026-08-02T02:51:55.365966Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.455904Z","title":null,"venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.455904Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:ab754e070e4771ffafde6e9caaedc642ae57a0f3ffbae763ba57cf2f781d4e4c","observation_id":"e04951de-eb89-4e6e-9bbf-3bfee322c2b9","resolution":{"observed_at":"2026-08-02T02:51:55.455904Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.621021Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.621021Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:1ffa875a9565c7dee33dfdd1eb559457f9d890578615e216f85e218a2cfb1afd","observation_id":"da508d98-c523-4a0f-a85b-91a3d3eaf4e9","resolution":{"observed_at":"2026-08-02T02:51:55.621021Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.766520Z","title":"Dalibard, F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.766520Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:a70a04729787700f6ab86587af3b5d2a13d93afbfc89b2265fc003361d6479c7","observation_id":"cc43d539-a376-45a2-977c-dd15bd4b545f","resolution":{"observed_at":"2026-08-02T02:51:55.766520Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.915481Z","title":"Matsubara, H","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.915481Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:e6d2ccfd38ff51a51ac731474f12429e14fd22b2f861cd58140616edfca76305","observation_id":"73638531-0116-4bf4-8082-ce809080cfd1","resolution":{"observed_at":"2026-08-02T02:51:55.915481Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:55.997575Z","title":"Tymczyszyn and E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:55.997575Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:8f4c3fe9ff50f9be55dbfb386217edcc8758d1b999aebbea88a317f5c38243ae","observation_id":"00eedc4c-cb8a-4ae4-862c-c60a12fac9e5","resolution":{"observed_at":"2026-08-02T02:51:55.997575Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.104960Z","title":"Coleman, Quantum sine-Gordon equation as the massive Thirring model, Phys","venue":null,"work_id":null,"year":2088},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.104960Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:78f7f582cdb72238790678614b4fb949155d717304ee11f02f98d4edd876f65f","observation_id":"5147a0a0-1bb8-47ca-838f-030661ffb09c","resolution":{"observed_at":"2026-08-02T02:51:56.104960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.223876Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.223876Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:e8ab09575429e088c2b2e846cc005cc9c500284ed94299cdac0ec27a205b8018","observation_id":"2f5c84c6-86ef-4721-b635-a2a7bef4feaa","resolution":{"observed_at":"2026-08-02T02:51:56.223876Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.335421Z","title":null,"venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.335421Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:9926aafa6522f249816d29b2a46e75b5fc6fb70f90599479f5c6dd0772a50d77","observation_id":"e6c70d7b-362b-4bd1-9e4f-473c60af157a","resolution":{"observed_at":"2026-08-02T02:51:56.335421Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.421678Z","title":"Yin, Paradigm for approaching the forbidden spontaneous phase transition in the one-dimensional Ising model at a fixed finite temperature, Phys","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.421678Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:2984663da75f4986bb911fd4a9e5b2af3faea99c923ec7aff73aa1a470df4cec","observation_id":"4e163383-1231-46c3-adea-3c59f2376349","resolution":{"observed_at":"2026-08-02T02:51:56.421678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.565550Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.565550Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:6dc56227fd164230081064d0d156251bda3e1aaf06727bcd1ff4d14847da4417","observation_id":"4240123a-e36f-4015-bfc0-359231e02fcc","resolution":{"observed_at":"2026-08-02T02:51:56.565550Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.683278Z","title":"Bena and G","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.683278Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:e3b762b3747b5519c4791c2e16cbf6686438ce00802ad91b0bb881cc74bc549f","observation_id":"02ae0a88-7009-4798-9977-3edf4e3ddf43","resolution":{"observed_at":"2026-08-02T02:51:56.683278Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.835635Z","title":"Watanabe, A Proof of the Bloch Theorem for Lattice Models, J Stat Phys 177, 717–726 (2019)","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.835635Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:3cf45869c9850ac12c75cc9b9a9c054372cc9e8444b6ac761632dbdd6dffb11c","observation_id":"b82c2ea2-f6cd-4dd3-90e0-a84e0d928257","resolution":{"observed_at":"2026-08-02T02:51:56.835635Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:56.927445Z","title":"Kapustin and L","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:56.927445Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:77b46b6987a3c463993973eaec009246167b9f5e11f82993acadd505c9b08765","observation_id":"6089cdae-d026-4f2e-993f-e99a3492563e","resolution":{"observed_at":"2026-08-02T02:51:56.927445Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:57.041784Z","title":"Gao and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:57.041784Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:1c24a055bde0c0ed24f85dd61ae771ce7efa388e797b519e9f05c7a58ed31c97","observation_id":"133f097a-2ee7-48be-a434-d045bf9c716f","resolution":{"observed_at":"2026-08-02T02:51:57.041784Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:57.179722Z","title":"Gao and K","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:57.179722Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:37cce5f5d37eb7c1b40b0114f81fbd7e95467cd4f7efac6746a7b0c45557ce38","observation_id":"1a90f252-4516-4f46-aae4-da45a65f8f30","resolution":{"observed_at":"2026-08-02T02:51:57.179722Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:57.286381Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:57.286381Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:fc9f5178c624be5545bb2251f3c310cae96aaac0a5a3dc47d1184404d9cebd7f","observation_id":"eae89d51-7022-41eb-8d8f-2674fd321850","resolution":{"observed_at":"2026-08-02T02:51:57.286381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:51:57.365240Z","title":"Hochbaum, R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-02T02:51:57.365240Z"},"links":{"citing_paper":"/paper/2607.14232"},"observation_digest":"sha256:5ff5734f56870a49bedc56fc249d9f25e15ddc9e7c688fe73c1127afbdeebdb6","observation_id":"feaaf8be-5abe-4349-8858-54f9e7f91f3b","resolution":{"observed_at":"2026-08-02T02:51:57.365240Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.14232","last_updated":"2026-07-15T18:00:42Z","latest_version":1,"primary_category":"cond-mat.mes-hall","snapshot_observed_at":"2026-08-16T09:13:10.036149Z","submitted_at":"2026-07-15T18:00:42Z","title":"Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":31,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":31},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2607.14232."}