{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4AO6QVKGO4NZQYOCTGNJSPV2JA","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":"3b1dd8d3c81071906e12d693d60ca00fa1bdfa955f89bd117ff9e95fa758af73","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-17T17:39:15Z","title_canon_sha256":"63f0830c422eb77f98a50f371b5c1db579733f797e69c60754895559a86823c8"},"schema_version":"1.0","source":{"id":"1512.05687","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05687","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05687v3","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05687","created_at":"2026-05-18T00:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"4AO6QVKGO4NZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AO6QVKGO4NZQYOC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AO6QVKG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:67395d31339022df538fc89876db1f54144f2fdb1635abc15624f7d3b1cafb78","target":"graph","created_at":"2026-05-18T00:24:31Z","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":"Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an approach gives completely misleading results: a translationally invariant, local Hamiltonian on a square lattice with open boundary conditions and constant spectral gap, which has a classical product ground state for all system sizes smaller than a particular threshold size, but a ground state with topological degeneracy for all system sizes larger than this threshold. Starting from a minimal case with spins of dimension ","authors_text":"Angelo Lucia, David Perez-Garcia, Johannes Bausch, Michael M. Wolf, Toby S. Cubitt","cross_cats":["cond-mat.other","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-17T17:39:15Z","title":"Size-Driven Quantum Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05687","kind":"arxiv","version":3},"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":"sha256:8217783b263276cefe60d8c21f2e289e03caf4bafbacc1a665a35c440ddc44d2","target":"record","created_at":"2026-05-18T00:24:31Z","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":"3b1dd8d3c81071906e12d693d60ca00fa1bdfa955f89bd117ff9e95fa758af73","cross_cats_sorted":["cond-mat.other","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-17T17:39:15Z","title_canon_sha256":"63f0830c422eb77f98a50f371b5c1db579733f797e69c60754895559a86823c8"},"schema_version":"1.0","source":{"id":"1512.05687","kind":"arxiv","version":3}},"canonical_sha256":"e01de85546771b9861c2999a993eba4815790ecb5cfbed67a6b24bb052b138e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e01de85546771b9861c2999a993eba4815790ecb5cfbed67a6b24bb052b138e3","first_computed_at":"2026-05-18T00:24:31.924079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:31.924079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJ9mw+ybHA8jyFwkREZicl7on5cUio4LK4I5PcxjHsekNS41JFdHBmv+3jD4D96ndoGMkSXhxv2gWOhYnntlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:31.924607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05687","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8217783b263276cefe60d8c21f2e289e03caf4bafbacc1a665a35c440ddc44d2","sha256:67395d31339022df538fc89876db1f54144f2fdb1635abc15624f7d3b1cafb78"],"state_sha256":"34b2f409032a9fb48c52900ed40edda2a122d951e2cb05714217e0cb6ae6bfcc"}