{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YDDRFEBDW3M7JL46WDV2RUZARW","short_pith_number":"pith:YDDRFEBD","canonical_record":{"source":{"id":"1009.5730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-29T01:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"7cf2f0a73a3e775d80e9f17344fb7682d02f53e49b0d23bc91093149519e3fd0","abstract_canon_sha256":"bb7fa39b0d6eaae98269ce966fddaa290688c03a4f638e16cf4e887bef66b889"},"schema_version":"1.0"},"canonical_sha256":"c0c7129023b6d9f4af9eb0eba8d3208da23d69ac2817264a5960bd9fa7dde67f","source":{"kind":"arxiv","id":"1009.5730","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5730","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5730v1","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5730","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"YDDRFEBDW3M7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YDDRFEBDW3M7JL46","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YDDRFEBD","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YDDRFEBDW3M7JL46WDV2RUZARW","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-29T01:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"7cf2f0a73a3e775d80e9f17344fb7682d02f53e49b0d23bc91093149519e3fd0","abstract_canon_sha256":"bb7fa39b0d6eaae98269ce966fddaa290688c03a4f638e16cf4e887bef66b889"},"schema_version":"1.0"},"canonical_sha256":"c0c7129023b6d9f4af9eb0eba8d3208da23d69ac2817264a5960bd9fa7dde67f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:09.070963Z","signature_b64":"/jInWbr+gUR7u6BxU7j9JkcPTrzSQCblvlOuUFzQcNe34Jdc/dLFa4pjleVrFEk8yi570VtL2nWQFISPugIoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0c7129023b6d9f4af9eb0eba8d3208da23d69ac2817264a5960bd9fa7dde67f","last_reissued_at":"2026-05-18T04:40:09.070539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:09.070539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5730","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ImvPaxnJj3zFXzLYEYC1lnst93FJQPSqM08BtLBtBuI1xlbZeOivzsC51w2KP0w8GH2U8qei7sugf64MuN4UAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:35:11.428992Z"},"content_sha256":"2a6d24c4c0c7c8e229585eed5e94fe4d0e019f7cf23c806493fc0fc511eedb0f","schema_version":"1.0","event_id":"sha256:2a6d24c4c0c7c8e229585eed5e94fe4d0e019f7cf23c806493fc0fc511eedb0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YDDRFEBDW3M7JL46WDV2RUZARW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Steiner equiangular tight frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dustin G. Mixon, Janet C. Tremain, Matthew Fickus","submitted_at":"2010-09-29T01:27:58Z","abstract_excerpt":"We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of infinite families of such frames. It provides great freedom in terms of the frame's size and redundancy. This method also explicitly constructs the frame vectors in their native domain, as opposed to implicitly defining them via their Gram matrix. Moreover, in this domain, the frame vectors are very sparse. The construction is extremely simple: a tensor-lik"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5730","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFrXwyjAYZ9iUnUZ07+Uuh7M3O3QyoMHk3je74pUoea+4DC4D9kAHZBchWq2DBUXtjyNOxgU5kBp9vlHIEGgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:35:11.429471Z"},"content_sha256":"c99150539009089ea13dc767ee2d099b4877f2ff9dc338925fceb03f8f795b7a","schema_version":"1.0","event_id":"sha256:c99150539009089ea13dc767ee2d099b4877f2ff9dc338925fceb03f8f795b7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YDDRFEBDW3M7JL46WDV2RUZARW/bundle.json","state_url":"https://pith.science/pith/YDDRFEBDW3M7JL46WDV2RUZARW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YDDRFEBDW3M7JL46WDV2RUZARW/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":"2026-06-24T20:35:11Z","links":{"resolver":"https://pith.science/pith/YDDRFEBDW3M7JL46WDV2RUZARW","bundle":"https://pith.science/pith/YDDRFEBDW3M7JL46WDV2RUZARW/bundle.json","state":"https://pith.science/pith/YDDRFEBDW3M7JL46WDV2RUZARW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YDDRFEBDW3M7JL46WDV2RUZARW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YDDRFEBDW3M7JL46WDV2RUZARW","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":"bb7fa39b0d6eaae98269ce966fddaa290688c03a4f638e16cf4e887bef66b889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-29T01:27:58Z","title_canon_sha256":"7cf2f0a73a3e775d80e9f17344fb7682d02f53e49b0d23bc91093149519e3fd0"},"schema_version":"1.0","source":{"id":"1009.5730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5730","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5730v1","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5730","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"YDDRFEBDW3M7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YDDRFEBDW3M7JL46","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YDDRFEBD","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:c99150539009089ea13dc767ee2d099b4877f2ff9dc338925fceb03f8f795b7a","target":"graph","created_at":"2026-05-18T04:40:09Z","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 provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of infinite families of such frames. It provides great freedom in terms of the frame's size and redundancy. This method also explicitly constructs the frame vectors in their native domain, as opposed to implicitly defining them via their Gram matrix. Moreover, in this domain, the frame vectors are very sparse. The construction is extremely simple: a tensor-lik","authors_text":"Dustin G. Mixon, Janet C. Tremain, Matthew Fickus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-29T01:27:58Z","title":"Steiner equiangular tight frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5730","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":"sha256:2a6d24c4c0c7c8e229585eed5e94fe4d0e019f7cf23c806493fc0fc511eedb0f","target":"record","created_at":"2026-05-18T04:40:09Z","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":"bb7fa39b0d6eaae98269ce966fddaa290688c03a4f638e16cf4e887bef66b889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-29T01:27:58Z","title_canon_sha256":"7cf2f0a73a3e775d80e9f17344fb7682d02f53e49b0d23bc91093149519e3fd0"},"schema_version":"1.0","source":{"id":"1009.5730","kind":"arxiv","version":1}},"canonical_sha256":"c0c7129023b6d9f4af9eb0eba8d3208da23d69ac2817264a5960bd9fa7dde67f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0c7129023b6d9f4af9eb0eba8d3208da23d69ac2817264a5960bd9fa7dde67f","first_computed_at":"2026-05-18T04:40:09.070539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.070539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/jInWbr+gUR7u6BxU7j9JkcPTrzSQCblvlOuUFzQcNe34Jdc/dLFa4pjleVrFEk8yi570VtL2nWQFISPugIoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.070963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a6d24c4c0c7c8e229585eed5e94fe4d0e019f7cf23c806493fc0fc511eedb0f","sha256:c99150539009089ea13dc767ee2d099b4877f2ff9dc338925fceb03f8f795b7a"],"state_sha256":"680c0b421ac5ad46f23578e7440a821d72a8db8c8395a32fb7d820151dbf904d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IL8mI232qzpgQQGk/8UalrjyInUMPIMg/vxMXInoBq6rbaAYmuKNrm0+s5nJmq89Rt84Mk2gomJdNdi9rovICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:35:11.432036Z","bundle_sha256":"800c6961412019c755b6a1adbb9eb5b48028b40905cc058d235c74fea699625d"}}