{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:S3FUKIJZ7RT5JXNQS6VGBNOJ4C","short_pith_number":"pith:S3FUKIJZ","canonical_record":{"source":{"id":"math/0106140","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-06-15T21:42:14Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"a9a8feb3ff396c9df31cad1b83a953dd438ffe79a8fcc70b6802bfafebeb276b","abstract_canon_sha256":"14cf50d13212806f06e56b7afd515950b0ddef0c74d9baf2f93d99e957b0aced"},"schema_version":"1.0"},"canonical_sha256":"96cb452139fc67d4ddb097aa60b5c9e0aa4a42abd0eef335c5e9ad543cafa462","source":{"kind":"arxiv","id":"math/0106140","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106140","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106140v2","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106140","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"S3FUKIJZ7RT5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3FUKIJZ7RT5JXNQ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3FUKIJZ","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:S3FUKIJZ7RT5JXNQS6VGBNOJ4C","target":"record","payload":{"canonical_record":{"source":{"id":"math/0106140","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-06-15T21:42:14Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"a9a8feb3ff396c9df31cad1b83a953dd438ffe79a8fcc70b6802bfafebeb276b","abstract_canon_sha256":"14cf50d13212806f06e56b7afd515950b0ddef0c74d9baf2f93d99e957b0aced"},"schema_version":"1.0"},"canonical_sha256":"96cb452139fc67d4ddb097aa60b5c9e0aa4a42abd0eef335c5e9ad543cafa462","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.915240Z","signature_b64":"nt/24hQLg3RmzjGf2sR5l0T3Zs17jZoliGyBhehzrfEgH6bk2ghI17Vl3LqiJPMDxICOdq4JeuKN2T4akiI9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96cb452139fc67d4ddb097aa60b5c9e0aa4a42abd0eef335c5e9ad543cafa462","last_reissued_at":"2026-05-18T01:38:29.914549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.914549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0106140","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGA51gj9EviPCShiC1boEEQ/BDKz3u62K81dKzII+J23u5UNDw34OcVCtKzL8Msb6qzsjrOwHqoLg8UUKX4SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:51:53.046502Z"},"content_sha256":"85fd7aba7de7f900f9c07ec8f834ffe6ee19e2e6ca1aa47c05bbc6bdc224f7f1","schema_version":"1.0","event_id":"sha256:85fd7aba7de7f900f9c07ec8f834ffe6ee19e2e6ca1aa47c05bbc6bdc224f7f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:S3FUKIJZ7RT5JXNQS6VGBNOJ4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Examples of mirror partners arising from integrable systems","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Michael Thaddeus, Tamas Hausel","submitted_at":"2001-06-15T21:42:14Z","abstract_excerpt":"In this note we present pairs of hyperkaehler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106140","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":"2026-05-18T01:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WB0hibmX1t9S+1ZJYqJotT2Mj14pIF2GY9y8jZVJel9+cBhgGExESS6AkMewJ2ue9IIV5qt0hbDVHailV18TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:51:53.047035Z"},"content_sha256":"bc6d27130b6278a16493b119b7655de56b2631e6da965772a1f080aca367d5d6","schema_version":"1.0","event_id":"sha256:bc6d27130b6278a16493b119b7655de56b2631e6da965772a1f080aca367d5d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/bundle.json","state_url":"https://pith.science/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/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":"2026-06-20T11:51:53Z","links":{"resolver":"https://pith.science/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C","bundle":"https://pith.science/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/bundle.json","state":"https://pith.science/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3FUKIJZ7RT5JXNQS6VGBNOJ4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:S3FUKIJZ7RT5JXNQS6VGBNOJ4C","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":"14cf50d13212806f06e56b7afd515950b0ddef0c74d9baf2f93d99e957b0aced","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.AG","submitted_at":"2001-06-15T21:42:14Z","title_canon_sha256":"a9a8feb3ff396c9df31cad1b83a953dd438ffe79a8fcc70b6802bfafebeb276b"},"schema_version":"1.0","source":{"id":"math/0106140","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106140","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106140v2","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106140","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"S3FUKIJZ7RT5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3FUKIJZ7RT5JXNQ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3FUKIJZ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:bc6d27130b6278a16493b119b7655de56b2631e6da965772a1f080aca367d5d6","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"In this note we present pairs of hyperkaehler orbifolds which satisfy two different versions of mirror symmetry. On the one hand, we show that their Hodge numbers (or more precisely, stringy E-polynomials) are equal. On the other hand, we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a Calabi-Yau and its mirror should fiber over the same real manifold, with special Lagrangian fibers which are tori dual to each other. Our examples arise as moduli spaces of local systems on a curve with s","authors_text":"Michael Thaddeus, Tamas Hausel","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-06-15T21:42:14Z","title":"Examples of mirror partners arising from integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106140","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":"sha256:85fd7aba7de7f900f9c07ec8f834ffe6ee19e2e6ca1aa47c05bbc6bdc224f7f1","target":"record","created_at":"2026-05-18T01:38:29Z","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":"14cf50d13212806f06e56b7afd515950b0ddef0c74d9baf2f93d99e957b0aced","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.AG","submitted_at":"2001-06-15T21:42:14Z","title_canon_sha256":"a9a8feb3ff396c9df31cad1b83a953dd438ffe79a8fcc70b6802bfafebeb276b"},"schema_version":"1.0","source":{"id":"math/0106140","kind":"arxiv","version":2}},"canonical_sha256":"96cb452139fc67d4ddb097aa60b5c9e0aa4a42abd0eef335c5e9ad543cafa462","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96cb452139fc67d4ddb097aa60b5c9e0aa4a42abd0eef335c5e9ad543cafa462","first_computed_at":"2026-05-18T01:38:29.914549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.914549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nt/24hQLg3RmzjGf2sR5l0T3Zs17jZoliGyBhehzrfEgH6bk2ghI17Vl3LqiJPMDxICOdq4JeuKN2T4akiI9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.915240Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0106140","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85fd7aba7de7f900f9c07ec8f834ffe6ee19e2e6ca1aa47c05bbc6bdc224f7f1","sha256:bc6d27130b6278a16493b119b7655de56b2631e6da965772a1f080aca367d5d6"],"state_sha256":"f91f5c2f2427e21c11907e2cdcd5f1dcdb942e2d5a5110b9972157dd27b5e8b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGOx4F7WpzMK4aem5RIWBEbNK280vT4h6b9dSox9c+ZmQTnIKk0GPbLQQJqYUYc/iSFHOOdxhDgeS9RPpYEcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:51:53.049699Z","bundle_sha256":"080b63a36d67ccdb330aaee4f5f0de5e5dbcf42630ea09f994af570f173dab8f"}}