{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EYSKQESFPBNPHHD3TJS6YZUPIT","short_pith_number":"pith:EYSKQESF","canonical_record":{"source":{"id":"2109.07123","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-15T07:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"cb16aff9e32460fd2321fa63a4b0c40503d30974136e81b0a40c3af38fac63e6","abstract_canon_sha256":"3730b309dec467b357716603f7de3fac7c9d2ef810bbd21feac6b9702fcd4233"},"schema_version":"1.0"},"canonical_sha256":"2624a81245785af39c7b9a65ec668f44f880d22bb54237dcf77032620d5d028c","source":{"kind":"arxiv","id":"2109.07123","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07123","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07123v3","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07123","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"EYSKQESFPBNP","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_16","alias_value":"EYSKQESFPBNPHHD3","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_8","alias_value":"EYSKQESF","created_at":"2026-07-05T05:38:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EYSKQESFPBNPHHD3TJS6YZUPIT","target":"record","payload":{"canonical_record":{"source":{"id":"2109.07123","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-15T07:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"cb16aff9e32460fd2321fa63a4b0c40503d30974136e81b0a40c3af38fac63e6","abstract_canon_sha256":"3730b309dec467b357716603f7de3fac7c9d2ef810bbd21feac6b9702fcd4233"},"schema_version":"1.0"},"canonical_sha256":"2624a81245785af39c7b9a65ec668f44f880d22bb54237dcf77032620d5d028c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:26.167160Z","signature_b64":"cx+WcKpRVIg9cOKE5Zy34rb2d9lpIAjtNUvmVLjWmWQ3oucwOsqyKsCZC3YcXF/Kmo9JA+K2QK3xgjwEThCtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2624a81245785af39c7b9a65ec668f44f880d22bb54237dcf77032620d5d028c","last_reissued_at":"2026-07-05T05:38:26.166735Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:26.166735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.07123","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cwVX0fCaFI5EsIwjJQIZGobCKFhTKmtxDZSDVzDxTt/PpQ5zcSzqs2kyOXN88+E4x5G3tel8IZgncRcBWyB+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:27:29.178945Z"},"content_sha256":"ae1d0554841ba81f5146bfbf2ca73a766eac2892b518b0b46f187b685ab906e1","schema_version":"1.0","event_id":"sha256:ae1d0554841ba81f5146bfbf2ca73a766eac2892b518b0b46f187b685ab906e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EYSKQESFPBNPHHD3TJS6YZUPIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase retrieval for affine groups over prime fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Bartusel, Hartmut F\\\"uhr, Vignon Oussa","submitted_at":"2021-09-15T07:17:47Z","abstract_excerpt":"We study phase retrieval for group frames arising from permutation representations, focusing on the action of the affine group of a finite field. We investigate various versions of the phase retrieval problem, including conjugate phase retrieval, sign retrieval, and matrix recovery. Our main result establishes that the canonical irreducible representation of the affine group $\\mathbb{Z}_p \\rtimes \\mathbb{Z}_p^\\ast$ (with $p$ prime), acting on the vectors in $\\mathbb{C}^{p}$ with zero-sum, has the strongest retrieval property, allowing to reconstruct matrices from scalar products with a group o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07123","kind":"arxiv","version":3},"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/2109.07123/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":"2026-07-05T05:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ahcCBkFB5MTsZavSMzi9WVbv934QBIxra/hsNbDj43BxEp5C5KBRb6GgiSCqPyZ3Qc1vujrZvJFka05Xscb5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:27:29.179334Z"},"content_sha256":"6c38d1250450b4cf21c01be0e056f0ae8d04a7d87a3c5e52d8ea4daadf7bea3f","schema_version":"1.0","event_id":"sha256:6c38d1250450b4cf21c01be0e056f0ae8d04a7d87a3c5e52d8ea4daadf7bea3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/bundle.json","state_url":"https://pith.science/