{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:BU5BFNHX7LBB6HA7KX37CO7O7I","short_pith_number":"pith:BU5BFNHX","canonical_record":{"source":{"id":"hep-th/9306120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-06-22T22:14:10Z","cross_cats_sorted":[],"title_canon_sha256":"6f77c446440ba3f68e90d33d3177c8d6ea8ce030ea942c7bb59e286c17c6f6ee","abstract_canon_sha256":"8affe03784cdd67caeea28390b60bb740acdc54d2062935bf263b697cf99f8b0"},"schema_version":"1.0"},"canonical_sha256":"0d3a12b4f7fac21f1c1f55f7f13beefa00dde7a89650d302d9b60c275f9bd94c","source":{"kind":"arxiv","id":"hep-th/9306120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9306120","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9306120v1","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9306120","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"BU5BFNHX7LBB","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"BU5BFNHX7LBB6HA7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"BU5BFNHX","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:BU5BFNHX7LBB6HA7KX37CO7O7I","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9306120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-06-22T22:14:10Z","cross_cats_sorted":[],"title_canon_sha256":"6f77c446440ba3f68e90d33d3177c8d6ea8ce030ea942c7bb59e286c17c6f6ee","abstract_canon_sha256":"8affe03784cdd67caeea28390b60bb740acdc54d2062935bf263b697cf99f8b0"},"schema_version":"1.0"},"canonical_sha256":"0d3a12b4f7fac21f1c1f55f7f13beefa00dde7a89650d302d9b60c275f9bd94c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:43.321299Z","signature_b64":"3kj2/MdGLosbVsgaQuxErSkeOFwcLzKOAF5jlu1TYwrCthmI0qn+4U6SV7CIM049F09Osh3UgMkNQeIv4lvLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d3a12b4f7fac21f1c1f55f7f13beefa00dde7a89650d302d9b60c275f9bd94c","last_reissued_at":"2026-05-18T04:37:43.320575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:43.320575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9306120","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":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNd4Y88IeUvUog17/oPNjTxnJFHR7188/5bsk6lwzHHiCXqhrNiGIAfGAFeUQijnBhS9yzGyPC2OEwXqxzskDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:30:25.968032Z"},"content_sha256":"a083374c989a5d4c9cce3a082d5cf811caa79f91d1ea281ad3e68dc71a96cd8d","schema_version":"1.0","event_id":"sha256:a083374c989a5d4c9cce3a082d5cf811caa79f91d1ea281ad3e68dc71a96cd8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:BU5BFNHX7LBB6HA7KX37CO7O7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedded Defects","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Manuel Barriola, Martin Bucher, Tanmay Vachaspati","submitted_at":"1993-06-22T22:14:10Z","abstract_excerpt":"We give a prescription for embedding classical solutions and, in particular, topological defects in field theories which are invariant under symmetry groups that are not necessarily simple. After providing examples of embedded defects in field theories based on simple groups, we consider the electroweak model and show that it contains the $Z$ string and a one parameter family of strings called the $W(\\alpha )$ string. It is argued that, although the members of this family are gauge equivalent when considered in isolation, each member should be considered distinct when multi-string solutions ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306120","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":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H1zEu58wu4bjyPS63kXaLWbsiTu0hp5YLXhTjfpTrL4afQApRsHefxxlA+W+61/Q9K+SILH3cLosTQRsHcTUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:30:25.968646Z"},"content_sha256":"a40f1da47c02cf66f6b0dee47daf85b5455346da0d0f97e6628f131d5aa41812","schema_version":"1.0","event_id":"sha256:a40f1da47c02cf66f6b0dee47daf85b5455346da0d0f97e6628f131d5aa41812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/bundle.json","state_url":"https://pith.science/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/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":"2026-05-27T04:30:25Z","links":{"resolver":"https://pith.science/pith/BU5BFNHX7LBB6HA7KX37CO7O7I","bundle":"https://pith.science/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/bundle.json","state":"https://pith.science/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BU5BFNHX7LBB6HA7KX37CO7O7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:BU5BFNHX7LBB6HA7KX37CO7O7I","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":"8affe03784cdd67caeea28390b60bb740acdc54d2062935bf263b697cf99f8b0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-22T22:14:10Z","title_canon_sha256":"6f77c446440ba3f68e90d33d3177c8d6ea8ce030ea942c7bb59e286c17c6f6ee"},"schema_version":"1.0","source":{"id":"hep-th/9306120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9306120","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9306120v1","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9306120","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"BU5BFNHX7LBB","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"BU5BFNHX7LBB6HA7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"BU5BFNHX","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:a40f1da47c02cf66f6b0dee47daf85b5455346da0d0f97e6628f131d5aa41812","target":"graph","created_at":"2026-05-18T04:37:43Z","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 give a prescription for embedding classical solutions and, in particular, topological defects in field theories which are invariant under symmetry groups that are not necessarily simple. After providing examples of embedded defects in field theories based on simple groups, we consider the electroweak model and show that it contains the $Z$ string and a one parameter family of strings called the $W(\\alpha )$ string. It is argued that, although the members of this family are gauge equivalent when considered in isolation, each member should be considered distinct when multi-string solutions ar","authors_text":"Manuel Barriola, Martin Bucher, Tanmay Vachaspati","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-06-22T22:14:10Z","title":"Embedded Defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9306120","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:a083374c989a5d4c9cce3a082d5cf811caa79f91d1ea281ad3e68dc71a96cd8d","target":"record","created_at":"2026-05-18T04:37:43Z","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":"8affe03784cdd67caeea28390b60bb740acdc54d2062935bf263b697cf99f8b0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-06-22T22:14:10Z","title_canon_sha256":"6f77c446440ba3f68e90d33d3177c8d6ea8ce030ea942c7bb59e286c17c6f6ee"},"schema_version":"1.0","source":{"id":"hep-th/9306120","kind":"arxiv","version":1}},"canonical_sha256":"0d3a12b4f7fac21f1c1f55f7f13beefa00dde7a89650d302d9b60c275f9bd94c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d3a12b4f7fac21f1c1f55f7f13beefa00dde7a89650d302d9b60c275f9bd94c","first_computed_at":"2026-05-18T04:37:43.320575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:43.320575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3kj2/MdGLosbVsgaQuxErSkeOFwcLzKOAF5jlu1TYwrCthmI0qn+4U6SV7CIM049F09Osh3UgMkNQeIv4lvLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:43.321299Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9306120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a083374c989a5d4c9cce3a082d5cf811caa79f91d1ea281ad3e68dc71a96cd8d","sha256:a40f1da47c02cf66f6b0dee47daf85b5455346da0d0f97e6628f131d5aa41812"],"state_sha256":"546094a87689de4f7f79ec3eb4f4bf6467978fd930759548c3da5c5794abc3d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GgNWaWSeQxedsnsPUu4zfSqJsHR2NzLrCY+X4iFZluswTRu0qiiVwlSfuAl9Ra3yckye6ZGhisWlKQolURVfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:30:25.971802Z","bundle_sha256":"ef8390e5eb37e59f34b13a9f3125668bd937080f8b33815d8e88bbfde6d738fc"}}