{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6DTGJ5GZOFX2FIY4TLTCGUYECD","short_pith_number":"pith:6DTGJ5GZ","canonical_record":{"source":{"id":"1601.04060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-15T20:45:55Z","cross_cats_sorted":[],"title_canon_sha256":"cc85dfba8ea51b1bfd80f2e1a71be0719ae47e9edd4c5a8caf67ef0ccb1da950","abstract_canon_sha256":"8d292eac918ca7cd94a38cb8de1759ffc7d049b142c5b07ab9b1940ace32f765"},"schema_version":"1.0"},"canonical_sha256":"f0e664f4d9716fa2a31c9ae623530410e94e7677479348afbd5af4ae04a577f6","source":{"kind":"arxiv","id":"1601.04060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04060","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04060v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04060","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"6DTGJ5GZOFX2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6DTGJ5GZOFX2FIY4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6DTGJ5GZ","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6DTGJ5GZOFX2FIY4TLTCGUYECD","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-15T20:45:55Z","cross_cats_sorted":[],"title_canon_sha256":"cc85dfba8ea51b1bfd80f2e1a71be0719ae47e9edd4c5a8caf67ef0ccb1da950","abstract_canon_sha256":"8d292eac918ca7cd94a38cb8de1759ffc7d049b142c5b07ab9b1940ace32f765"},"schema_version":"1.0"},"canonical_sha256":"f0e664f4d9716fa2a31c9ae623530410e94e7677479348afbd5af4ae04a577f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.732938Z","signature_b64":"W8JMTkXtKuOe7dYTB7UMk0e46jHg6MISyxbP5U9EQeYr1KDo3F/+vwYu+K2K1Xwx9gQFfHIYarxsvCkk3r5kDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0e664f4d9716fa2a31c9ae623530410e94e7677479348afbd5af4ae04a577f6","last_reissued_at":"2026-05-18T00:50:13.732441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.732441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04060","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBJutgA7JWGcN8ZTdZB70ITOSc6Qy4VSbEYuLg4IFpKkbK2w6R7407urmPR0QeSF5l7kbZ0qhbXSCasTjtsyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:04.550197Z"},"content_sha256":"0a26323a7b5e9db15d6423e674d09f5ae91e39bb5ec513779320fb11c84326c0","schema_version":"1.0","event_id":"sha256:0a26323a7b5e9db15d6423e674d09f5ae91e39bb5ec513779320fb11c84326c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6DTGJ5GZOFX2FIY4TLTCGUYECD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexandre Eremenko, Andrei Gabrielov","submitted_at":"2016-01-15T20:45:55Z","abstract_excerpt":"We study spherical quadrilaterals whose angles are odd multiples of pi/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are finitely many one-dimensional continuous families which we enumerate. In each family the conformal modulus is either bounded from above or bounded from below, but not both, and the numbers of families of these two types are equal. The results can be translated to classification of Heun's equations with real parameters, whose exponent differences are odd multi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04060","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+etQD3ZCC21DU0Z8Mce6CLbeBGE/B8AgxjKGjR0t0hmUu4rNrKmUY7lijkwl0LvoWJW+bwlver/rVfm4yyrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:04.550606Z"},"content_sha256":"0f5f92b7ccb0b3fe048c3dc0cf6568daf58a4ad026070d829c9cd285786ecdee","schema_version":"1.0","event_id":"sha256:0f5f92b7ccb0b3fe048c3dc0cf6568daf58a4ad026070d829c9cd285786ecdee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/bundle.json","state_url":"https://pith.science/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/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":"2026-05-29T14:57:04Z","links":{"resolver":"https://pith.science/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD","bundle":"https://pith.science/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/bundle.json","state":"https://pith.science/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DTGJ5GZOFX2FIY4TLTCGUYECD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6DTGJ5GZOFX2FIY4TLTCGUYECD","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":"8d292eac918ca7cd94a38cb8de1759ffc7d049b142c5b07ab9b1940ace32f765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-15T20:45:55Z","title_canon_sha256":"cc85dfba8ea51b1bfd80f2e1a71be0719ae47e9edd4c5a8caf67ef0ccb1da950"},"schema_version":"1.0","source":{"id":"1601.04060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04060","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04060v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04060","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"6DTGJ5GZOFX2","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6DTGJ5GZOFX2FIY4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6DTGJ5GZ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:0f5f92b7ccb0b3fe048c3dc0cf6568daf58a4ad026070d829c9cd285786ecdee","target":"graph","created_at":"2026-05-18T00:50:13Z","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 study spherical quadrilaterals whose angles are odd multiples of pi/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are finitely many one-dimensional continuous families which we enumerate. In each family the conformal modulus is either bounded from above or bounded from below, but not both, and the numbers of families of these two types are equal. The results can be translated to classification of Heun's equations with real parameters, whose exponent differences are odd multi","authors_text":"Alexandre Eremenko, Andrei Gabrielov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-15T20:45:55Z","title":"Spherical rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04060","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":"sha256:0a26323a7b5e9db15d6423e674d09f5ae91e39bb5ec513779320fb11c84326c0","target":"record","created_at":"2026-05-18T00:50:13Z","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":"8d292eac918ca7cd94a38cb8de1759ffc7d049b142c5b07ab9b1940ace32f765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-15T20:45:55Z","title_canon_sha256":"cc85dfba8ea51b1bfd80f2e1a71be0719ae47e9edd4c5a8caf67ef0ccb1da950"},"schema_version":"1.0","source":{"id":"1601.04060","kind":"arxiv","version":1}},"canonical_sha256":"f0e664f4d9716fa2a31c9ae623530410e94e7677479348afbd5af4ae04a577f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0e664f4d9716fa2a31c9ae623530410e94e7677479348afbd5af4ae04a577f6","first_computed_at":"2026-05-18T00:50:13.732441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.732441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W8JMTkXtKuOe7dYTB7UMk0e46jHg6MISyxbP5U9EQeYr1KDo3F/+vwYu+K2K1Xwx9gQFfHIYarxsvCkk3r5kDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.732938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a26323a7b5e9db15d6423e674d09f5ae91e39bb5ec513779320fb11c84326c0","sha256:0f5f92b7ccb0b3fe048c3dc0cf6568daf58a4ad026070d829c9cd285786ecdee"],"state_sha256":"14a6c445efd6f641c51bf79b811a3ce4377812e2954a14a35227cfdc94716e8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6uy32AFzDM4G0ijJlXROoKokRSIt7r7gM3RCPN9qTOwT2GuKVMJrMPHReTOnvx8aXq5hocTD3ogzDuY6Bm0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:57:04.553519Z","bundle_sha256":"6173c72ce32108bc13205a1062b9f8db1ff12425bc41563696731340a3d5acce"}}