{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MUHTOW3LUHGQ6PUJY7PFPMRLID","short_pith_number":"pith:MUHTOW3L","canonical_record":{"source":{"id":"1603.05182","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-16T17:19:14Z","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"title_canon_sha256":"58edbb165cecbb02d4a40cd0027c827c76e75bf36fcf815d1bc9a6fe7ed9eaa0","abstract_canon_sha256":"e45401e9714fec8c25f3d0de6627eeb6165e9438b30842f83363028a2edacb0e"},"schema_version":"1.0"},"canonical_sha256":"650f375b6ba1cd0f3e89c7de57b22b40cdebe0dac6f1e5c534189cbee38039d7","source":{"kind":"arxiv","id":"1603.05182","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05182","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05182v3","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05182","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"MUHTOW3LUHGQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MUHTOW3LUHGQ6PUJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MUHTOW3L","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MUHTOW3LUHGQ6PUJY7PFPMRLID","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05182","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-16T17:19:14Z","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"title_canon_sha256":"58edbb165cecbb02d4a40cd0027c827c76e75bf36fcf815d1bc9a6fe7ed9eaa0","abstract_canon_sha256":"e45401e9714fec8c25f3d0de6627eeb6165e9438b30842f83363028a2edacb0e"},"schema_version":"1.0"},"canonical_sha256":"650f375b6ba1cd0f3e89c7de57b22b40cdebe0dac6f1e5c534189cbee38039d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:07.251641Z","signature_b64":"+QPucU3E2V57HbWmqeAv8N67TuynAC8z+0KS2SGB5WFe6HKqPOUTMldLb6DpjClR8mMcIuuxzdQoe+iY4kYUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"650f375b6ba1cd0f3e89c7de57b22b40cdebe0dac6f1e5c534189cbee38039d7","last_reissued_at":"2026-05-18T00:33:07.250990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:07.250990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05182","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z724uU7o83H19B7C/A2qBULVvaXVQj98AvLQ0FteZ+Adw97vBxU79Gjbb5HE9qc7VME7/IrlNO8UUwrqQ3vpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:54:31.210348Z"},"content_sha256":"b27a9b796eb4aecdf50f3b9b5dd2d6e18494463aa44bd3ee648cc19a24d9fc41","schema_version":"1.0","event_id":"sha256:b27a9b796eb4aecdf50f3b9b5dd2d6e18494463aa44bd3ee648cc19a24d9fc41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MUHTOW3LUHGQ6PUJY7PFPMRLID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal symmetries: Ungauging the cubic code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-lat"],"primary_cat":"quant-ph","authors_text":"Dominic J. Williamson","submitted_at":"2016-03-16T17:19:14Z","abstract_excerpt":"Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post-gauging models and use this to construct short-range entangled phases with fractal-like symmetries, one of which is mapped to the cubic code by the gauging."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05182","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIkFwtaw3b3InL18r0Kr2Xu+ZIFimPtFYjgHersRnnbQKrVojCILweFEj255HPP/e/JYQdcGo74HrS0a4jaoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T09:54:31.211292Z"},"content_sha256":"eb33765e76ab979bbc80fa12c2de24c548e8eb7126f73f6028baa6b22a9513fc","schema_version":"1.0","event_id":"sha256:eb33765e76ab979bbc80fa12c2de24c548e8eb7126f73f6028baa6b22a9513fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/bundle.json","state_url":"https://pith.science/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T09:54:31Z","links":{"resolver":"https://pith.science/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID","bundle":"https://pith.science/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/bundle.json","state":"https://pith.science/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUHTOW3LUHGQ6PUJY7PFPMRLID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MUHTOW3LUHGQ6PUJY7PFPMRLID","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":"e45401e9714fec8c25f3d0de6627eeb6165e9438b30842f83363028a2edacb0e","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-16T17:19:14Z","title_canon_sha256":"58edbb165cecbb02d4a40cd0027c827c76e75bf36fcf815d1bc9a6fe7ed9eaa0"},"schema_version":"1.0","source":{"id":"1603.05182","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05182","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05182v3","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05182","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"MUHTOW3LUHGQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MUHTOW3LUHGQ6PUJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MUHTOW3L","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:eb33765e76ab979bbc80fa12c2de24c548e8eb7126f73f6028baa6b22a9513fc","target":"graph","created_at":"2026-05-18T00:33:07Z","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":"Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post-gauging models and use this to construct short-range entangled phases with fractal-like symmetries, one of which is mapped to the cubic code by the gauging.","authors_text":"Dominic J. Williamson","cross_cats":["cond-mat.str-el","hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-16T17:19:14Z","title":"Fractal symmetries: Ungauging the cubic code"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05182","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:b27a9b796eb4aecdf50f3b9b5dd2d6e18494463aa44bd3ee648cc19a24d9fc41","target":"record","created_at":"2026-05-18T00:33:07Z","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":"e45401e9714fec8c25f3d0de6627eeb6165e9438b30842f83363028a2edacb0e","cross_cats_sorted":["cond-mat.str-el","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-16T17:19:14Z","title_canon_sha256":"58edbb165cecbb02d4a40cd0027c827c76e75bf36fcf815d1bc9a6fe7ed9eaa0"},"schema_version":"1.0","source":{"id":"1603.05182","kind":"arxiv","version":3}},"canonical_sha256":"650f375b6ba1cd0f3e89c7de57b22b40cdebe0dac6f1e5c534189cbee38039d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"650f375b6ba1cd0f3e89c7de57b22b40cdebe0dac6f1e5c534189cbee38039d7","first_computed_at":"2026-05-18T00:33:07.250990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:07.250990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+QPucU3E2V57HbWmqeAv8N67TuynAC8z+0KS2SGB5WFe6HKqPOUTMldLb6DpjClR8mMcIuuxzdQoe+iY4kYUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:07.251641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05182","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b27a9b796eb4aecdf50f3b9b5dd2d6e18494463aa44bd3ee648cc19a24d9fc41","sha256:eb33765e76ab979bbc80fa12c2de24c548e8eb7126f73f6028baa6b22a9513fc"],"state_sha256":"14cc00ef0156cf63ffcb2704e26b03f56be11f64194167923a3d94bab8808c71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4fc6HQkA+a0nMkmhO1C28ZAuMj5j4f2JCS0W+L6dZYa8/V2vwGVWPq00fvM09v8WK9jhjyeQw8uxod+BZDHkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T09:54:31.218290Z","bundle_sha256":"b73298f914030d889b3428ae90e2eda3fc4f8185a5ee0be8da81ffc672b30aee"}}