{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FU7O5PYHWPR45GNKRUJ4NVAXB5","short_pith_number":"pith:FU7O5PYH","canonical_record":{"source":{"id":"1105.4159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-05-20T19:22:15Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"title_canon_sha256":"8ee68b0de7b3f06e18a7216c31b4602feed2ba3af0b1ca7c519837a43402c921","abstract_canon_sha256":"6e1412f5fb73e825cc0e3dea35f976df36853e1c55abc36f4a2194296c275a6e"},"schema_version":"1.0"},"canonical_sha256":"2d3eeebf07b3e3ce99aa8d13c6d4170f501184a71df0ab91ac77b26f8803c602","source":{"kind":"arxiv","id":"1105.4159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4159","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4159v1","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4159","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"pith_short_12","alias_value":"FU7O5PYHWPR4","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FU7O5PYHWPR45GNK","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FU7O5PYH","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FU7O5PYHWPR45GNKRUJ4NVAXB5","target":"record","payload":{"canonical_record":{"source":{"id":"1105.4159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-05-20T19:22:15Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"title_canon_sha256":"8ee68b0de7b3f06e18a7216c31b4602feed2ba3af0b1ca7c519837a43402c921","abstract_canon_sha256":"6e1412f5fb73e825cc0e3dea35f976df36853e1c55abc36f4a2194296c275a6e"},"schema_version":"1.0"},"canonical_sha256":"2d3eeebf07b3e3ce99aa8d13c6d4170f501184a71df0ab91ac77b26f8803c602","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:39.520178Z","signature_b64":"2tDQ+OtznSiikMBy7Gd5Om0QCKqwjA4xualD+9Q1ia1tsSC/wG/Mx1b7TKwimCYsemXER8+QLLTo9Kl9ja4aAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d3eeebf07b3e3ce99aa8d13c6d4170f501184a71df0ab91ac77b26f8803c602","last_reissued_at":"2026-05-18T04:11:39.519728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:39.519728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.4159","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcRFyfr11kBjZ5PeYlwGDCkwVn22uvEKJQ0bgaoNLai2oppa+mVy9Vn5+kyn8w1gO9qdWf8A18RY8aduH+MbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:29:41.839978Z"},"content_sha256":"8d0113427513559808c96d562111fb104aa048452f44beb4181d1c447958b5d3","schema_version":"1.0","event_id":"sha256:8d0113427513559808c96d562111fb104aa048452f44beb4181d1c447958b5d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FU7O5PYHWPR45GNKRUJ4NVAXB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the energy landscape of 3D spin Hamiltonians with topological order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Jeongwan Haah, Sergey Bravyi","submitted_at":"2011-05-20T19:22:15Z","abstract_excerpt":"We explore feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we characterize the energy landscape of stabilizer code Hamiltonians with local bounded-strength interactions which have a topologically ordered ground state but do not have string-like logical operators. We prove that any sequence of local errors mapping a ground state of such Hamiltonian to an orthogonal ground state must cross an energy barrier growing at least as a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4159","kind":"arxiv","version":1},"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":"2026-05-18T04:11:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VubCx6UYgijyINyoh8i/mHWbkESEIduolgC0XxCYy4vD6BWF3Z5+1se37+HVutZ8Y3ysT4RLkOaIuNINh7DWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:29:41.840734Z"},"content_sha256":"b0310981ddeb05158cf516b8a4e29b70bf49ddb30e45abea47b6a150a7de5f8b","schema_version":"1.0","event_id":"sha256:b0310981ddeb05158cf516b8a4e29b70bf49ddb30e45abea47b6a150a7de5f8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/bundle.json","state_url":"https://pith.science/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/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":"2026-08-17T01:29:41Z","links":{"resolver":"https://pith.science/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5","bundle":"https://pith.science/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/bundle.json","state":"https://pith.science/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FU7O5PYHWPR45GNKRUJ4NVAXB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FU7O5PYHWPR45GNKRUJ4NVAXB5","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":"6e1412f5fb73e825cc0e3dea35f976df36853e1c55abc36f4a2194296c275a6e","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-05-20T19:22:15Z","title_canon_sha256":"8ee68b0de7b3f06e18a7216c31b4602feed2ba3af0b1ca7c519837a43402c921"},"schema_version":"1.0","source":{"id":"1105.4159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4159","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4159v1","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4159","created_at":"2026-05-18T04:11:39Z"},{"alias_kind":"pith_short_12","alias_value":"FU7O5PYHWPR4","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FU7O5PYHWPR45GNK","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FU7O5PYH","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:b0310981ddeb05158cf516b8a4e29b70bf49ddb30e45abea47b6a150a7de5f8b","target":"graph","created_at":"2026-05-18T04:11:39Z","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":"We explore feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we characterize the energy landscape of stabilizer code Hamiltonians with local bounded-strength interactions which have a topologically ordered ground state but do not have string-like logical operators. We prove that any sequence of local errors mapping a ground state of such Hamiltonian to an orthogonal ground state must cross an energy barrier growing at least as a ","authors_text":"Jeongwan Haah, Sergey Bravyi","cross_cats":["cond-mat.stat-mech","cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-05-20T19:22:15Z","title":"On the energy landscape of 3D spin Hamiltonians with topological order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4159","kind":"arxiv","version":1},"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":"sha256:8d0113427513559808c96d562111fb104aa048452f44beb4181d1c447958b5d3","target":"record","created_at":"2026-05-18T04:11:39Z","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":"6e1412f5fb73e825cc0e3dea35f976df36853e1c55abc36f4a2194296c275a6e","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-05-20T19:22:15Z","title_canon_sha256":"8ee68b0de7b3f06e18a7216c31b4602feed2ba3af0b1ca7c519837a43402c921"},"schema_version":"1.0","source":{"id":"1105.4159","kind":"arxiv","version":1}},"canonical_sha256":"2d3eeebf07b3e3ce99aa8d13c6d4170f501184a71df0ab91ac77b26f8803c602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d3eeebf07b3e3ce99aa8d13c6d4170f501184a71df0ab91ac77b26f8803c602","first_computed_at":"2026-05-18T04:11:39.519728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:39.519728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2tDQ+OtznSiikMBy7Gd5Om0QCKqwjA4xualD+9Q1ia1tsSC/wG/Mx1b7TKwimCYsemXER8+QLLTo9Kl9ja4aAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:39.520178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d0113427513559808c96d562111fb104aa048452f44beb4181d1c447958b5d3","sha256:b0310981ddeb05158cf516b8a4e29b70bf49ddb30e45abea47b6a150a7de5f8b"],"state_sha256":"a62c6988f9561550b167bb8d8419cbf067879dd3b40a64dbf0fed8c6ddc560e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+p8ZRS803FHnpWTXzz6O2/FekSzjhd7iYx1ZdJlo/r5xk47BCDMAKXC8hAwYmjT5Axwq7/x9atqHoU7jqHCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:29:41.846901Z","bundle_sha256":"309eb11bb481d7f8d8e7227864ce5f16d278f2b671af1f1c2cbe58219e0c4ab7"}}