{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3IWJ3DJPLOD7BC7BKEWIKOXEEO","short_pith_number":"pith:3IWJ3DJP","canonical_record":{"source":{"id":"2302.13466","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-02-27T01:37:37Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"f4229b1ab467628d0621f4c096560fb2f8363c8d3c9742a38027987cdda6a961","abstract_canon_sha256":"5d222a02ee2cec113495cbbcd94e232d27e2b152dcb392c407ae20f7074420e0"},"schema_version":"1.0"},"canonical_sha256":"da2c9d8d2f5b87f08be1512c853ae423acb5a6df751665dccd77db5789d47604","source":{"kind":"arxiv","id":"2302.13466","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.13466","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"2302.13466v3","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.13466","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"3IWJ3DJPLOD7","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"3IWJ3DJPLOD7BC7B","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"3IWJ3DJP","created_at":"2026-07-05T07:31:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3IWJ3DJPLOD7BC7BKEWIKOXEEO","target":"record","payload":{"canonical_record":{"source":{"id":"2302.13466","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-02-27T01:37:37Z","cross_cats_sorted":["hep-lat"],"title_canon_sha256":"f4229b1ab467628d0621f4c096560fb2f8363c8d3c9742a38027987cdda6a961","abstract_canon_sha256":"5d222a02ee2cec113495cbbcd94e232d27e2b152dcb392c407ae20f7074420e0"},"schema_version":"1.0"},"canonical_sha256":"da2c9d8d2f5b87f08be1512c853ae423acb5a6df751665dccd77db5789d47604","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:31:51.515781Z","signature_b64":"XDL6gQeha0TEdAK2+f0MeRGX4aK6mK1BgIUV/vdZcNIr6k4ocNDRbCAbNpG6v1DJmRSKDcIUObnb0Vd6OGQiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da2c9d8d2f5b87f08be1512c853ae423acb5a6df751665dccd77db5789d47604","last_reissued_at":"2026-07-05T07:31:51.515400Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:31:51.515400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.13466","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":"2026-07-05T07:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0/uSFeRZIiZGCDk8D/Tv9oDnLOw+DPztsZvhoinwOYQDBQ88C7Qq+7K5ouhD83pbEag+isMEsftzbNrQFeJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:49.495686Z"},"content_sha256":"2f858f8c038eba8cf7f8d1ef1ac1e174be3fa9fdc55c0190ee0b06bae67b881f","schema_version":"1.0","event_id":"sha256:2f858f8c038eba8cf7f8d1ef1ac1e174be3fa9fdc55c0190ee0b06bae67b881f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3IWJ3DJPLOD7BC7BKEWIKOXEEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-group structure in lattice Abelian gauge theory under instanton-sum modification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"hep-th","authors_text":"Hiroki Wada, Naoto Kan, Okuto Morikawa, Yuta Nagoya","submitted_at":"2023-02-27T01:37:37Z","abstract_excerpt":"We consider the $U(1)$ gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green--Schwarz mechanism, between $\\mathbb{Z}_q$ $1$-form and $\\mathbb{Z}_{pq}$ $3$-form symmetries. Here, $\\mathbb{Z}_q$ is a subgroup of the center of~$U(1)$. Following the recent study of the lattice construction of the $U(1)/\\mathbb{Z}_q$ principal bundle, we examine how such a structure is realized on the basis of lattice regularization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.13466","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.13466/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sOq/UeJpj+kkrz2u14TcoC7Rn2ODHZH87p1lcyYVWeIv78f7EqgG9jMLgpnKwVXOfC8yN33IWJy1fcYAom7UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:49.496197Z"},"content_sha256":"504d437534c7ed1692319de0ae5c4f46cfab68b85259fe09d55be5e61f8f6096","schema_version":"1.0","event_id":"sha256:504d437534c7ed1692319de0ae5c4f46cfab68b85259fe09d55be5e61f8f6096"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/bundle.json","state_url":"https://pith.science/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/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":"2026-08-09T04:01:49Z","links":{"resolver":"https://pith.science/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO","bundle":"https://pith.science/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/bundle.json","state":"https://pith.science/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IWJ3DJPLOD7BC7BKEWIKOXEEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3IWJ3DJPLOD7BC7BKEWIKOXEEO","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":"5d222a02ee2cec113495cbbcd94e232d27e2b152dcb392c407ae20f7074420e0","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-02-27T01:37:37Z","title_canon_sha256":"f4229b1ab467628d0621f4c096560fb2f8363c8d3c9742a38027987cdda6a961"},"schema_version":"1.0","source":{"id":"2302.13466","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.13466","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"2302.13466v3","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.13466","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"3IWJ3DJPLOD7","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"3IWJ3DJPLOD7BC7B","created_at":"2026-07-05T07:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"3IWJ3DJP","created_at":"2026-07-05T07:31:51Z"}],"graph_snapshots":[{"event_id":"sha256:504d437534c7ed1692319de0ae5c4f46cfab68b85259fe09d55be5e61f8f6096","target":"graph","created_at":"2026-07-05T07:31:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.13466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the $U(1)$ gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green--Schwarz mechanism, between $\\mathbb{Z}_q$ $1$-form and $\\mathbb{Z}_{pq}$ $3$-form symmetries. Here, $\\mathbb{Z}_q$ is a subgroup of the center of~$U(1)$. Following the recent study of the lattice construction of the $U(1)/\\mathbb{Z}_q$ principal bundle, we examine how such a structure is realized on the basis of lattice regularization.","authors_text":"Hiroki Wada, Naoto Kan, Okuto Morikawa, Yuta Nagoya","cross_cats":["hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-02-27T01:37:37Z","title":"Higher-group structure in lattice Abelian gauge theory under instanton-sum modification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.13466","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":"sha256:2f858f8c038eba8cf7f8d1ef1ac1e174be3fa9fdc55c0190ee0b06bae67b881f","target":"record","created_at":"2026-07-05T07:31:51Z","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":"5d222a02ee2cec113495cbbcd94e232d27e2b152dcb392c407ae20f7074420e0","cross_cats_sorted":["hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-02-27T01:37:37Z","title_canon_sha256":"f4229b1ab467628d0621f4c096560fb2f8363c8d3c9742a38027987cdda6a961"},"schema_version":"1.0","source":{"id":"2302.13466","kind":"arxiv","version":3}},"canonical_sha256":"da2c9d8d2f5b87f08be1512c853ae423acb5a6df751665dccd77db5789d47604","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da2c9d8d2f5b87f08be1512c853ae423acb5a6df751665dccd77db5789d47604","first_computed_at":"2026-07-05T07:31:51.515400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:31:51.515400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDL6gQeha0TEdAK2+f0MeRGX4aK6mK1BgIUV/vdZcNIr6k4ocNDRbCAbNpG6v1DJmRSKDcIUObnb0Vd6OGQiBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:31:51.515781Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.13466","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f858f8c038eba8cf7f8d1ef1ac1e174be3fa9fdc55c0190ee0b06bae67b881f","sha256:504d437534c7ed1692319de0ae5c4f46cfab68b85259fe09d55be5e61f8f6096"],"state_sha256":"e13dbfc52fe1d8fbb3538382788130af1fd55fc3aa43ba607282fe7e50727f84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9QKe0pv1WoFDxajZFzbFp8r2xRkBoCWJOzNUzIDjIb/OteRThWIDt7id91wOTf59F94PHUUpJ5b2EBRDirhLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:01:49.499464Z","bundle_sha256":"acfb338ee7863e8105b32a2588f79ab7758de758acd2c3daf17c01fdda779614"}}