{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AIJUCCWYBA75SOY6J7OGEUANBK","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":"42eb33fabfb50f23bfd534c2e719bf994cbfa8ee88d9ee31318e4e1d80f0cc36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-07-21T22:46:20Z","title_canon_sha256":"592032062dd477755aaf8cf24799e12e90750e438b9d61726bff6de3fb1251a9"},"schema_version":"1.0","source":{"id":"1907.09048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09048","created_at":"2026-07-05T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09048v2","created_at":"2026-07-05T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09048","created_at":"2026-07-05T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"AIJUCCWYBA75","created_at":"2026-07-05T01:33:57Z"},{"alias_kind":"pith_short_16","alias_value":"AIJUCCWYBA75SOY6","created_at":"2026-07-05T01:33:57Z"},{"alias_kind":"pith_short_8","alias_value":"AIJUCCWY","created_at":"2026-07-05T01:33:57Z"}],"graph_snapshots":[{"event_id":"sha256:19c60e79e6afec522dec9289555ac3deb005f34a43ddecbf61d4d0d15b2d9c9b","target":"graph","created_at":"2026-07-05T01:33:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.09048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of `foliated fracton order' proposed in Phys. Rev. X 8, 031051 (2018). We have found that many of the known type I fracton models, although they appear very different, have the same foliated fracton order, known as `X-cube' order. In this paper, we identify three-dimensional fracton models with different kinds of foliated fracton order. Whereas the X-cube order corresponds to the gauge theory of a simple paramagnet with subsystem p","authors_text":"Kevin Slagle, Wilbur Shirley, Xie Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-07-21T22:46:20Z","title":"Twisted foliated fracton phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09048","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":"sha256:8d7a5c0c542af6342d46049788bd3873eda1c0a0eb33ebce15728f96866a9d2f","target":"record","created_at":"2026-07-05T01:33:57Z","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":"42eb33fabfb50f23bfd534c2e719bf994cbfa8ee88d9ee31318e4e1d80f0cc36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-07-21T22:46:20Z","title_canon_sha256":"592032062dd477755aaf8cf24799e12e90750e438b9d61726bff6de3fb1251a9"},"schema_version":"1.0","source":{"id":"1907.09048","kind":"arxiv","version":2}},"canonical_sha256":"0213410ad8083fd93b1e4fdc62500d0ab058403f8f9664b3711cadc2d6d429ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0213410ad8083fd93b1e4fdc62500d0ab058403f8f9664b3711cadc2d6d429ce","first_computed_at":"2026-07-05T01:33:57.125118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:57.125118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIDfb4uk9Xq5jHxcw5yBKGEdl+3m8eQjhJv2GcUc3dUWjcP9yf/+Q7Rq9XAkEpFTqTOzA2zPl1tyFLMxUS77Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:57.125503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d7a5c0c542af6342d46049788bd3873eda1c0a0eb33ebce15728f96866a9d2f","sha256:19c60e79e6afec522dec9289555ac3deb005f34a43ddecbf61d4d0d15b2d9c9b"],"state_sha256":"11e16d0f9675247aad2c8645212cb960c5bc6d7bc75ea3cb03af2a3fa9a8ede4"}