{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IDBY3I5EUYDLPDEB7BPALX5LM6","short_pith_number":"pith:IDBY3I5E","canonical_record":{"source":{"id":"1607.07081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-24T19:16:31Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9a07a3179981cae2c1200400893807fc27f0f2713ab7e6c5e41c1b4e85cbce2f","abstract_canon_sha256":"9d0439df5610ffc3da5188353456ada9f46890889a9edbcaabef0bf363350b01"},"schema_version":"1.0"},"canonical_sha256":"40c38da3a4a606b78c81f85e05dfab6798fa04dbc6b5d70af5bf9153177d470c","source":{"kind":"arxiv","id":"1607.07081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07081","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07081v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07081","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"IDBY3I5EUYDL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IDBY3I5EUYDLPDEB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IDBY3I5E","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IDBY3I5EUYDLPDEB7BPALX5LM6","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-24T19:16:31Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9a07a3179981cae2c1200400893807fc27f0f2713ab7e6c5e41c1b4e85cbce2f","abstract_canon_sha256":"9d0439df5610ffc3da5188353456ada9f46890889a9edbcaabef0bf363350b01"},"schema_version":"1.0"},"canonical_sha256":"40c38da3a4a606b78c81f85e05dfab6798fa04dbc6b5d70af5bf9153177d470c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:34.860538Z","signature_b64":"/dOGP2PkmvR77A+f+5d/o1Xb9tN2D88e8GyYjUd5mXl+5asFO9xkFAfGeO40gbzm8DFZoX2Isz2uptgdyLv4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40c38da3a4a606b78c81f85e05dfab6798fa04dbc6b5d70af5bf9153177d470c","last_reissued_at":"2026-05-18T01:10:34.859765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:34.859765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07081","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":"2026-05-18T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpdGb5H75tzxkHcrNsKsO5u2EVnQF11pNIbN+gaA85aa0dwKhp0YfquXLhVL8OuTkynp+WXegL/3MODZL/tzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:16.002848Z"},"content_sha256":"d0b32e09f8b8d3f1b1d6cb74e74180bdc67c36f23d670688ed62c24a60d1e09d","schema_version":"1.0","event_id":"sha256:d0b32e09f8b8d3f1b1d6cb74e74180bdc67c36f23d670688ed62c24a60d1e09d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IDBY3I5EUYDLPDEB7BPALX5LM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orbifold autoequivalent exceptional unimodal singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.QA","authors_text":"Ana Ros Camacho, Rachel Newton","submitted_at":"2016-07-24T19:16:31Z","abstract_excerpt":"We prove that different expressions of the same exceptional unimodal singularity are orbifold equivalent. As in our previous paper, the matrix factorizations proving these orbifold equivalences depend again on certain parameters satisfying some equations whose solutions are permuted by Galois groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07081","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":""},"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":"2026-05-18T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPpZI1KqPUH/Bj+e75LXwsKi34XuM8tfhGU3XKgQmabKrmPv+uQ+fuvjj0DUtbXUzp+JSx1cFCV0/laVqmA+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:16.003199Z"},"content_sha256":"6c82531fae86bc7d85ba78e48bf757d5b6f88757206fb1c25168890deccf2e17","schema_version":"1.0","event_id":"sha256:6c82531fae86bc7d85ba78e48bf757d5b6f88757206fb1c25168890deccf2e17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/bundle.json","state_url":"https://pith.science/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/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":"2026-06-03T18:37:16Z","links":{"resolver":"https://pith.science/pith/IDBY3I5EUYDLPDEB7BPALX5LM6","bundle":"https://pith.science/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/bundle.json","state":"https://pith.science/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDBY3I5EUYDLPDEB7BPALX5LM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IDBY3I5EUYDLPDEB7BPALX5LM6","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":"9d0439df5610ffc3da5188353456ada9f46890889a9edbcaabef0bf363350b01","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-24T19:16:31Z","title_canon_sha256":"9a07a3179981cae2c1200400893807fc27f0f2713ab7e6c5e41c1b4e85cbce2f"},"schema_version":"1.0","source":{"id":"1607.07081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07081","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07081v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07081","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"IDBY3I5EUYDL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IDBY3I5EUYDLPDEB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IDBY3I5E","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:6c82531fae86bc7d85ba78e48bf757d5b6f88757206fb1c25168890deccf2e17","target":"graph","created_at":"2026-05-18T01:10:34Z","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 prove that different expressions of the same exceptional unimodal singularity are orbifold equivalent. As in our previous paper, the matrix factorizations proving these orbifold equivalences depend again on certain parameters satisfying some equations whose solutions are permuted by Galois groups.","authors_text":"Ana Ros Camacho, Rachel Newton","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-24T19:16:31Z","title":"Orbifold autoequivalent exceptional unimodal singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07081","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:d0b32e09f8b8d3f1b1d6cb74e74180bdc67c36f23d670688ed62c24a60d1e09d","target":"record","created_at":"2026-05-18T01:10:34Z","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":"9d0439df5610ffc3da5188353456ada9f46890889a9edbcaabef0bf363350b01","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-24T19:16:31Z","title_canon_sha256":"9a07a3179981cae2c1200400893807fc27f0f2713ab7e6c5e41c1b4e85cbce2f"},"schema_version":"1.0","source":{"id":"1607.07081","kind":"arxiv","version":1}},"canonical_sha256":"40c38da3a4a606b78c81f85e05dfab6798fa04dbc6b5d70af5bf9153177d470c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c38da3a4a606b78c81f85e05dfab6798fa04dbc6b5d70af5bf9153177d470c","first_computed_at":"2026-05-18T01:10:34.859765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:34.859765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dOGP2PkmvR77A+f+5d/o1Xb9tN2D88e8GyYjUd5mXl+5asFO9xkFAfGeO40gbzm8DFZoX2Isz2uptgdyLv4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:34.860538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b32e09f8b8d3f1b1d6cb74e74180bdc67c36f23d670688ed62c24a60d1e09d","sha256:6c82531fae86bc7d85ba78e48bf757d5b6f88757206fb1c25168890deccf2e17"],"state_sha256":"c339f9544dcb7730dea7eafe3a4390b68940a572249ddc675da4703e4002faf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7E2ulka/R6Pdkj9w7HeigBJhpB/gl3kwbngZ7qUi2XHrywezgxTcZE0Xm0n1gAmUG33vJ3So6Hb60LjCS44BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:16.005243Z","bundle_sha256":"73154600b37be2b49f1d58d0570a520bee1e168b5a7157ba053ed1dc28abd5d8"}}