{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EYLKY2SLJKK4GSG5K37ERKCM33","short_pith_number":"pith:EYLKY2SL","schema_version":"1.0","canonical_sha256":"2616ac6a4b4a95c348dd56fe48a84cded064af84bbd5e1fef4760e8b4d4b3758","source":{"kind":"arxiv","id":"1809.00147","version":2},"attestation_state":"computed","paper":{"title":"Computability at zero temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Michael Burr","submitted_at":"2018-09-01T10:23:05Z","abstract_excerpt":"In this paper, we investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure is known to exist. We characterize the computability of the zero-temperature measure and its entropy for potentials that are constant on cylinders of a given length k. In particular,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.00147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-01T10:23:05Z","cross_cats_sorted":[],"title_canon_sha256":"fa3b86df6d4585fc8bd7126a195ae27bfc4ad75791516a2d33c942c85a7c1a03","abstract_canon_sha256":"1baba7f0e4e0d192dbfc5fe79df6511933d62892c331797ea0b75c2bf39914ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:19.940701Z","signature_b64":"WIbPNbLJjcupjoCsSvFPwtZv8ITle7FFzt2/kZowTOs9F/j1mqkC9keLn+7B+jf2WPpIz4h+b3vd5k6fQ74MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2616ac6a4b4a95c348dd56fe48a84cded064af84bbd5e1fef4760e8b4d4b3758","last_reissued_at":"2026-05-18T00:06:19.940204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:19.940204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computability at zero temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Wolf, Michael Burr","submitted_at":"2018-09-01T10:23:05Z","abstract_excerpt":"In this paper, we investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure is known to exist. We characterize the computability of the zero-temperature measure and its entropy for potentials that are constant on cylinders of a given length k. In particular,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00147","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.00147","created_at":"2026-05-18T00:06:19.940295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.00147v2","created_at":"2026-05-18T00:06:19.940295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00147","created_at":"2026-05-18T00:06:19.940295+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYLKY2SLJKK4","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYLKY2SLJKK4GSG5","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYLKY2SL","created_at":"2026-05-18T12:32:22.470017+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33","json":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33.json","graph_json":"https://pith.science/api/pith-number/EYLKY2SLJKK4GSG5K37ERKCM33/graph.json","events_json":"https://pith.science/api/pith-number/EYLKY2SLJKK4GSG5K37ERKCM33/events.json","paper":"https://pith.science/paper/EYLKY2SL"},"agent_actions":{"view_html":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33","download_json":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33.json","view_paper":"https://pith.science/paper/EYLKY2SL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.00147&json=true","fetch_graph":"https://pith.science/api/pith-number/EYLKY2SLJKK4GSG5K37ERKCM33/graph.json","fetch_events":"https://pith.science/api/pith-number/EYLKY2SLJKK4GSG5K37ERKCM33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33/action/storage_attestation","attest_author":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33/action/author_attestation","sign_citation":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33/action/citation_signature","submit_replication":"https://pith.science/pith/EYLKY2SLJKK4GSG5K37ERKCM33/action/replication_record"}},"created_at":"2026-05-18T00:06:19.940295+00:00","updated_at":"2026-05-18T00:06:19.940295+00:00"}