{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PUQHBLRT4MWND2PTFVKRXAISCQ","short_pith_number":"pith:PUQHBLRT","canonical_record":{"source":{"id":"1507.02605","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-07-09T17:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"96723afc5d90463bcaf83a21dd99de09eaef5566ae271096f4b8a86e7dc499e4","abstract_canon_sha256":"5976224929c206b161b50f842c0140e1ac6f3a7525fb7f20414c8c1f2aadaec8"},"schema_version":"1.0"},"canonical_sha256":"7d2070ae33e32cd1e9f32d551b8112141f24ba9d3f9db0f886412653147aac19","source":{"kind":"arxiv","id":"1507.02605","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02605","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02605v3","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02605","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"PUQHBLRT4MWN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PUQHBLRT4MWND2PT","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PUQHBLRT","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PUQHBLRT4MWND2PTFVKRXAISCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02605","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-07-09T17:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"96723afc5d90463bcaf83a21dd99de09eaef5566ae271096f4b8a86e7dc499e4","abstract_canon_sha256":"5976224929c206b161b50f842c0140e1ac6f3a7525fb7f20414c8c1f2aadaec8"},"schema_version":"1.0"},"canonical_sha256":"7d2070ae33e32cd1e9f32d551b8112141f24ba9d3f9db0f886412653147aac19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:23.168253Z","signature_b64":"JqL2zoSZ/rIkBvfUAnmXPtJDbp19JL1lous7u30LIQJ41C4cO2Nf2eM1K5MW09fcH40wDfqxVBs40Kn5w+taAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d2070ae33e32cd1e9f32d551b8112141f24ba9d3f9db0f886412653147aac19","last_reissued_at":"2026-05-18T01:27:23.167743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:23.167743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02605","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":"2026-05-18T01:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+EqGo/CpbWbdfy4i6UPiUDTm2iQKxl+uCFW+v6hPr5whZVv6fhHkj9li4SxdfXaUqpvgRNwV5hUIdhsv6ejMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:55:26.461738Z"},"content_sha256":"aa18b2b418a7a80c6f8695dc3c41b2ed2f3405b8bb43052c9828a848c6e9df8e","schema_version":"1.0","event_id":"sha256:aa18b2b418a7a80c6f8695dc3c41b2ed2f3405b8bb43052c9828a848c6e9df8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PUQHBLRT4MWND2PTFVKRXAISCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantization of Topological Invariants under Symmetry-Breaking Disorder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Emil Prodan, Juntao Song","submitted_at":"2015-07-09T17:18:45Z","abstract_excerpt":"In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be topological invariants displaying an exact $\\mathbb Z_2$ quantization. This quantization is stabilized by the symmetries. In the present work, we investigate the fate of such symmetry-stabilized topological invariants in the presence of a disorder which breaks the symmetries but restores them on average. Using a rigorous analysis, we conclude that the strict qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02605","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":"2026-05-18T01:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwkevWmX9xqwdskkSejskM4GzStxp/Cl4ubDAcNKHnJsKrWcQHgYR7F+kbbxFndlsz0xGnRj2tMoPZySPXqnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:55:26.462442Z"},"content_sha256":"7845f14e8be3749657498417497e858770dc0bf3e103ff53aa9395c218a0a7b5","schema_version":"1.0","event_id":"sha256:7845f14e8be3749657498417497e858770dc0bf3e103ff53aa9395c218a0a7b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/bundle.json","state_url":"https://pith.science/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/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":"2026-05-27T22:55:26Z","links":{"resolver":"https://pith.science/pith/PUQHBLRT4MWND2PTFVKRXAISCQ","bundle":"https://pith.science/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/bundle.json","state":"https://pith.science/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUQHBLRT4MWND2PTFVKRXAISCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PUQHBLRT4MWND2PTFVKRXAISCQ","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":"5976224929c206b161b50f842c0140e1ac6f3a7525fb7f20414c8c1f2aadaec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-07-09T17:18:45Z","title_canon_sha256":"96723afc5d90463bcaf83a21dd99de09eaef5566ae271096f4b8a86e7dc499e4"},"schema_version":"1.0","source":{"id":"1507.02605","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02605","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02605v3","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02605","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"PUQHBLRT4MWN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PUQHBLRT4MWND2PT","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PUQHBLRT","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7845f14e8be3749657498417497e858770dc0bf3e103ff53aa9395c218a0a7b5","target":"graph","created_at":"2026-05-18T01:27:23Z","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":"In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be topological invariants displaying an exact $\\mathbb Z_2$ quantization. This quantization is stabilized by the symmetries. In the present work, we investigate the fate of such symmetry-stabilized topological invariants in the presence of a disorder which breaks the symmetries but restores them on average. Using a rigorous analysis, we conclude that the strict qu","authors_text":"Emil Prodan, Juntao Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-07-09T17:18:45Z","title":"Quantization of Topological Invariants under Symmetry-Breaking Disorder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02605","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:aa18b2b418a7a80c6f8695dc3c41b2ed2f3405b8bb43052c9828a848c6e9df8e","target":"record","created_at":"2026-05-18T01:27:23Z","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":"5976224929c206b161b50f842c0140e1ac6f3a7525fb7f20414c8c1f2aadaec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-07-09T17:18:45Z","title_canon_sha256":"96723afc5d90463bcaf83a21dd99de09eaef5566ae271096f4b8a86e7dc499e4"},"schema_version":"1.0","source":{"id":"1507.02605","kind":"arxiv","version":3}},"canonical_sha256":"7d2070ae33e32cd1e9f32d551b8112141f24ba9d3f9db0f886412653147aac19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d2070ae33e32cd1e9f32d551b8112141f24ba9d3f9db0f886412653147aac19","first_computed_at":"2026-05-18T01:27:23.167743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:23.167743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JqL2zoSZ/rIkBvfUAnmXPtJDbp19JL1lous7u30LIQJ41C4cO2Nf2eM1K5MW09fcH40wDfqxVBs40Kn5w+taAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:23.168253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02605","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa18b2b418a7a80c6f8695dc3c41b2ed2f3405b8bb43052c9828a848c6e9df8e","sha256:7845f14e8be3749657498417497e858770dc0bf3e103ff53aa9395c218a0a7b5"],"state_sha256":"07ef6330c303406cc3e59931623e7db75342af463595690e8719cdfbab0d2cda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdIU4qVR7l8fGO81TRWWsyKvsC77Bzyv462YYJHjZV1MCRMJ6sAQX0RdLNNo23LU58m9kLJOnvPjJC/p3iMxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:55:26.466265Z","bundle_sha256":"22042a6b849580e89f77b7e7803a75a2e3148055465a2e1a1c00dbf8ba5038d6"}}