{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VQBWG6XLPQGQW627J6ULG6LZ2B","short_pith_number":"pith:VQBWG6XL","canonical_record":{"source":{"id":"2508.00564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-08-01T12:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"c0b4422843a23aeb643e007bac43107a0dbf0e34cfedb09892a971736101464e","abstract_canon_sha256":"53372c04e76fd7eecc6073a8148a2743ee27b5b029e706f853ebf587feddb8a6"},"schema_version":"1.0"},"canonical_sha256":"ac03637aeb7c0d0b7b5f4fa8b37979d05ba5801c45263dbcc0fabb485afe7b8c","source":{"kind":"arxiv","id":"2508.00564","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00564","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00564v1","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00564","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"VQBWG6XLPQGQ","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_16","alias_value":"VQBWG6XLPQGQW627","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_8","alias_value":"VQBWG6XL","created_at":"2026-07-05T11:46:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VQBWG6XLPQGQW627J6ULG6LZ2B","target":"record","payload":{"canonical_record":{"source":{"id":"2508.00564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-08-01T12:04:49Z","cross_cats_sorted":[],"title_canon_sha256":"c0b4422843a23aeb643e007bac43107a0dbf0e34cfedb09892a971736101464e","abstract_canon_sha256":"53372c04e76fd7eecc6073a8148a2743ee27b5b029e706f853ebf587feddb8a6"},"schema_version":"1.0"},"canonical_sha256":"ac03637aeb7c0d0b7b5f4fa8b37979d05ba5801c45263dbcc0fabb485afe7b8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:58.147593Z","signature_b64":"AmUX8r7GWVYAXF13cTl68KW56ZV/jJLrcFhY2b4+aYLbAVemAzeCV+9Joz7XtgC6Al9QIUNZUVziPfAyIEfkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac03637aeb7c0d0b7b5f4fa8b37979d05ba5801c45263dbcc0fabb485afe7b8c","last_reissued_at":"2026-07-05T11:46:58.147085Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:58.147085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.00564","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":"2026-07-05T11:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQeJMP9uW3pvJ6Mz6FY996yppeAOXYllHPKwaXpAjAZWEI8Np9X4vNknsL0XkYOElhspuMk4Lk6Hgc+I/GlzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:05:44.427808Z"},"content_sha256":"2bd43a4b29a9ad85ec2f1a16c1c8f1b756fbcfcb0014e59828c30b62896f4b8b","schema_version":"1.0","event_id":"sha256:2bd43a4b29a9ad85ec2f1a16c1c8f1b756fbcfcb0014e59828c30b62896f4b8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VQBWG6XLPQGQW627J6ULG6LZ2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Aspects of 4d $\\mathcal{N}=1$ $ADE$ gauge theories from M-theory: decomposition, automorphisms, and generalised symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Marwan Najjar, Osama Khlaif","submitted_at":"2025-08-01T12:04:49Z","abstract_excerpt":"We study the decomposition of 4d $\\mathcal{N}=1$ gauge theories with Lie algebras of type $\\mathfrak{su}(N)$, $\\mathfrak{so}(2N)$, and $\\mathfrak{e}_{6}$, realized via M-theory geometric engineering. These theories, together with their novel decomposition structure, arise from quotienting the Bryant--Salamon spin bundle over the 3-sphere by special finite subgroups acting simultaneously on both the fiber and base. We show that these gauge theories admit both inner and outer automorphisms, enabling sequences of gauge theory breaking. In particular, outer automorphisms extend the decomposition s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00564","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.00564/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":"2026-07-05T11:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQE69Rv1WwSopujPa0TYwoSLB5knIaHRkiUGwCrHffGSui6N8dQFUM8J23dWdIYjht3JcWdKGHEWnx+cdfJOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:05:44.428331Z"},"content_sha256":"450b1395f0d896ec10b8cb32adc54ebf54ec6e51d723ca3ddb5a6afc13d39f56","schema_version":"1.0","event_id":"sha256:450b1395f0d896ec10b8cb32adc54ebf54ec6e51d723ca3ddb5a6afc13d39f56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/bundle.json","state_url":