{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ILU4WN2BXVTJVZJO46JNMRTSCR","short_pith_number":"pith:ILU4WN2B","canonical_record":{"source":{"id":"1301.7009","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2013-01-29T18:19:03Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"title_canon_sha256":"83d38cdb77931b55209474aca78dec8ad0a68fee884d22a31e4556c3254c3310","abstract_canon_sha256":"0a9de09461a992733b15df35d25dc9b55b3a223f44c8be5a66a2a9b924486e8c"},"schema_version":"1.0"},"canonical_sha256":"42e9cb3741bd669ae52ee792d64672145330dc68a537a600d73c8c5741e27bfe","source":{"kind":"arxiv","id":"1301.7009","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7009","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7009v2","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7009","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"ILU4WN2BXVTJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ILU4WN2BXVTJVZJO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ILU4WN2B","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ILU4WN2BXVTJVZJO46JNMRTSCR","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7009","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2013-01-29T18:19:03Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"title_canon_sha256":"83d38cdb77931b55209474aca78dec8ad0a68fee884d22a31e4556c3254c3310","abstract_canon_sha256":"0a9de09461a992733b15df35d25dc9b55b3a223f44c8be5a66a2a9b924486e8c"},"schema_version":"1.0"},"canonical_sha256":"42e9cb3741bd669ae52ee792d64672145330dc68a537a600d73c8c5741e27bfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:40.392396Z","signature_b64":"IdnK+lZL4OJ5UhGdB3B6yttTnuZbE43MHuHaSQPBq5LeZaoayfAdAMOz9IZfeqSH/dARKjgdYdMsl8J4rjhmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42e9cb3741bd669ae52ee792d64672145330dc68a537a600d73c8c5741e27bfe","last_reissued_at":"2026-05-18T03:29:40.391763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:40.391763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7009","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8U4ZL+Hb8gJoFwOmmWfJZhckeVmBTa5GizGFXwUzl3KI9XeRbgmoud/0u9bJ2PdEBZkX9SEfDHoPX7K3OsbbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:00:14.848795Z"},"content_sha256":"8ed82e13be46a9a5b22c6670693747beafb4a511d79e8a4fcaa8df384dcc8b93","schema_version":"1.0","event_id":"sha256:8ed82e13be46a9a5b22c6670693747beafb4a511d79e8a4fcaa8df384dcc8b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ILU4WN2BXVTJVZJO46JNMRTSCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Amending the Vafa-Witten Theorem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"primary_cat":"hep-th","authors_text":"Chuan Li, Qing Wang","submitted_at":"2013-01-29T18:19:03Z","abstract_excerpt":"The strong version of the Vafa-Witten theorem is shown may not to hold because the zero condensate from a direct computation of the order parameter is found to be a result on the symmetric vacuum. The validity of the Vafa-Witten theorem relies then on its weak version, that the Goldstone boson is absent in vector-like gauge theories with vanishing \\theta-angle. The existence of a charged \\rho-meson condensate, which violates electromagnetic gauge symmetry, is consistent with this weak version of the Vafa-Witten theorem when applied to strong magnetic fields in QCD."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7009","kind":"arxiv","version":2},"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":"2026-05-18T03:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jaTqSmwYldvR/ifyq7NdBHTApFCx8S+BOAUbsQYv2JfTvCUT/bim0xdSpVkAq2t6cVJM1PFr9M3BCQKaLlizBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:00:14.849142Z"},"content_sha256":"e6051f1c16b5457cf5634a746677aafc21d7826a94d70320e7a72438d2f68646","schema_version":"1.0","event_id":"sha256:e6051f1c16b5457cf5634a746677aafc21d7826a94d70320e7a72438d2f68646"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/bundle.json","state_url":"https://pith.science/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/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":"2026-06-01T10:00:14Z","links":{"resolver":"https://pith.science/pith/ILU4WN2BXVTJVZJO46JNMRTSCR","bundle":"https://pith.science/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/bundle.json","state":"https://pith.science/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ILU4WN2BXVTJVZJO46JNMRTSCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ILU4WN2BXVTJVZJO46JNMRTSCR","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":"0a9de09461a992733b15df35d25dc9b55b3a223f44c8be5a66a2a9b924486e8c","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2013-01-29T18:19:03Z","title_canon_sha256":"83d38cdb77931b55209474aca78dec8ad0a68fee884d22a31e4556c3254c3310"},"schema_version":"1.0","source":{"id":"1301.7009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7009","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7009v2","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7009","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"ILU4WN2BXVTJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ILU4WN2BXVTJVZJO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ILU4WN2B","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:e6051f1c16b5457cf5634a746677aafc21d7826a94d70320e7a72438d2f68646","target":"graph","created_at":"2026-05-18T03:29:40Z","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":"The strong version of the Vafa-Witten theorem is shown may not to hold because the zero condensate from a direct computation of the order parameter is found to be a result on the symmetric vacuum. The validity of the Vafa-Witten theorem relies then on its weak version, that the Goldstone boson is absent in vector-like gauge theories with vanishing \\theta-angle. The existence of a charged \\rho-meson condensate, which violates electromagnetic gauge symmetry, is consistent with this weak version of the Vafa-Witten theorem when applied to strong magnetic fields in QCD.","authors_text":"Chuan Li, Qing Wang","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2013-01-29T18:19:03Z","title":"Amending the Vafa-Witten Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7009","kind":"arxiv","version":2},"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":"sha256:8ed82e13be46a9a5b22c6670693747beafb4a511d79e8a4fcaa8df384dcc8b93","target":"record","created_at":"2026-05-18T03:29:40Z","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":"0a9de09461a992733b15df35d25dc9b55b3a223f44c8be5a66a2a9b924486e8c","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2013-01-29T18:19:03Z","title_canon_sha256":"83d38cdb77931b55209474aca78dec8ad0a68fee884d22a31e4556c3254c3310"},"schema_version":"1.0","source":{"id":"1301.7009","kind":"arxiv","version":2}},"canonical_sha256":"42e9cb3741bd669ae52ee792d64672145330dc68a537a600d73c8c5741e27bfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42e9cb3741bd669ae52ee792d64672145330dc68a537a600d73c8c5741e27bfe","first_computed_at":"2026-05-18T03:29:40.391763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:40.391763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IdnK+lZL4OJ5UhGdB3B6yttTnuZbE43MHuHaSQPBq5LeZaoayfAdAMOz9IZfeqSH/dARKjgdYdMsl8J4rjhmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:40.392396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed82e13be46a9a5b22c6670693747beafb4a511d79e8a4fcaa8df384dcc8b93","sha256:e6051f1c16b5457cf5634a746677aafc21d7826a94d70320e7a72438d2f68646"],"state_sha256":"68abfe8c5b0067fd20db3ab9dbfa412e82f3992acc6d973380f1f073ad52b5fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7zcjNRFHMSshVPBNNiKpD/6yFpfZqCuTtdULchyRIKJ86WuTC7JNbb6UNru2mdJKuIMql29pvz/xjdu3uiKJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:00:14.851169Z","bundle_sha256":"80b9a8ba1125c83c447b18a3cbc433d428760ccafc66670ec6e9f7744472b5ae"}}