{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UL4XFGH5ECHPV2FSHAHMSYXXBP","short_pith_number":"pith:UL4XFGH5","canonical_record":{"source":{"id":"2605.12083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T13:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"7a0718b7eeb9b7cb1d83935cdcf0f5c264bca1223f29e5589344214aa91902fc","abstract_canon_sha256":"1603b6d150b9ecf5c3621c5286176f891c31a815edb7698fb15c5f4896edf182"},"schema_version":"1.0"},"canonical_sha256":"a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db","source":{"kind":"arxiv","id":"2605.12083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12083","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12083v2","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12083","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"UL4XFGH5ECHP","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"UL4XFGH5ECHPV2FS","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"UL4XFGH5","created_at":"2026-06-09T02:08:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UL4XFGH5ECHPV2FSHAHMSYXXBP","target":"record","payload":{"canonical_record":{"source":{"id":"2605.12083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T13:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"7a0718b7eeb9b7cb1d83935cdcf0f5c264bca1223f29e5589344214aa91902fc","abstract_canon_sha256":"1603b6d150b9ecf5c3621c5286176f891c31a815edb7698fb15c5f4896edf182"},"schema_version":"1.0"},"canonical_sha256":"a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:43.802073Z","signature_b64":"2M1epoPdVtEfD9q049Hb8TaCh6M/SBd/RkzAH3gT0GV6qw+SIKarwB69JsHabGLWjyJ0F9giqi5Vq0AfpCDFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db","last_reissued_at":"2026-06-09T02:08:43.801244Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:43.801244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.12083","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmQrQggu2RZMp7EVplDKsK5TRbBiZoj5uajs1yKJL957TL03yiwJlnkd0OFMzkOV5ExkydCXeMXSVvuGCSr9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:30:37.722701Z"},"content_sha256":"e17bb059fd9b89f152cbea0a7b0973918fc67eb0242c51ae609ab6581ef93e44","schema_version":"1.0","event_id":"sha256:e17bb059fd9b89f152cbea0a7b0973918fc67eb0242c51ae609ab6581ef93e44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UL4XFGH5ECHPV2FSHAHMSYXXBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugacy of Isometries in Real Orthogonal Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ziyang Zhu","submitted_at":"2026-05-12T13:07:22Z","abstract_excerpt":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The quadratic space is finite-dimensional, non-degenerate, and the base field is the reals; the proof likely relies on standard canonical form theorems for orthogonal matrices over R without additional restrictions stated in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper classifies orthogonal transformations over real quadratic spaces such that GL-conjugacy implies O-conjugacy.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6c16135e4eeaa92507a55d9aed125302350392c86313ab2b677554e5d70cf826"},"source":{"id":"2605.12083","kind":"arxiv","version":2},"verdict":{"id":"167c5299-add6-4e88-bf3d-747d51e7af42","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T03:48:05.474410Z","strongest_claim":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.","one_line_summary":"The paper classifies orthogonal transformations over real quadratic spaces such that GL-conjugacy implies O-conjugacy.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The quadratic space is finite-dimensional, non-degenerate, and the base field is the reals; the proof likely relies on standard canonical form theorems for orthogonal matrices over R without additional restrictions stated in the abstract.","pith_extraction_headline":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.12083/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-26T15:43:04.388811Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T17:01:26.266481Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T11:15:58.128728Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:01:58.391004Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c58e9c4514515027b90ceb75be165f3ee778eceed3bef243cffb597f7e10e45e"},"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":"167c5299-add6-4e88-bf3d-747d51e7af42"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47bw/Bfqu2/22HrjMdZLW06x8Q0BFEmkkewjvXCsTTiah5IjD1EOZByMdAnSpTa555lYl2flj5F1OlGlSmbIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:30:37.723234Z"},"content_sha256":"092cc4bb76cea788683da250c9c135a543911258601c43cba58d335dcbba7a84","schema_version":"1.0","event_id":"sha256:092cc4bb76cea788683da250c9c135a543911258601c43cba58d335dcbba7a84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/bundle.json","state_url":"https://pith.science/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/