{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ADI6RAUIMAPEPAAJWOVU34C6DN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f26746631a25ac4b787f5a381cae8be233b6a61d368fd290a285da763afc5e56","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-22T06:41:13Z","title_canon_sha256":"897c1ddb2803a6f9bb51afa9fca0c7cf489da5a766e5dbae559b197107cd5859"},"schema_version":"1.0","source":{"id":"1008.3678","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3678","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3678v2","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3678","created_at":"2026-05-18T04:24:54Z"},{"alias_kind":"pith_short_12","alias_value":"ADI6RAUIMAPE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"ADI6RAUIMAPEPAAJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"ADI6RAUI","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:8afb24308f9128419bad8ab24a9ee1e97612fb4ab73acf41138d15bdaffbe941","target":"graph","created_at":"2026-05-18T04:24:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is that for such particle systems with Coulomb interactions and neutralizing background, the so-called \"jellium\", at any temperature and at any finite-strip width there is translation symmetry breaking. This extends the previous result on Laughlin states in thin, two-dimensional strips by Jansen, Lieb and Seiler (2009). The structural argument which is used here b","authors_text":"Michael Aizenman, Paul Jung, Sabine Jansen","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-22T06:41:13Z","title":"Symmetry breaking in quasi-1D Coulomb systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3678","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:62af278581c926c2f20ccd60037f53ff471a20eb7e958bdc13c2af7c0ec9acca","target":"record","created_at":"2026-05-18T04:24:54Z","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":"f26746631a25ac4b787f5a381cae8be233b6a61d368fd290a285da763afc5e56","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-22T06:41:13Z","title_canon_sha256":"897c1ddb2803a6f9bb51afa9fca0c7cf489da5a766e5dbae559b197107cd5859"},"schema_version":"1.0","source":{"id":"1008.3678","kind":"arxiv","version":2}},"canonical_sha256":"00d1e88288601e478009b3ab4df05e1b52c765a5f890bf9a53f75cc045be34aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00d1e88288601e478009b3ab4df05e1b52c765a5f890bf9a53f75cc045be34aa","first_computed_at":"2026-05-18T04:24:54.394948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:54.394948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ublj0mH1e/83kK7D5CWPnT2JwtHtP+s9SxWtol+JF1iIHi5MsRob3tqcxc7J+IJUzCqN4c8TbzJtKqooI9R/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:54.395517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3678","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62af278581c926c2f20ccd60037f53ff471a20eb7e958bdc13c2af7c0ec9acca","sha256:8afb24308f9128419bad8ab24a9ee1e97612fb4ab73acf41138d15bdaffbe941"],"state_sha256":"860f41dd8277598f06b48da296052a7729ff14f1012f3a78f8a908d4daf0efe2"}