{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WGIXXHFFHMQLXDPGEGWA4FVRYP","short_pith_number":"pith:WGIXXHFF","canonical_record":{"source":{"id":"1611.09479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-29T04:06:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b0c2e10d7f1dbd383b66223d79ffdb71892c1c18b280c05eb514f3ce4fbc444b","abstract_canon_sha256":"f855534d26378814272d94d89d640162b11eebb08b901653d1c8215c376493bb"},"schema_version":"1.0"},"canonical_sha256":"b1917b9ca53b20bb8de621ac0e16b1c3dee22a9c17bb9a2f594ea656047bfc38","source":{"kind":"arxiv","id":"1611.09479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09479","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09479v1","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09479","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"WGIXXHFFHMQL","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WGIXXHFFHMQLXDPG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WGIXXHFF","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WGIXXHFFHMQLXDPGEGWA4FVRYP","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-29T04:06:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b0c2e10d7f1dbd383b66223d79ffdb71892c1c18b280c05eb514f3ce4fbc444b","abstract_canon_sha256":"f855534d26378814272d94d89d640162b11eebb08b901653d1c8215c376493bb"},"schema_version":"1.0"},"canonical_sha256":"b1917b9ca53b20bb8de621ac0e16b1c3dee22a9c17bb9a2f594ea656047bfc38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:11.678265Z","signature_b64":"jOq49YhtROlKooWE+zRSaopEU6KGuCaJZTQ/83UcZqV+RtgW4TGqM5SqBhf/S2E2d31DRrGWjqOlPSkaSCG+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1917b9ca53b20bb8de621ac0e16b1c3dee22a9c17bb9a2f594ea656047bfc38","last_reissued_at":"2026-05-18T00:56:11.677789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:11.677789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09479","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":"2026-05-18T00:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIE/szq1Wue+HzKlBXot9IBD569y1k+Pyry3/GXGnfg/31bWhwTOAn+hLTghEBYNrTE9YUpDZD1z4Sdv8ECGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:28:55.123510Z"},"content_sha256":"a25a9d20d1c33f7ed5ba53bcbd55aea13ccaac5c47b54bb3c66c3f4fd7191ad7","schema_version":"1.0","event_id":"sha256:a25a9d20d1c33f7ed5ba53bcbd55aea13ccaac5c47b54bb3c66c3f4fd7191ad7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WGIXXHFFHMQLXDPGEGWA4FVRYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bounds for $s$-distance sets and equiangular lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alexey Glazyrin, Wei-Hsuan Yu","submitted_at":"2016-11-29T04:06:20Z","abstract_excerpt":"The set of points in a metric space is called an $s$-distance set if pairwise distances between these points admit only $s$ distinct values. Two-distance spherical sets with the set of scalar products $\\{\\alpha, -\\alpha\\}$, $\\alpha\\in[0,1)$, are called equiangular. The problem of determining the maximum size of $s$-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an $s$-distance set in compact two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-dista"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09479","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":"2026-05-18T00:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CD/i0u2Z5H8bTx82sf7Dk4fXsoIVBs9dwiBitI/o6yoj48yFtmBi8V9vh3hI46bOhHK5yLHBRjarxZ4AGpb+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:28:55.124241Z"},"content_sha256":"0df6116010f51c075aef1e98295df9c72642a47ba659afdf133852d7f215f0b0","schema_version":"1.0","event_id":"sha256:0df6116010f51c075aef1e98295df9c72642a47ba659afdf133852d7f215f0b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/bundle.json","state_url":"https://pith.science/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/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":"2026-06-07T18:28:55Z","links":{"resolver":"https://pith.science/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP","bundle":"https://pith.science/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/bundle.json","state":"https://pith.science/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGIXXHFFHMQLXDPGEGWA4FVRYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WGIXXHFFHMQLXDPGEGWA4FVRYP","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":"f855534d26378814272d94d89d640162b11eebb08b901653d1c8215c376493bb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-29T04:06:20Z","title_canon_sha256":"b0c2e10d7f1dbd383b66223d79ffdb71892c1c18b280c05eb514f3ce4fbc444b"},"schema_version":"1.0","source":{"id":"1611.09479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09479","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09479v1","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09479","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"WGIXXHFFHMQL","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WGIXXHFFHMQLXDPG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WGIXXHFF","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:0df6116010f51c075aef1e98295df9c72642a47ba659afdf133852d7f215f0b0","target":"graph","created_at":"2026-05-18T00:56:11Z","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":"The set of points in a metric space is called an $s$-distance set if pairwise distances between these points admit only $s$ distinct values. Two-distance spherical sets with the set of scalar products $\\{\\alpha, -\\alpha\\}$, $\\alpha\\in[0,1)$, are called equiangular. The problem of determining the maximum size of $s$-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an $s$-distance set in compact two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-dista","authors_text":"Alexey Glazyrin, Wei-Hsuan Yu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-29T04:06:20Z","title":"Upper bounds for $s$-distance sets and equiangular lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09479","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:a25a9d20d1c33f7ed5ba53bcbd55aea13ccaac5c47b54bb3c66c3f4fd7191ad7","target":"record","created_at":"2026-05-18T00:56:11Z","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":"f855534d26378814272d94d89d640162b11eebb08b901653d1c8215c376493bb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-29T04:06:20Z","title_canon_sha256":"b0c2e10d7f1dbd383b66223d79ffdb71892c1c18b280c05eb514f3ce4fbc444b"},"schema_version":"1.0","source":{"id":"1611.09479","kind":"arxiv","version":1}},"canonical_sha256":"b1917b9ca53b20bb8de621ac0e16b1c3dee22a9c17bb9a2f594ea656047bfc38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1917b9ca53b20bb8de621ac0e16b1c3dee22a9c17bb9a2f594ea656047bfc38","first_computed_at":"2026-05-18T00:56:11.677789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:11.677789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jOq49YhtROlKooWE+zRSaopEU6KGuCaJZTQ/83UcZqV+RtgW4TGqM5SqBhf/S2E2d31DRrGWjqOlPSkaSCG+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:11.678265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a25a9d20d1c33f7ed5ba53bcbd55aea13ccaac5c47b54bb3c66c3f4fd7191ad7","sha256:0df6116010f51c075aef1e98295df9c72642a47ba659afdf133852d7f215f0b0"],"state_sha256":"732188ac88cb0dbc1713ad7b30e817ac188754b46115cb29f6dfb523a31d43d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCv60eYTD3fCm+N1HoiyCCzkrVYANv86lkkOsXNdz+eJV9/pUlQlNEWqW6/ynax0hqXWav5cHwUzAUtX4wNwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:28:55.128364Z","bundle_sha256":"e384c6b460794e0562dc1712dac073c08ba9defd818cafedcb1d97fc77ca3ac7"}}