{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FJJ4IRITSVE7P2QEECMV3UMQR5","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":"fff6d5c445a107043ebce8530a6f8b3d47d1dda59fc2208dccee00b90caa669a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-25T19:09:29Z","title_canon_sha256":"497087641b56cf7d66dd47f6575a0873ec8dfbe4ff6aaeec7e1f3b3aa498a80a"},"schema_version":"1.0","source":{"id":"2506.20778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.20778","created_at":"2026-07-05T11:27:33Z"},{"alias_kind":"arxiv_version","alias_value":"2506.20778v1","created_at":"2026-07-05T11:27:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20778","created_at":"2026-07-05T11:27:33Z"},{"alias_kind":"pith_short_12","alias_value":"FJJ4IRITSVE7","created_at":"2026-07-05T11:27:33Z"},{"alias_kind":"pith_short_16","alias_value":"FJJ4IRITSVE7P2QE","created_at":"2026-07-05T11:27:33Z"},{"alias_kind":"pith_short_8","alias_value":"FJJ4IRIT","created_at":"2026-07-05T11:27:33Z"}],"graph_snapshots":[{"event_id":"sha256:28995a42ec749146111158c05cdc65140da5e0f7bf2aa6786abcd882c8c5b68e","target":"graph","created_at":"2026-07-05T11:27:33Z","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/2506.20778/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs exhibit Weyl--Heisenberg symmetry, some of our new SICs exhibit trivial automorphism groups. We conjecture that such \\textit{totally asymmetric} SICs exist in infinitely many dimensions in the finite field setting.","authors_text":"Dustin G. Mixon, Joseph W. Iverson","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-25T19:09:29Z","title":"Asymmetric SICs over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20778","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:e1ad7e3acee6c6d63d5851ebd94911a6e16f35b4f2d6cfe2c68530fb3bbb3200","target":"record","created_at":"2026-07-05T11:27:33Z","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":"fff6d5c445a107043ebce8530a6f8b3d47d1dda59fc2208dccee00b90caa669a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-25T19:09:29Z","title_canon_sha256":"497087641b56cf7d66dd47f6575a0873ec8dfbe4ff6aaeec7e1f3b3aa498a80a"},"schema_version":"1.0","source":{"id":"2506.20778","kind":"arxiv","version":1}},"canonical_sha256":"2a53c445139549f7ea0420995dd1908f4e30ec1bad90085f921193d870a74538","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a53c445139549f7ea0420995dd1908f4e30ec1bad90085f921193d870a74538","first_computed_at":"2026-07-05T11:27:33.885170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:33.885170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ye3YR8CBekQdQEJie8vZc5vkczvNkrO6DZsLcHxwoaK7XMe4rkwfdLjBzAeaMaNCozASJUXZWOlPf+EMOce7Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:33.885692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.20778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1ad7e3acee6c6d63d5851ebd94911a6e16f35b4f2d6cfe2c68530fb3bbb3200","sha256:28995a42ec749146111158c05cdc65140da5e0f7bf2aa6786abcd882c8c5b68e"],"state_sha256":"c7761ea176789106a7c4ca976ae4bfee58b5e398cbbc2a0d8729f32ac2975bb9"}