{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3577GMGG5TWZCQC53EZITNP5PU","short_pith_number":"pith:3577GMGG","canonical_record":{"source":{"id":"1302.4803","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-20T03:40:05Z","cross_cats_sorted":[],"title_canon_sha256":"c42c6d1543d0138f7b5f3adc9ef5f1a987fb498613a0063fb7e9d5168974228a","abstract_canon_sha256":"999f180db462be074fda71dc050215231276e0c755cb7e4b466e33a0509983ef"},"schema_version":"1.0"},"canonical_sha256":"df7ff330c6eced91405dd93289b5fd7d1bae85c2959a53a4f0c8e610e35a9b09","source":{"kind":"arxiv","id":"1302.4803","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4803","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4803v3","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4803","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"3577GMGG5TWZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3577GMGG5TWZCQC5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3577GMGG","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3577GMGG5TWZCQC53EZITNP5PU","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4803","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-20T03:40:05Z","cross_cats_sorted":[],"title_canon_sha256":"c42c6d1543d0138f7b5f3adc9ef5f1a987fb498613a0063fb7e9d5168974228a","abstract_canon_sha256":"999f180db462be074fda71dc050215231276e0c755cb7e4b466e33a0509983ef"},"schema_version":"1.0"},"canonical_sha256":"df7ff330c6eced91405dd93289b5fd7d1bae85c2959a53a4f0c8e610e35a9b09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:28.113423Z","signature_b64":"Y4qnokP7UAwZi2mxwgVWA0t5CSpYTXgV6D7PsjH2LW547cdve/QyJUd+zXG12zRJWzxmVZzlnBPdzNr9QDVRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df7ff330c6eced91405dd93289b5fd7d1bae85c2959a53a4f0c8e610e35a9b09","last_reissued_at":"2026-05-18T02:54:28.112900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:28.112900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4803","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":"2026-05-18T02:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1DIGD3zskwW42zs8RGh3TWXkocMmmnqVu2vrljZY5ni+D8fOKSp/+awOjU5kbHI7XkfWUnr/KCqkClz37amABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:19:58.419188Z"},"content_sha256":"bdee3cdbba35a536cc03497b0c1ac124f3c97ee40f06147605450b686a241049","schema_version":"1.0","event_id":"sha256:bdee3cdbba35a536cc03497b0c1ac124f3c97ee40f06147605450b686a241049"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3577GMGG5TWZCQC53EZITNP5PU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Meng Cheng, Zheng-Cheng Gu","submitted_at":"2013-02-20T03:40:05Z","abstract_excerpt":"It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with $\\mathbb{Z}_m$ symmetry and find the classification of SPT phases dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4803","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":"2026-05-18T02:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yy8kTNFLyoG/LvubKkBLsEG55k9rJQjGa/TpLNX3w4MIV84Onz6FAfVZ0NqReQqZ3E3e9LwhkVQAB8qo3mUMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:19:58.419604Z"},"content_sha256":"edbfe05c11a931bcec9911a0bc79e53b429ad55829dd693e32421433e1a11e0e","schema_version":"1.0","event_id":"sha256:edbfe05c11a931bcec9911a0bc79e53b429ad55829dd693e32421433e1a11e0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3577GMGG5TWZCQC53EZITNP5PU/bundle.json","state_url":"https://pith.science/pith/3577GMGG5TWZCQC53EZITNP5PU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3577GMGG5TWZCQC53EZITNP5PU/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":"2026-05-26T22:19:58Z","links":{"resolver":"https://pith.science/pith/3577GMGG5TWZCQC53EZITNP5PU","bundle":"https://pith.science/pith/3577GMGG5TWZCQC53EZITNP5PU/bundle.json","state":"https://pith.science/pith/3577GMGG5TWZCQC53EZITNP5PU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3577GMGG5TWZCQC53EZITNP5PU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3577GMGG5TWZCQC53EZITNP5PU","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":"999f180db462be074fda71dc050215231276e0c755cb7e4b466e33a0509983ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-20T03:40:05Z","title_canon_sha256":"c42c6d1543d0138f7b5f3adc9ef5f1a987fb498613a0063fb7e9d5168974228a"},"schema_version":"1.0","source":{"id":"1302.4803","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4803","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4803v3","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4803","created_at":"2026-05-18T02:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"3577GMGG5TWZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3577GMGG5TWZCQC5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3577GMGG","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:edbfe05c11a931bcec9911a0bc79e53b429ad55829dd693e32421433e1a11e0e","target":"graph","created_at":"2026-05-18T02:54:28Z","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":"It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with $\\mathbb{Z}_m$ symmetry and find the classification of SPT phases dep","authors_text":"Meng Cheng, Zheng-Cheng Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-20T03:40:05Z","title":"Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4803","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:bdee3cdbba35a536cc03497b0c1ac124f3c97ee40f06147605450b686a241049","target":"record","created_at":"2026-05-18T02:54:28Z","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":"999f180db462be074fda71dc050215231276e0c755cb7e4b466e33a0509983ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2013-02-20T03:40:05Z","title_canon_sha256":"c42c6d1543d0138f7b5f3adc9ef5f1a987fb498613a0063fb7e9d5168974228a"},"schema_version":"1.0","source":{"id":"1302.4803","kind":"arxiv","version":3}},"canonical_sha256":"df7ff330c6eced91405dd93289b5fd7d1bae85c2959a53a4f0c8e610e35a9b09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df7ff330c6eced91405dd93289b5fd7d1bae85c2959a53a4f0c8e610e35a9b09","first_computed_at":"2026-05-18T02:54:28.112900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:28.112900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4qnokP7UAwZi2mxwgVWA0t5CSpYTXgV6D7PsjH2LW547cdve/QyJUd+zXG12zRJWzxmVZzlnBPdzNr9QDVRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:28.113423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4803","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdee3cdbba35a536cc03497b0c1ac124f3c97ee40f06147605450b686a241049","sha256:edbfe05c11a931bcec9911a0bc79e53b429ad55829dd693e32421433e1a11e0e"],"state_sha256":"5fd9934f617c0ec83bf11ae5c98fa8d11de8bbdf27b44b017396c2e5e2219d44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAT4d86yxT3nitf1UvN37z/0NVEBxUn4/mhdAE2zRdDT1+XaJKUarE1tQZin+LSUaV3QkHpCrWjG66J34CZ8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:19:58.422797Z","bundle_sha256":"55c066e682d3bc8f795020ea250b99535ec7c2ba53785ea441beb2ce1b80f249"}}