{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PDD2WLWMR6N7X2FNYW367SPIFK","short_pith_number":"pith:PDD2WLWM","canonical_record":{"source":{"id":"1810.12964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-10-30T18:51:52Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"5f1bbf35b8e73a531ad7999c6330c38f80df3dcb84a38074284ff7e8fddc484c","abstract_canon_sha256":"e3af4f6ec6982c01c1b2f3ae1d3914655380b765f84dc1eac62527924ac762b1"},"schema_version":"1.0"},"canonical_sha256":"78c7ab2ecc8f9bfbe8adc5b7efc9e82a9a80b5624c0cb9c163edffc24937432c","source":{"kind":"arxiv","id":"1810.12964","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12964","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12964v1","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12964","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"PDD2WLWMR6N7","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDD2WLWMR6N7X2FN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDD2WLWM","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PDD2WLWMR6N7X2FNYW367SPIFK","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-10-30T18:51:52Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"5f1bbf35b8e73a531ad7999c6330c38f80df3dcb84a38074284ff7e8fddc484c","abstract_canon_sha256":"e3af4f6ec6982c01c1b2f3ae1d3914655380b765f84dc1eac62527924ac762b1"},"schema_version":"1.0"},"canonical_sha256":"78c7ab2ecc8f9bfbe8adc5b7efc9e82a9a80b5624c0cb9c163edffc24937432c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:52.599342Z","signature_b64":"NP2V2LlSJhNHRA/euNFj+eDGeWYdpfXZKVbmCvkt2vHgzluoaGeNYwt3nVnWNEWfKBpYjDtXyHV8XQ1QwvZtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78c7ab2ecc8f9bfbe8adc5b7efc9e82a9a80b5624c0cb9c163edffc24937432c","last_reissued_at":"2026-05-18T00:01:52.598937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:52.598937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12964","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":"2026-05-18T00:01:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oq87W1Eq8pYySJrtnX6sb2DEIy7qmhchMQctFeXeuWgR74KCJaI/iiESua+K0IAiMlo9fw4TgEQyfPz3FJWMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:30:51.169919Z"},"content_sha256":"8e9386b780fb11262ab2d64c522242c77ee206f32975a9c33002fc07ad36a0c0","schema_version":"1.0","event_id":"sha256:8e9386b780fb11262ab2d64c522242c77ee206f32975a9c33002fc07ad36a0c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PDD2WLWMR6N7X2FNYW367SPIFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the classification of topological defects and textures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Abhishodh Prakash, J.P. Ang","submitted_at":"2018-10-30T18:51:52Z","abstract_excerpt":"Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model. In simple cases, this can be expressed in terms of homotopy groups of the target space; but in general, it is a complicated affair -- even in two dimensions -- and a general method is lacking. In this letter, we introduce a technique to systematically classify topological sectors of sigma models in various dimensions using a framework based on higher categori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12964","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":"2026-05-18T00:01:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbRwfKGssYnBxjR3K/zP4IXYB/5IXUKxs2dZuGjc+lXOgMy5St0U5Dg5zvPMiM+cx3URISc4lgVXD2i8yOVJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T07:30:51.170255Z"},"content_sha256":"fb3b797f4e39d354561f1622edb6e3ee7399385266f924c0d341460c3fc5b3b4","schema_version":"1.0","event_id":"sha256:fb3b797f4e39d354561f1622edb6e3ee7399385266f924c0d341460c3fc5b3b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDD2WLWMR6N7X2FNYW367SPIFK/bundle.json","state_url":"https://pith.science/pith/PDD2WLWMR6N7X2FNYW367SPIFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDD2WLWMR6N7X2FNYW367SPIFK/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":"2026-07-06T07:30:51Z","links":{"resolver":"https://pith.science/pith/PDD2WLWMR6N7X2FNYW367SPIFK","bundle":"https://pith.science/pith/PDD2WLWMR6N7X2FNYW367SPIFK/bundle.json","state":"https://pith.science/pith/PDD2WLWMR6N7X2FNYW367SPIFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDD2WLWMR6N7X2FNYW367SPIFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PDD2WLWMR6N7X2FNYW367SPIFK","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":"e3af4f6ec6982c01c1b2f3ae1d3914655380b765f84dc1eac62527924ac762b1","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-10-30T18:51:52Z","title_canon_sha256":"5f1bbf35b8e73a531ad7999c6330c38f80df3dcb84a38074284ff7e8fddc484c"},"schema_version":"1.0","source":{"id":"1810.12964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12964","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12964v1","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12964","created_at":"2026-05-18T00:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"PDD2WLWMR6N7","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDD2WLWMR6N7X2FN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDD2WLWM","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:fb3b797f4e39d354561f1622edb6e3ee7399385266f924c0d341460c3fc5b3b4","target":"graph","created_at":"2026-05-18T00:01:52Z","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":"Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model. In simple cases, this can be expressed in terms of homotopy groups of the target space; but in general, it is a complicated affair -- even in two dimensions -- and a general method is lacking. In this letter, we introduce a technique to systematically classify topological sectors of sigma models in various dimensions using a framework based on higher categori","authors_text":"Abhishodh Prakash, J.P. Ang","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-10-30T18:51:52Z","title":"On the classification of topological defects and textures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12964","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":"sha256:8e9386b780fb11262ab2d64c522242c77ee206f32975a9c33002fc07ad36a0c0","target":"record","created_at":"2026-05-18T00:01:52Z","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":"e3af4f6ec6982c01c1b2f3ae1d3914655380b765f84dc1eac62527924ac762b1","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-10-30T18:51:52Z","title_canon_sha256":"5f1bbf35b8e73a531ad7999c6330c38f80df3dcb84a38074284ff7e8fddc484c"},"schema_version":"1.0","source":{"id":"1810.12964","kind":"arxiv","version":1}},"canonical_sha256":"78c7ab2ecc8f9bfbe8adc5b7efc9e82a9a80b5624c0cb9c163edffc24937432c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78c7ab2ecc8f9bfbe8adc5b7efc9e82a9a80b5624c0cb9c163edffc24937432c","first_computed_at":"2026-05-18T00:01:52.598937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:52.598937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NP2V2LlSJhNHRA/euNFj+eDGeWYdpfXZKVbmCvkt2vHgzluoaGeNYwt3nVnWNEWfKBpYjDtXyHV8XQ1QwvZtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:52.599342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e9386b780fb11262ab2d64c522242c77ee206f32975a9c33002fc07ad36a0c0","sha256:fb3b797f4e39d354561f1622edb6e3ee7399385266f924c0d341460c3fc5b3b4"],"state_sha256":"b755dcc9829ed4e1f713ccdb0665ffda782a04f1785214616d54c16149c72533"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXqJ1HiImNh0sjc0zhyb1QYqxV3tntphKtv3HJumW+A2JQNiHvgLbfGnRQHGlH339G/wEnfvRbIUi0XqH1E6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T07:30:51.172102Z","bundle_sha256":"6946abb16d04300e3d3dfaff93eebc77aec92fb22e30a9b0026c2c0ba4d11e97"}}