{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HRO5CLPXBV27LPHA7OKMKGPFFZ","short_pith_number":"pith:HRO5CLPX","canonical_record":{"source":{"id":"2606.23535","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-22T16:13:03Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bf8204c2fee06a9ea088fe530325cc5799499517c4f48afa9767544109f846b7","abstract_canon_sha256":"de47d29b291dcb2c142eec99c54c495f3b02e2344c3764692daa5c22a5856871"},"schema_version":"1.0"},"canonical_sha256":"3c5dd12df70d75f5bce0fb94c519e52e4570a206ca2877a6dd52169c7170dd74","source":{"kind":"arxiv","id":"2606.23535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23535","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23535v1","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23535","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"HRO5CLPXBV27","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_16","alias_value":"HRO5CLPXBV27LPHA","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_8","alias_value":"HRO5CLPX","created_at":"2026-06-23T03:14:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HRO5CLPXBV27LPHA7OKMKGPFFZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23535","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-22T16:13:03Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"bf8204c2fee06a9ea088fe530325cc5799499517c4f48afa9767544109f846b7","abstract_canon_sha256":"de47d29b291dcb2c142eec99c54c495f3b02e2344c3764692daa5c22a5856871"},"schema_version":"1.0"},"canonical_sha256":"3c5dd12df70d75f5bce0fb94c519e52e4570a206ca2877a6dd52169c7170dd74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:29.391541Z","signature_b64":"9QEz3E1Sbjsc+ewuLIEQnSjyM9uGsu/L+kMPgvJpN9s/EVNmLn7jFC1Xkn+A0fKQZPOdxzFq3Llrv1Kfpl4nAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c5dd12df70d75f5bce0fb94c519e52e4570a206ca2877a6dd52169c7170dd74","last_reissued_at":"2026-06-23T03:14:29.391141Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:29.391141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23535","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":"2026-06-23T03:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkq1n/DyAdQt68RPnFZwTUGQdHK3pvq6A37dUzWLC8WzRjuJrFONYVOk60wJFHZJsxGkzRwaONTigoDKXWwwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:41:07.088077Z"},"content_sha256":"1a41ea1afd1269f0dab7358747d8387d63339f70f006fa1f19266a6a58b6daaa","schema_version":"1.0","event_id":"sha256:1a41ea1afd1269f0dab7358747d8387d63339f70f006fa1f19266a6a58b6daaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HRO5CLPXBV27LPHA7OKMKGPFFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Stark units enter SIC overlaps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"quant-ph","authors_text":"Gary McConnell, Ingemar Bengtsson","submitted_at":"2026-06-22T16:13:03Z","abstract_excerpt":"It has been observed that the mutual scalar products of the vectors in a SIC-POVM are given by algebraic units, and at least in some cases by square roots of Stark units. The full picture is somewhat more complicated, especially if non-minimal SIC-POVMs are considered. We present a mixture of exact and numerical evidence suggesting that the overlap units are always products of integral powers of square roots of Stark units from ray class fields all of which are attached to the maximal ring of integers in the base field. In the non-minimal case a lattice of such ray class fields is involved. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23535","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/2606.23535/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":"2026-06-23T03:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lnRlwyW0JRphyEMfDQhZqheqXs3KKMLFuE5YjMq99y5tqLHyMkxEUwg+uG37LtavNh9zC/AWENOPuj8tHtJwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:41:07.088582Z"},"content_sha256":"5a1cb7c678918d32cff498f701818ad889df4b9f3391dc6476dde82ccc36eed6","schema_version":"1.0","event_id":"sha256:5a1cb7c678918d32cff498f701818ad889df4b9f3391dc6476dde82ccc36eed6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/bundle.json","state_url":"https://pith.science/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/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":"2026-08-09T06:41:07Z","links":{"resolver":"https://pith.science/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ","bundle":"https://pith.science/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/bundle.json","state":"https://pith.science/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRO5CLPXBV27LPHA7OKMKGPFFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HRO5CLPXBV27LPHA7OKMKGPFFZ","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":"de47d29b291dcb2c142eec99c54c495f3b02e2344c3764692daa5c22a5856871","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-22T16:13:03Z","title_canon_sha256":"bf8204c2fee06a9ea088fe530325cc5799499517c4f48afa9767544109f846b7"},"schema_version":"1.0","source":{"id":"2606.23535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23535","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23535v1","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23535","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"HRO5CLPXBV27","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_16","alias_value":"HRO5CLPXBV27LPHA","created_at":"2026-06-23T03:14:29Z"},{"alias_kind":"pith_short_8","alias_value":"HRO5CLPX","created_at":"2026-06-23T03:14:29Z"}],"graph_snapshots":[{"event_id":"sha256:5a1cb7c678918d32cff498f701818ad889df4b9f3391dc6476dde82ccc36eed6","target":"graph","created_at":"2026-06-23T03:14:29Z","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/2606.23535/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has been observed that the mutual scalar products of the vectors in a SIC-POVM are given by algebraic units, and at least in some cases by square roots of Stark units. The full picture is somewhat more complicated, especially if non-minimal SIC-POVMs are considered. We present a mixture of exact and numerical evidence suggesting that the overlap units are always products of integral powers of square roots of Stark units from ray class fields all of which are attached to the maximal ring of integers in the base field. In the non-minimal case a lattice of such ray class fields is involved. In","authors_text":"Gary McConnell, Ingemar Bengtsson","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-22T16:13:03Z","title":"How Stark units enter SIC overlaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23535","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":"sha256:1a41ea1afd1269f0dab7358747d8387d63339f70f006fa1f19266a6a58b6daaa","target":"record","created_at":"2026-06-23T03:14:29Z","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":"de47d29b291dcb2c142eec99c54c495f3b02e2344c3764692daa5c22a5856871","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-22T16:13:03Z","title_canon_sha256":"bf8204c2fee06a9ea088fe530325cc5799499517c4f48afa9767544109f846b7"},"schema_version":"1.0","source":{"id":"2606.23535","kind":"arxiv","version":1}},"canonical_sha256":"3c5dd12df70d75f5bce0fb94c519e52e4570a206ca2877a6dd52169c7170dd74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c5dd12df70d75f5bce0fb94c519e52e4570a206ca2877a6dd52169c7170dd74","first_computed_at":"2026-06-23T03:14:29.391141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:29.391141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9QEz3E1Sbjsc+ewuLIEQnSjyM9uGsu/L+kMPgvJpN9s/EVNmLn7jFC1Xkn+A0fKQZPOdxzFq3Llrv1Kfpl4nAw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:29.391541Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a41ea1afd1269f0dab7358747d8387d63339f70f006fa1f19266a6a58b6daaa","sha256:5a1cb7c678918d32cff498f701818ad889df4b9f3391dc6476dde82ccc36eed6"],"state_sha256":"c580ea23048dbe68cfca0c9635f77ef5df2fc0cc0633c1158956817b56035952"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xS3acL1IKLA720ZUhwhrpX0RN9cgntZQYRhMomwwFogomIbgfc4mB1+2j9C6v2IN2vZyqBaGEvbCSHf3L9xzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:41:07.092486Z","bundle_sha256":"7c7ead1d151de1f65ad081c46a02d62dcd2325cefb052428994b45da6a794bd6"}}