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/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":"2026-07-07T08:27:29Z","links":{"resolver":"https://pith.science/pith/EYSKQESFPBNPHHD3TJS6YZUPIT","bundle":"https://pith.science/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/bundle.json","state":"https://pith.science/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYSKQESFPBNPHHD3TJS6YZUPIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EYSKQESFPBNPHHD3TJS6YZUPIT","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":"3730b309dec467b357716603f7de3fac7c9d2ef810bbd21feac6b9702fcd4233","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-15T07:17:47Z","title_canon_sha256":"cb16aff9e32460fd2321fa63a4b0c40503d30974136e81b0a40c3af38fac63e6"},"schema_version":"1.0","source":{"id":"2109.07123","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07123","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07123v3","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07123","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"EYSKQESFPBNP","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_16","alias_value":"EYSKQESFPBNPHHD3","created_at":"2026-07-05T05:38:26Z"},{"alias_kind":"pith_short_8","alias_value":"EYSKQESF","created_at":"2026-07-05T05:38:26Z"}],"graph_snapshots":[{"event_id":"sha256:6c38d1250450b4cf21c01be0e056f0ae8d04a7d87a3c5e52d8ea4daadf7bea3f","target":"graph","created_at":"2026-07-05T05:38:26Z","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/2109.07123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study phase retrieval for group frames arising from permutation representations, focusing on the action of the affine group of a finite field. We investigate various versions of the phase retrieval problem, including conjugate phase retrieval, sign retrieval, and matrix recovery. Our main result establishes that the canonical irreducible representation of the affine group $\\mathbb{Z}_p \\rtimes \\mathbb{Z}_p^\\ast$ (with $p$ prime), acting on the vectors in $\\mathbb{C}^{p}$ with zero-sum, has the strongest retrieval property, allowing to reconstruct matrices from scalar products with a group o","authors_text":"David Bartusel, Hartmut F\\\"uhr, Vignon Oussa","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-15T07:17:47Z","title":"Phase retrieval for affine groups over prime fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07123","kind":"arxiv","version":3},"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:ae1d0554841ba81f5146bfbf2ca73a766eac2892b518b0b46f187b685ab906e1","target":"record","created_at":"2026-07-05T05:38:26Z","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":"3730b309dec467b357716603f7de3fac7c9d2ef810bbd21feac6b9702fcd4233","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2021-09-15T07:17:47Z","title_canon_sha256":"cb16aff9e32460fd2321fa63a4b0c40503d30974136e81b0a40c3af38fac63e6"},"schema_version":"1.0","source":{"id":"2109.07123","kind":"arxiv","version":3}},"canonical_sha256":"2624a81245785af39c7b9a65ec668f44f880d22bb54237dcf77032620d5d028c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2624a81245785af39c7b9a65ec668f44f880d22bb54237dcf77032620d5d028c","first_computed_at":"2026-07-05T05:38:26.166735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:38:26.166735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cx+WcKpRVIg9cOKE5Zy34rb2d9lpIAjtNUvmVLjWmWQ3oucwOsqyKsCZC3YcXF/Kmo9JA+K2QK3xgjwEThCtBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:38:26.167160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.07123","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1d0554841ba81f5146bfbf2ca73a766eac2892b518b0b46f187b685ab906e1","sha256:6c38d1250450b4cf21c01be0e056f0ae8d04a7d87a3c5e52d8ea4daadf7bea3f"],"state_sha256":"a3dd1be62fd183cb74d7e80c75454cb53414c5aa40371274ff629a9890c292c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhq8XsEg1DL6E0UKfV77DPvB9amYigqn0LpWipIv/3AeG4OZ0Ay6F7AM54RsMBBCCylblCCzLFJY1/hXSYDWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:27:29.181466Z","bundle_sha256":"5556056eebf0f2391fe67583a5ebd73bb858c8fae2bed1983873675c7b669f16"}}