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":"2026-06-10T18:30:37Z","links":{"resolver":"https://pith.science/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP","bundle":"https://pith.science/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/bundle.json","state":"https://pith.science/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UL4XFGH5ECHPV2FSHAHMSYXXBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UL4XFGH5ECHPV2FSHAHMSYXXBP","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":"1603b6d150b9ecf5c3621c5286176f891c31a815edb7698fb15c5f4896edf182","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T13:07:22Z","title_canon_sha256":"7a0718b7eeb9b7cb1d83935cdcf0f5c264bca1223f29e5589344214aa91902fc"},"schema_version":"1.0","source":{"id":"2605.12083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12083","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12083v2","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12083","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"UL4XFGH5ECHP","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"UL4XFGH5ECHPV2FS","created_at":"2026-06-09T02:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"UL4XFGH5","created_at":"2026-06-09T02:08:43Z"}],"graph_snapshots":[{"event_id":"sha256:092cc4bb76cea788683da250c9c135a543911258601c43cba58d335dcbba7a84","target":"graph","created_at":"2026-06-09T02:08:43Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The quadratic space is finite-dimensional, non-degenerate, and the base field is the reals; the proof likely relies on standard canonical form theorems for orthogonal matrices over R without additional restrictions stated in the abstract."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The paper classifies orthogonal transformations over real quadratic spaces such that GL-conjugacy implies O-conjugacy."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy."}],"snapshot_sha256":"6c16135e4eeaa92507a55d9aed125302350392c86313ab2b677554e5d70cf826"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-26T15:43:04.388811Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T17:01:26.266481Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-20T11:15:58.128728Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T23:01:58.391004Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.12083/integrity.json","findings":[],"snapshot_sha256":"c58e9c4514515027b90ceb75be165f3ee778eceed3bef243cffb597f7e10e45e","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.","authors_text":"Ziyang Zhu","cross_cats":[],"headline":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T13:07:22Z","title":"Conjugacy of Isometries in Real Orthogonal Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12083","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T03:48:05.474410Z","id":"167c5299-add6-4e88-bf3d-747d51e7af42","model_set":{"reader":"grok-4.3"},"one_line_summary":"The paper classifies orthogonal transformations over real quadratic spaces such that GL-conjugacy implies O-conjugacy.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy.","strongest_claim":"We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.","weakest_assumption":"The quadratic space is finite-dimensional, non-degenerate, and the base field is the reals; the proof likely relies on standard canonical form theorems for orthogonal matrices over R without additional restrictions stated in the abstract."}},"verdict_id":"167c5299-add6-4e88-bf3d-747d51e7af42"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e17bb059fd9b89f152cbea0a7b0973918fc67eb0242c51ae609ab6581ef93e44","target":"record","created_at":"2026-06-09T02:08:43Z","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":"1603b6d150b9ecf5c3621c5286176f891c31a815edb7698fb15c5f4896edf182","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T13:07:22Z","title_canon_sha256":"7a0718b7eeb9b7cb1d83935cdcf0f5c264bca1223f29e5589344214aa91902fc"},"schema_version":"1.0","source":{"id":"2605.12083","kind":"arxiv","version":2}},"canonical_sha256":"a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db","first_computed_at":"2026-06-09T02:08:43.801244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:43.801244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2M1epoPdVtEfD9q049Hb8TaCh6M/SBd/RkzAH3gT0GV6qw+SIKarwB69JsHabGLWjyJ0F9giqi5Vq0AfpCDFBA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:43.802073Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e17bb059fd9b89f152cbea0a7b0973918fc67eb0242c51ae609ab6581ef93e44","sha256:092cc4bb76cea788683da250c9c135a543911258601c43cba58d335dcbba7a84"],"state_sha256":"3eab966485ed5a524359cbdbd99fa8ef8be4508cf224d1af37058fd0310a6b66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhgM8S5VzT4+gx0C9Mo3MzcnTqwFnufqc7VIRs/JByPhaFosFVnlsNv1ob1WGxoO6vpTErYGRCdhinGfR07FCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:30:37.725591Z","bundle_sha256":"e0498372f59b0ab2eb9f77cff496d0803882df42e4142a4c70585ed1ecad4be6"}}