{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:G4YP6HU3QBVG3EDJHJI6OMMY7W","short_pith_number":"pith:G4YP6HU3","canonical_record":{"source":{"id":"1707.03528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-12T03:43:35Z","cross_cats_sorted":[],"title_canon_sha256":"58fd68587aa55bd48cace05ae884d683a17741dc635f34dee4908e0140347ef4","abstract_canon_sha256":"11261fb7b0adddccd193a450b4dd93c72af14bb153771b8affd56621b0c5a6e8"},"schema_version":"1.0"},"canonical_sha256":"3730ff1e9b806a6d90693a51e73198fdad33ad05ca6b936b22c6a08455268823","source":{"kind":"arxiv","id":"1707.03528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03528","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03528v1","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03528","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"G4YP6HU3QBVG","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G4YP6HU3QBVG3EDJ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G4YP6HU3","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:G4YP6HU3QBVG3EDJHJI6OMMY7W","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-12T03:43:35Z","cross_cats_sorted":[],"title_canon_sha256":"58fd68587aa55bd48cace05ae884d683a17741dc635f34dee4908e0140347ef4","abstract_canon_sha256":"11261fb7b0adddccd193a450b4dd93c72af14bb153771b8affd56621b0c5a6e8"},"schema_version":"1.0"},"canonical_sha256":"3730ff1e9b806a6d90693a51e73198fdad33ad05ca6b936b22c6a08455268823","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:25.718585Z","signature_b64":"lDe8bRgPZfg5k9dZPNe5GnLf7VTNUd/cxtQwADGWlATYQKt30ncpuX52/v1Xq7o8BQq2nrWs803CIuP2okgzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3730ff1e9b806a6d90693a51e73198fdad33ad05ca6b936b22c6a08455268823","last_reissued_at":"2026-05-18T00:40:25.718087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:25.718087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03528","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":"2026-05-18T00:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEQ+f9jIit93K/EUlD6+EYICW6j1V5HQc3UnZE5YzZkC1OCEfYVaT44e78jLLpk2wx6wwlHxuXtXJVuHB+tgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:08:13.572853Z"},"content_sha256":"078959b098447cb9dc2b9e566feb597930cc780be7e02464754c95f39d692265","schema_version":"1.0","event_id":"sha256:078959b098447cb9dc2b9e566feb597930cc780be7e02464754c95f39d692265"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:G4YP6HU3QBVG3EDJHJI6OMMY7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low frame coherence via zero-mean tensor embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernhard G. Bodmann, John I. Haas IV","submitted_at":"2017-07-12T03:43:35Z","abstract_excerpt":"This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other geometric optimality criteria need to be identified. To this end, we use an iteration of the embedding technique by Conway, Hardin and Sloane. As a consequence of their work, a quadratic mapping embeds equiangular lines into a simplex in a real Euclidean space. Here, higher degree polynomial maps embed highly redundant unit-norm frames to simplices in high-dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03528","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":"2026-05-18T00:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VmpqaGYbPYiCRB16MrIpV6QF0oO00Rd8QYHLNJEgaIR0xpBuU4cfeBzCC2aLjb05t59wpwWikjfOvS4NqMppBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:08:13.573195Z"},"content_sha256":"ff94aa53ef4c9d944227c913d09740d124c12e2d69caeb66a2460d2d67e66099","schema_version":"1.0","event_id":"sha256:ff94aa53ef4c9d944227c913d09740d124c12e2d69caeb66a2460d2d67e66099"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/bundle.json","state_url":"https://pith.science/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/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":"2026-06-02T12:08:13Z","links":{"resolver":"https://pith.science/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W","bundle":"https://pith.science/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/bundle.json","state":"https://pith.science/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4YP6HU3QBVG3EDJHJI6OMMY7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G4YP6HU3QBVG3EDJHJI6OMMY7W","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":"11261fb7b0adddccd193a450b4dd93c72af14bb153771b8affd56621b0c5a6e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-12T03:43:35Z","title_canon_sha256":"58fd68587aa55bd48cace05ae884d683a17741dc635f34dee4908e0140347ef4"},"schema_version":"1.0","source":{"id":"1707.03528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03528","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03528v1","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03528","created_at":"2026-05-18T00:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"G4YP6HU3QBVG","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G4YP6HU3QBVG3EDJ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G4YP6HU3","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ff94aa53ef4c9d944227c913d09740d124c12e2d69caeb66a2460d2d67e66099","target":"graph","created_at":"2026-05-18T00:40:25Z","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":"This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other geometric optimality criteria need to be identified. To this end, we use an iteration of the embedding technique by Conway, Hardin and Sloane. As a consequence of their work, a quadratic mapping embeds equiangular lines into a simplex in a real Euclidean space. Here, higher degree polynomial maps embed highly redundant unit-norm frames to simplices in high-dimensi","authors_text":"Bernhard G. Bodmann, John I. Haas IV","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-12T03:43:35Z","title":"Low frame coherence via zero-mean tensor embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03528","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":"sha256:078959b098447cb9dc2b9e566feb597930cc780be7e02464754c95f39d692265","target":"record","created_at":"2026-05-18T00:40:25Z","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":"11261fb7b0adddccd193a450b4dd93c72af14bb153771b8affd56621b0c5a6e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-12T03:43:35Z","title_canon_sha256":"58fd68587aa55bd48cace05ae884d683a17741dc635f34dee4908e0140347ef4"},"schema_version":"1.0","source":{"id":"1707.03528","kind":"arxiv","version":1}},"canonical_sha256":"3730ff1e9b806a6d90693a51e73198fdad33ad05ca6b936b22c6a08455268823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3730ff1e9b806a6d90693a51e73198fdad33ad05ca6b936b22c6a08455268823","first_computed_at":"2026-05-18T00:40:25.718087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:25.718087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lDe8bRgPZfg5k9dZPNe5GnLf7VTNUd/cxtQwADGWlATYQKt30ncpuX52/v1Xq7o8BQq2nrWs803CIuP2okgzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:25.718585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:078959b098447cb9dc2b9e566feb597930cc780be7e02464754c95f39d692265","sha256:ff94aa53ef4c9d944227c913d09740d124c12e2d69caeb66a2460d2d67e66099"],"state_sha256":"9f3a5052c56de18313a42826ae97ca065b71c2cb4b56dee5ad80b9e2fb6850ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Diuru6Krj6CcqnEsM4q6kLYYmzEoJwyIJ7N/j8qRzaoyC6gwVokCpS0d0+SwW5TLyg7TO1ARHZwA80JrbJfWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:08:13.575092Z","bundle_sha256":"e2bfe54cc2a094da8aa536d8fbf3be1e2fdd80bf86bc68222383c7f5eba72f40"}}