{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QRGY6WGQPQLUUEORSWQJJVRUGW","short_pith_number":"pith:QRGY6WGQ","canonical_record":{"source":{"id":"2506.21259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-26T13:41:01Z","cross_cats_sorted":[],"title_canon_sha256":"2f5752314d563935384f8a97477fd64aea7b024041d95c11d062de83ed642d7c","abstract_canon_sha256":"c381887d818d120204047a8891c590b25e7ab471fd904a70b5ac015efedbf4e9"},"schema_version":"1.0"},"canonical_sha256":"844d8f58d07c174a11d195a094d63435b619fe64b5f3f756554c5b346c58bec7","source":{"kind":"arxiv","id":"2506.21259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21259","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21259v1","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21259","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"QRGY6WGQPQLU","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_16","alias_value":"QRGY6WGQPQLUUEOR","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_8","alias_value":"QRGY6WGQ","created_at":"2026-07-05T11:27:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QRGY6WGQPQLUUEORSWQJJVRUGW","target":"record","payload":{"canonical_record":{"source":{"id":"2506.21259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-26T13:41:01Z","cross_cats_sorted":[],"title_canon_sha256":"2f5752314d563935384f8a97477fd64aea7b024041d95c11d062de83ed642d7c","abstract_canon_sha256":"c381887d818d120204047a8891c590b25e7ab471fd904a70b5ac015efedbf4e9"},"schema_version":"1.0"},"canonical_sha256":"844d8f58d07c174a11d195a094d63435b619fe64b5f3f756554c5b346c58bec7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:42.394136Z","signature_b64":"9VcEe+UpHztKSg32FZC+hxUm4vp4gL3Jn/gk2yrjoVYqhp7+QW9kBrH8kdpBWkqTfgYemXV0DdG6T8XlG+9/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"844d8f58d07c174a11d195a094d63435b619fe64b5f3f756554c5b346c58bec7","last_reissued_at":"2026-07-05T11:27:42.393723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:42.393723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.21259","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":"2026-07-05T11:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5a8UVgN/j4M/+eAdaqTbFWxDuU8uubvpIicfBxQ/H01F9rUwz7ADerbfCddVEeT0ZwrWBKpQxaV75rMm6vZ9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:27:53.548873Z"},"content_sha256":"30686ea6cf5f57cf0a51828c1491cacc5c8e55dcfbce239fb3ae50753afb6067","schema_version":"1.0","event_id":"sha256:30686ea6cf5f57cf0a51828c1491cacc5c8e55dcfbce239fb3ae50753afb6067"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QRGY6WGQPQLUUEORSWQJJVRUGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An isovariant Blakers--Massey theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Inbar Klang, Sarah Yeakel","submitted_at":"2025-06-26T13:41:01Z","abstract_excerpt":"An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and its $n$-cubical generalization, define a suitable notion of suspension (by a trivial representation sphere) in the isovariant category, and prove an isovariant Freudenthal suspension theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21259","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/2506.21259/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":"2026-07-05T11:27:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlZzX1xudewJ3YatrR91OfK1jGcpH91bBekdH432egyl6Pk6rB+vCAzBADoqI5Lyj6olWfRBEWmsqCOaha4PBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:27:53.550004Z"},"content_sha256":"a296717f50da9113b96f52df5439d35827d82e7883655393c4cc93be1a557846","schema_version":"1.0","event_id":"sha256:a296717f50da9113b96f52df5439d35827d82e7883655393c4cc93be1a557846"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/bundle.json","state_url":"https://pith.science/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/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":"2026-08-17T14:27:53Z","links":{"resolver":"https://pith.science/pith/QRGY6WGQPQLUUEORSWQJJVRUGW","bundle":"https://pith.science/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/bundle.json","state":"https://pith.science/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QRGY6WGQPQLUUEORSWQJJVRUGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QRGY6WGQPQLUUEORSWQJJVRUGW","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":"c381887d818d120204047a8891c590b25e7ab471fd904a70b5ac015efedbf4e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-26T13:41:01Z","title_canon_sha256":"2f5752314d563935384f8a97477fd64aea7b024041d95c11d062de83ed642d7c"},"schema_version":"1.0","source":{"id":"2506.21259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21259","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21259v1","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21259","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"QRGY6WGQPQLU","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_16","alias_value":"QRGY6WGQPQLUUEOR","created_at":"2026-07-05T11:27:42Z"},{"alias_kind":"pith_short_8","alias_value":"QRGY6WGQ","created_at":"2026-07-05T11:27:42Z"}],"graph_snapshots":[{"event_id":"sha256:a296717f50da9113b96f52df5439d35827d82e7883655393c4cc93be1a557846","target":"graph","created_at":"2026-07-05T11:27:42Z","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/2506.21259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and its $n$-cubical generalization, define a suitable notion of suspension (by a trivial representation sphere) in the isovariant category, and prove an isovariant Freudenthal suspension theorem.","authors_text":"Inbar Klang, Sarah Yeakel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-26T13:41:01Z","title":"An isovariant Blakers--Massey theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21259","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":"sha256:30686ea6cf5f57cf0a51828c1491cacc5c8e55dcfbce239fb3ae50753afb6067","target":"record","created_at":"2026-07-05T11:27:42Z","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":"c381887d818d120204047a8891c590b25e7ab471fd904a70b5ac015efedbf4e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-26T13:41:01Z","title_canon_sha256":"2f5752314d563935384f8a97477fd64aea7b024041d95c11d062de83ed642d7c"},"schema_version":"1.0","source":{"id":"2506.21259","kind":"arxiv","version":1}},"canonical_sha256":"844d8f58d07c174a11d195a094d63435b619fe64b5f3f756554c5b346c58bec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"844d8f58d07c174a11d195a094d63435b619fe64b5f3f756554c5b346c58bec7","first_computed_at":"2026-07-05T11:27:42.393723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:42.393723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9VcEe+UpHztKSg32FZC+hxUm4vp4gL3Jn/gk2yrjoVYqhp7+QW9kBrH8kdpBWkqTfgYemXV0DdG6T8XlG+9/Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:42.394136Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30686ea6cf5f57cf0a51828c1491cacc5c8e55dcfbce239fb3ae50753afb6067","sha256:a296717f50da9113b96f52df5439d35827d82e7883655393c4cc93be1a557846"],"state_sha256":"508c8efc5a5c1c4775de31e2c37936d17ca4e11e79a527cd54a27227239e5143"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gR/7GgRQ9s4VQyx0pAILzgkSBm35uU6cgH7PYIrpVenHhzpMPXEq5zKdbq7V/MxE7KYlNyBYkf7Q26fHQGMZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:27:53.593358Z","bundle_sha256":"84ac2f908231510a17e24f0172b020be09f1af9223391618b1bf76a1c0fe1eb6"}}