"https://pith.science/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/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":"2026-08-11T19:05:44Z","links":{"resolver":"https://pith.science/pith/VQBWG6XLPQGQW627J6ULG6LZ2B","bundle":"https://pith.science/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/bundle.json","state":"https://pith.science/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQBWG6XLPQGQW627J6ULG6LZ2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VQBWG6XLPQGQW627J6ULG6LZ2B","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":"53372c04e76fd7eecc6073a8148a2743ee27b5b029e706f853ebf587feddb8a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-08-01T12:04:49Z","title_canon_sha256":"c0b4422843a23aeb643e007bac43107a0dbf0e34cfedb09892a971736101464e"},"schema_version":"1.0","source":{"id":"2508.00564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00564","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00564v1","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00564","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"VQBWG6XLPQGQ","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_16","alias_value":"VQBWG6XLPQGQW627","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_8","alias_value":"VQBWG6XL","created_at":"2026-07-05T11:46:58Z"}],"graph_snapshots":[{"event_id":"sha256:450b1395f0d896ec10b8cb32adc54ebf54ec6e51d723ca3ddb5a6afc13d39f56","target":"graph","created_at":"2026-07-05T11:46:58Z","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/2508.00564/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the decomposition of 4d $\\mathcal{N}=1$ gauge theories with Lie algebras of type $\\mathfrak{su}(N)$, $\\mathfrak{so}(2N)$, and $\\mathfrak{e}_{6}$, realized via M-theory geometric engineering. These theories, together with their novel decomposition structure, arise from quotienting the Bryant--Salamon spin bundle over the 3-sphere by special finite subgroups acting simultaneously on both the fiber and base. We show that these gauge theories admit both inner and outer automorphisms, enabling sequences of gauge theory breaking. In particular, outer automorphisms extend the decomposition s","authors_text":"Marwan Najjar, Osama Khlaif","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-08-01T12:04:49Z","title":"Aspects of 4d $\\mathcal{N}=1$ $ADE$ gauge theories from M-theory: decomposition, automorphisms, and generalised symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00564","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":"sha256:2bd43a4b29a9ad85ec2f1a16c1c8f1b756fbcfcb0014e59828c30b62896f4b8b","target":"record","created_at":"2026-07-05T11:46:58Z","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":"53372c04e76fd7eecc6073a8148a2743ee27b5b029e706f853ebf587feddb8a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-08-01T12:04:49Z","title_canon_sha256":"c0b4422843a23aeb643e007bac43107a0dbf0e34cfedb09892a971736101464e"},"schema_version":"1.0","source":{"id":"2508.00564","kind":"arxiv","version":1}},"canonical_sha256":"ac03637aeb7c0d0b7b5f4fa8b37979d05ba5801c45263dbcc0fabb485afe7b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac03637aeb7c0d0b7b5f4fa8b37979d05ba5801c45263dbcc0fabb485afe7b8c","first_computed_at":"2026-07-05T11:46:58.147085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:58.147085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AmUX8r7GWVYAXF13cTl68KW56ZV/jJLrcFhY2b4+aYLbAVemAzeCV+9Joz7XtgC6Al9QIUNZUVziPfAyIEfkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:58.147593Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.00564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bd43a4b29a9ad85ec2f1a16c1c8f1b756fbcfcb0014e59828c30b62896f4b8b","sha256:450b1395f0d896ec10b8cb32adc54ebf54ec6e51d723ca3ddb5a6afc13d39f56"],"state_sha256":"5486d2ea290ea89d2242cc56ea9013f2dd244784354120b6b247173546a60e96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uosfJCfQy4vqJfwRLcIR9gC/ue42Yh3BctaheHUW2BHHd2d/+MwPqqXB6rdyITfhK2qlsStRYVoSfAZVCxReAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T19:05:44.434814Z","bundle_sha256":"2b54275f18f37681b80404db7a0a3f3e0922f9b08869f6ef4f6dc9c54d82c8d5"}}