{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:T6DDYA4X6J6MP3FZGPKTZMB5E2","short_pith_number":"pith:T6DDYA4X","canonical_record":{"source":{"id":"2006.03030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-04T17:33:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"011c847439324cf7294f9d740c0d43f32ef92a49a4f4c1040705d306f1a20e8e","abstract_canon_sha256":"8ac4daf1e7a150803788d21f30aab87c5d54d0ae23c85b0c236d3ced1dd9de51"},"schema_version":"1.0"},"canonical_sha256":"9f863c0397f27cc7ecb933d53cb03d2693a76c774ddff91d842485760cf15498","source":{"kind":"arxiv","id":"2006.03030","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.03030","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"2006.03030v3","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.03030","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"T6DDYA4X6J6M","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_16","alias_value":"T6DDYA4X6J6MP3FZ","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_8","alias_value":"T6DDYA4X","created_at":"2026-07-05T03:35:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:T6DDYA4X6J6MP3FZGPKTZMB5E2","target":"record","payload":{"canonical_record":{"source":{"id":"2006.03030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-04T17:33:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"011c847439324cf7294f9d740c0d43f32ef92a49a4f4c1040705d306f1a20e8e","abstract_canon_sha256":"8ac4daf1e7a150803788d21f30aab87c5d54d0ae23c85b0c236d3ced1dd9de51"},"schema_version":"1.0"},"canonical_sha256":"9f863c0397f27cc7ecb933d53cb03d2693a76c774ddff91d842485760cf15498","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:35:58.294946Z","signature_b64":"4bBcpTXbBxX7+QuQ0LmDEduKoELfg/vAiHKm/hwfHzARwm5DFEnGJ5MRnhxQAS5FCx3nJApxKjYqSFtAGayzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f863c0397f27cc7ecb933d53cb03d2693a76c774ddff91d842485760cf15498","last_reissued_at":"2026-07-05T03:35:58.294548Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:35:58.294548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.03030","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":"2026-07-05T03:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vooDqXCv/JdvJ1+1+6oG1Eeot/U9j647yjvtwegTKeC4zzTYPDQvFufEFNSS2XEXF9H/hHm380SVLEvbxQCkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T16:00:27.630877Z"},"content_sha256":"9dae4a97249d3622879ae46cad5e7e9688c90b5def5ba1ea81f012e6dc2fdf0a","schema_version":"1.0","event_id":"sha256:9dae4a97249d3622879ae46cad5e7e9688c90b5def5ba1ea81f012e6dc2fdf0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:T6DDYA4X6J6MP3FZGPKTZMB5E2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic Blowup Equations for 6d SCFTs. IV: Matters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Albrecht Klemm, Babak Haghighat, Jie Gu, Kaiwen Sun, Xin Wang","submitted_at":"2020-06-04T17:33:18Z","abstract_excerpt":"Given the recent geometrical classification of 6d $(1,0)$ SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d $(1,0)$ SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity- and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which det"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.03030","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/2006.03030/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":"2026-07-05T03:35:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zp6Vlll3QO9wwbgE2KB+FIdCYW3jOsRx4bGe+I1tIk29DgpCxVen+4sUzHudzmsuWF7MofZEuD32hY7CEWWNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T16:00:27.631263Z"},"content_sha256":"8ebe57bd54219149ea351780003e4490ef65a61395ed1ec130913553cbf2099c","schema_version":"1.0","event_id":"sha256:8ebe57bd54219149ea351780003e4490ef65a61395ed1ec130913553cbf2099c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/bundle.json","state_url":"https://pith.science/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/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":"2026-07-11T16:00:27Z","links":{"resolver":"https://pith.science/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2","bundle":"https://pith.science/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/bundle.json","state":"https://pith.science/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6DDYA4X6J6MP3FZGPKTZMB5E2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:T6DDYA4X6J6MP3FZGPKTZMB5E2","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":"8ac4daf1e7a150803788d21f30aab87c5d54d0ae23c85b0c236d3ced1dd9de51","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-04T17:33:18Z","title_canon_sha256":"011c847439324cf7294f9d740c0d43f32ef92a49a4f4c1040705d306f1a20e8e"},"schema_version":"1.0","source":{"id":"2006.03030","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.03030","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"2006.03030v3","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.03030","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"T6DDYA4X6J6M","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_16","alias_value":"T6DDYA4X6J6MP3FZ","created_at":"2026-07-05T03:35:58Z"},{"alias_kind":"pith_short_8","alias_value":"T6DDYA4X","created_at":"2026-07-05T03:35:58Z"}],"graph_snapshots":[{"event_id":"sha256:8ebe57bd54219149ea351780003e4490ef65a61395ed1ec130913553cbf2099c","target":"graph","created_at":"2026-07-05T03:35:58Z","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/2006.03030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given the recent geometrical classification of 6d $(1,0)$ SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d $(1,0)$ SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity- and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which det","authors_text":"Albrecht Klemm, Babak Haghighat, Jie Gu, Kaiwen Sun, Xin Wang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-04T17:33:18Z","title":"Elliptic Blowup Equations for 6d SCFTs. IV: Matters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.03030","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":"sha256:9dae4a97249d3622879ae46cad5e7e9688c90b5def5ba1ea81f012e6dc2fdf0a","target":"record","created_at":"2026-07-05T03:35:58Z","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":"8ac4daf1e7a150803788d21f30aab87c5d54d0ae23c85b0c236d3ced1dd9de51","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-06-04T17:33:18Z","title_canon_sha256":"011c847439324cf7294f9d740c0d43f32ef92a49a4f4c1040705d306f1a20e8e"},"schema_version":"1.0","source":{"id":"2006.03030","kind":"arxiv","version":3}},"canonical_sha256":"9f863c0397f27cc7ecb933d53cb03d2693a76c774ddff91d842485760cf15498","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f863c0397f27cc7ecb933d53cb03d2693a76c774ddff91d842485760cf15498","first_computed_at":"2026-07-05T03:35:58.294548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:35:58.294548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bBcpTXbBxX7+QuQ0LmDEduKoELfg/vAiHKm/hwfHzARwm5DFEnGJ5MRnhxQAS5FCx3nJApxKjYqSFtAGayzDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:35:58.294946Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.03030","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dae4a97249d3622879ae46cad5e7e9688c90b5def5ba1ea81f012e6dc2fdf0a","sha256:8ebe57bd54219149ea351780003e4490ef65a61395ed1ec130913553cbf2099c"],"state_sha256":"8c15d7dc29be3693da1eeb09749d53cf3009bd938d46fc88469e6e44ab273340"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBJDKgHAg9H73r6L2GAgsHchwaJJ0rWNJtySQJfYPraRJFowayI2sCE55Ba964RctodsUi6LrreKGmuchPDDCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T16:00:27.633339Z","bundle_sha256":"50d708419a3b1a740d1a7279d5a814a90ea74058d5432be3bad17ac8ab889467"}}