{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3NNUMOZXUODWRYAPFSEDWZZV6V","short_pith_number":"pith:3NNUMOZX","canonical_record":{"source":{"id":"1503.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-17T18:46:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c638345b20b03932e1e406f69128738c61b49e6c5b5486c344eff54cbc64c561","abstract_canon_sha256":"67093b640e4b96b4c599ed9255117a9f117bd910996faa4da13c18d12177bcee"},"schema_version":"1.0"},"canonical_sha256":"db5b463b37a38768e00f2c883b6735f5512e6c94fe787ebf33c04c1cf901f4d5","source":{"kind":"arxiv","id":"1503.05159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05159","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05159v2","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05159","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"3NNUMOZXUODW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3NNUMOZXUODWRYAP","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3NNUMOZX","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3NNUMOZXUODWRYAPFSEDWZZV6V","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-17T18:46:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c638345b20b03932e1e406f69128738c61b49e6c5b5486c344eff54cbc64c561","abstract_canon_sha256":"67093b640e4b96b4c599ed9255117a9f117bd910996faa4da13c18d12177bcee"},"schema_version":"1.0"},"canonical_sha256":"db5b463b37a38768e00f2c883b6735f5512e6c94fe787ebf33c04c1cf901f4d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:33.689944Z","signature_b64":"PWEyQVkSvV+gXTQxkQXl6Kf3jINFPWL7MKXCoEe1mmcIP+eYP1vcFyTnKPZVGI303QeDIB3pRBCPaKSP5Nk5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db5b463b37a38768e00f2c883b6735f5512e6c94fe787ebf33c04c1cf901f4d5","last_reissued_at":"2026-05-18T01:36:33.689558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:33.689558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05159","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":"2026-05-18T01:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nfl1+76vFicVv9jaFqDG+YUX/lwpsOArMqau2WqfbLsvkbtZMTSEYv/TiMaiQD/1kgXzZYpjoWhZidAC0ZnQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:59:40.069571Z"},"content_sha256":"2e9569222016479345722115a2ad51bb25fb2e2c1f882e5576152c4d01ee325f","schema_version":"1.0","event_id":"sha256:2e9569222016479345722115a2ad51bb25fb2e2c1f882e5576152c4d01ee325f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3NNUMOZXUODWRYAPFSEDWZZV6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N=1 theories of class S_k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Davide Gaiotto, Shlomo S. Razamat","submitted_at":"2015-03-17T18:46:10Z","abstract_excerpt":"We construct classes of ${\\cal N}=1$ superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two integers (N,k). The k=1 case coincides with A_{N-1} ${\\cal N}=2$ theories of class S and simple examples of theories with k>1 are Z_k orbifolds of some of the A_{N-1} class S theories. For the space of ${\\cal N}=1$ theories to be complete in an appropriate sense we find it necessary to conjecture existence of new ${\\cal N}=1$ strongly coupled SCFTs. These S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05159","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":"2026-05-18T01:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QAQD4owtR+IGjy2L88XO/r7Je12CudqVei0D1gUX6mR4+LlZy3jDsOjpQLZGT1Mz5clsSnn8gfmLqjNyfq5XAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:59:40.070238Z"},"content_sha256":"bbccfaaeef57027d7029d6f14f1789c4b68d23500a9f617d910b86d807235bbe","schema_version":"1.0","event_id":"sha256:bbccfaaeef57027d7029d6f14f1789c4b68d23500a9f617d910b86d807235bbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/bundle.json","state_url":"https://pith.science/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/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":"2026-05-26T19:59:40Z","links":{"resolver":"https://pith.science/pith/3NNUMOZXUODWRYAPFSEDWZZV6V","bundle":"https://pith.science/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/bundle.json","state":"https://pith.science/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NNUMOZXUODWRYAPFSEDWZZV6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3NNUMOZXUODWRYAPFSEDWZZV6V","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":"67093b640e4b96b4c599ed9255117a9f117bd910996faa4da13c18d12177bcee","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-17T18:46:10Z","title_canon_sha256":"c638345b20b03932e1e406f69128738c61b49e6c5b5486c344eff54cbc64c561"},"schema_version":"1.0","source":{"id":"1503.05159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05159","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05159v2","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05159","created_at":"2026-05-18T01:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"3NNUMOZXUODW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3NNUMOZXUODWRYAP","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3NNUMOZX","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:bbccfaaeef57027d7029d6f14f1789c4b68d23500a9f617d910b86d807235bbe","target":"graph","created_at":"2026-05-18T01:36:33Z","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 construct classes of ${\\cal N}=1$ superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two integers (N,k). The k=1 case coincides with A_{N-1} ${\\cal N}=2$ theories of class S and simple examples of theories with k>1 are Z_k orbifolds of some of the A_{N-1} class S theories. For the space of ${\\cal N}=1$ theories to be complete in an appropriate sense we find it necessary to conjecture existence of new ${\\cal N}=1$ strongly coupled SCFTs. These S","authors_text":"Davide Gaiotto, Shlomo S. Razamat","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-17T18:46:10Z","title":"N=1 theories of class S_k"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05159","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":"sha256:2e9569222016479345722115a2ad51bb25fb2e2c1f882e5576152c4d01ee325f","target":"record","created_at":"2026-05-18T01:36:33Z","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":"67093b640e4b96b4c599ed9255117a9f117bd910996faa4da13c18d12177bcee","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-17T18:46:10Z","title_canon_sha256":"c638345b20b03932e1e406f69128738c61b49e6c5b5486c344eff54cbc64c561"},"schema_version":"1.0","source":{"id":"1503.05159","kind":"arxiv","version":2}},"canonical_sha256":"db5b463b37a38768e00f2c883b6735f5512e6c94fe787ebf33c04c1cf901f4d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db5b463b37a38768e00f2c883b6735f5512e6c94fe787ebf33c04c1cf901f4d5","first_computed_at":"2026-05-18T01:36:33.689558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:33.689558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PWEyQVkSvV+gXTQxkQXl6Kf3jINFPWL7MKXCoEe1mmcIP+eYP1vcFyTnKPZVGI303QeDIB3pRBCPaKSP5Nk5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:33.689944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e9569222016479345722115a2ad51bb25fb2e2c1f882e5576152c4d01ee325f","sha256:bbccfaaeef57027d7029d6f14f1789c4b68d23500a9f617d910b86d807235bbe"],"state_sha256":"29d8287e45fa0d73f0d93b72c7761abc22f2f5c83bad52f4145d071f39b49443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nplk3VdlA1lK7hnE6l1PyUXfdkYDRgVoAG6OgyiEMLIDthIQ2OQnXBMcLkNpnvjEDHOjH0V8k4rlhZYdRrLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:59:40.073648Z","bundle_sha256":"1e18f25ea8f8fc7fba9f2053eca542bf420d7a0944a327117947784821a7402a"}}