{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SVBZY4DYXNDBJNTPLGXZXSLKPF","short_pith_number":"pith:SVBZY4DY","canonical_record":{"source":{"id":"2606.01376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-31T18:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"e7876a0fe929e641c95bf753c5f4906b54fa9bb5e2979adbdebfc2faa3347e36","abstract_canon_sha256":"1ef8ec36f07a0447b4c0487249febf74e7665e5bbc0af94214bcf17b1847e6ea"},"schema_version":"1.0"},"canonical_sha256":"95439c7078bb4614b66f59af9bc96a7944caf447b0b4bed3b9b0ece8f9cde730","source":{"kind":"arxiv","id":"2606.01376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01376","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01376v1","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01376","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"SVBZY4DYXNDB","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_16","alias_value":"SVBZY4DYXNDBJNTP","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_8","alias_value":"SVBZY4DY","created_at":"2026-06-02T02:04:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SVBZY4DYXNDBJNTPLGXZXSLKPF","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-31T18:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"e7876a0fe929e641c95bf753c5f4906b54fa9bb5e2979adbdebfc2faa3347e36","abstract_canon_sha256":"1ef8ec36f07a0447b4c0487249febf74e7665e5bbc0af94214bcf17b1847e6ea"},"schema_version":"1.0"},"canonical_sha256":"95439c7078bb4614b66f59af9bc96a7944caf447b0b4bed3b9b0ece8f9cde730","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:31.736849Z","signature_b64":"fNv4JkEmlxFkQGAgqE898BsylewLiXUSq+l6Nq5REqIABcS0DJCAV8zHnNYZffxGCBRlivXobeMa58tovK2XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95439c7078bb4614b66f59af9bc96a7944caf447b0b4bed3b9b0ece8f9cde730","last_reissued_at":"2026-06-02T02:04:31.736497Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:31.736497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01376","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":"2026-06-02T02:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GI8RZjSLKFASvBhFH9Au1KudhBct/ya8hx1QZoxcVXxEfsO2/l8BT3JoNP4oKhT7pQ4YQaiqGA+9Ww7G1yDQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:54:35.090048Z"},"content_sha256":"ba89ae33e6e680960fe2e8a073b98fff4b558d292451d7a16a7baaf418b030f0","schema_version":"1.0","event_id":"sha256:ba89ae33e6e680960fe2e8a073b98fff4b558d292451d7a16a7baaf418b030f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SVBZY4DYXNDBJNTPLGXZXSLKPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A construction of spherical $5$-designs with $O(d^2)$ points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrii Arman, Andriy Bondarenko, Andriy Prymak, Danylo Radchenko","submitted_at":"2026-05-31T18:06:43Z","abstract_excerpt":"For every $d\\geq1$ we give an explicit equal-weight spherical $5$-design in $\\mathbb{S}^{d-1}\\subset\\mathbb{R}^d$ with at most $72d^2$ points. Our approach utilizes recent construction of complex projective $2$-designs based on Sidon sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01376/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":"2026-06-02T02:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nXYB0cifz3zKooPCvvznnalu0u01faveFazlaUnY28L1i/v/hvTmNrX1mpdeUfTFd5RB1Z+ATyVstIQXvfczAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:54:35.090438Z"},"content_sha256":"6f3684cc60a7a6380cabd065c94a22d0c24fbced2b9b6acff8bef1753248495c","schema_version":"1.0","event_id":"sha256:6f3684cc60a7a6380cabd065c94a22d0c24fbced2b9b6acff8bef1753248495c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/bundle.json","state_url":"https://pith.science/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/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":"2026-06-04T22:54:35Z","links":{"resolver":"https://pith.science/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF","bundle":"https://pith.science/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/bundle.json","state":"https://pith.science/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVBZY4DYXNDBJNTPLGXZXSLKPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SVBZY4DYXNDBJNTPLGXZXSLKPF","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":"1ef8ec36f07a0447b4c0487249febf74e7665e5bbc0af94214bcf17b1847e6ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-31T18:06:43Z","title_canon_sha256":"e7876a0fe929e641c95bf753c5f4906b54fa9bb5e2979adbdebfc2faa3347e36"},"schema_version":"1.0","source":{"id":"2606.01376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01376","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01376v1","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01376","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"SVBZY4DYXNDB","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_16","alias_value":"SVBZY4DYXNDBJNTP","created_at":"2026-06-02T02:04:31Z"},{"alias_kind":"pith_short_8","alias_value":"SVBZY4DY","created_at":"2026-06-02T02:04:31Z"}],"graph_snapshots":[{"event_id":"sha256:6f3684cc60a7a6380cabd065c94a22d0c24fbced2b9b6acff8bef1753248495c","target":"graph","created_at":"2026-06-02T02:04:31Z","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/2606.01376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For every $d\\geq1$ we give an explicit equal-weight spherical $5$-design in $\\mathbb{S}^{d-1}\\subset\\mathbb{R}^d$ with at most $72d^2$ points. Our approach utilizes recent construction of complex projective $2$-designs based on Sidon sets.","authors_text":"Andrii Arman, Andriy Bondarenko, Andriy Prymak, Danylo Radchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-31T18:06:43Z","title":"A construction of spherical $5$-designs with $O(d^2)$ points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01376","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:ba89ae33e6e680960fe2e8a073b98fff4b558d292451d7a16a7baaf418b030f0","target":"record","created_at":"2026-06-02T02:04:31Z","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":"1ef8ec36f07a0447b4c0487249febf74e7665e5bbc0af94214bcf17b1847e6ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-31T18:06:43Z","title_canon_sha256":"e7876a0fe929e641c95bf753c5f4906b54fa9bb5e2979adbdebfc2faa3347e36"},"schema_version":"1.0","source":{"id":"2606.01376","kind":"arxiv","version":1}},"canonical_sha256":"95439c7078bb4614b66f59af9bc96a7944caf447b0b4bed3b9b0ece8f9cde730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95439c7078bb4614b66f59af9bc96a7944caf447b0b4bed3b9b0ece8f9cde730","first_computed_at":"2026-06-02T02:04:31.736497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:31.736497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fNv4JkEmlxFkQGAgqE898BsylewLiXUSq+l6Nq5REqIABcS0DJCAV8zHnNYZffxGCBRlivXobeMa58tovK2XAw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:31.736849Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba89ae33e6e680960fe2e8a073b98fff4b558d292451d7a16a7baaf418b030f0","sha256:6f3684cc60a7a6380cabd065c94a22d0c24fbced2b9b6acff8bef1753248495c"],"state_sha256":"5e5e6b1828dfe45b8272e44003c88d31224baf2bb1d75ce1533a807758197784"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jHsoUmZUgypEMx8+DKucggHBdwOwOwDs1QyM3oMQOMEAskBRqqQt5ZrVM2wrjHBozNwgJNB8++JTxhLhPUUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:54:35.092698Z","bundle_sha256":"6583dd1ad79ee1ebee463f1fbebed6fe35f71f0ae15af2c89e7a640fac49e40e"}}