{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3KGXMPAXFMWVMGSR4WBWAYFWBT","short_pith_number":"pith:3KGXMPAX","canonical_record":{"source":{"id":"2601.00124","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2025-12-31T21:58:20Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a25564d2280f3cd0f965d6ac31b936a3c9b70b3345803c22c52508ce7df3325d","abstract_canon_sha256":"229a27c4a8b31109eead9cb2c2148b7377ade37c0ad4cbd3d9f1a72f1e7cea18"},"schema_version":"1.0"},"canonical_sha256":"da8d763c172b2d561a51e5836060b60ce04134a7213fb2bf931d606330f8c0c4","source":{"kind":"arxiv","id":"2601.00124","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.00124","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"2601.00124v3","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.00124","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"3KGXMPAXFMWV","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_16","alias_value":"3KGXMPAXFMWVMGSR","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_8","alias_value":"3KGXMPAX","created_at":"2026-06-30T01:16:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3KGXMPAXFMWVMGSR4WBWAYFWBT","target":"record","payload":{"canonical_record":{"source":{"id":"2601.00124","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2025-12-31T21:58:20Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a25564d2280f3cd0f965d6ac31b936a3c9b70b3345803c22c52508ce7df3325d","abstract_canon_sha256":"229a27c4a8b31109eead9cb2c2148b7377ade37c0ad4cbd3d9f1a72f1e7cea18"},"schema_version":"1.0"},"canonical_sha256":"da8d763c172b2d561a51e5836060b60ce04134a7213fb2bf931d606330f8c0c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:16:27.472567Z","signature_b64":"7EHwG+EudwpbturjRQFmGuwvM8EgFFHinRYmMn2OM8/l/sKjZx496iJk1hL9HeeAsl6tZNI4bNrj6YEvDRT5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da8d763c172b2d561a51e5836060b60ce04134a7213fb2bf931d606330f8c0c4","last_reissued_at":"2026-06-30T01:16:27.472010Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:16:27.472010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.00124","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":"2026-06-30T01:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wX8iQEuznVb3Y9weQo8Q3TxxF9E7KPSeq4UekS2t1QprfGVxwaf2YGMHBvP/rn1YFm7iJSckTXccY/xq9EqqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:13:29.075076Z"},"content_sha256":"2e8ea0756dcd6030a0ed13c50d64d87a1403d111ee800325d03da5dc24293960","schema_version":"1.0","event_id":"sha256:2e8ea0756dcd6030a0ed13c50d64d87a1403d111ee800325d03da5dc24293960"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3KGXMPAXFMWVMGSR4WBWAYFWBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hall induction for cotangent representations and wheel conditions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Danil Gubarevich","submitted_at":"2025-12-31T21:58:20Z","abstract_excerpt":"In this short note we study the Hall induction of cotangent representations of reductive groups. We prove its torsion freeness in Borel-Moore homology. In K-theory we find an analog of wheel conditions verified by the image of restriction map to the fixed point and consider examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.00124","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/2601.00124/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":"2026-06-30T01:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BpJFZJGJb0LvKvoh/s/U+sXNCbVzUF+B2Vcd50ouM3u71NjRoGxM6DNFb/CPNRPo9C/iucZr6fpE6E+n0tlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:13:29.075570Z"},"content_sha256":"f61efdff3ddfd545b36321cef26bb3f73634eed5ced91b4086337c4f8bf48650","schema_version":"1.0","event_id":"sha256:f61efdff3ddfd545b36321cef26bb3f73634eed5ced91b4086337c4f8bf48650"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/bundle.json","state_url":"https://pith.science/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/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":"2026-08-03T21:13:29Z","links":{"resolver":"https://pith.science/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT","bundle":"https://pith.science/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/bundle.json","state":"https://pith.science/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KGXMPAXFMWVMGSR4WBWAYFWBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3KGXMPAXFMWVMGSR4WBWAYFWBT","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":"229a27c4a8b31109eead9cb2c2148b7377ade37c0ad4cbd3d9f1a72f1e7cea18","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2025-12-31T21:58:20Z","title_canon_sha256":"a25564d2280f3cd0f965d6ac31b936a3c9b70b3345803c22c52508ce7df3325d"},"schema_version":"1.0","source":{"id":"2601.00124","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.00124","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"2601.00124v3","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.00124","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"3KGXMPAXFMWV","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_16","alias_value":"3KGXMPAXFMWVMGSR","created_at":"2026-06-30T01:16:27Z"},{"alias_kind":"pith_short_8","alias_value":"3KGXMPAX","created_at":"2026-06-30T01:16:27Z"}],"graph_snapshots":[{"event_id":"sha256:f61efdff3ddfd545b36321cef26bb3f73634eed5ced91b4086337c4f8bf48650","target":"graph","created_at":"2026-06-30T01:16:27Z","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/2601.00124/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short note we study the Hall induction of cotangent representations of reductive groups. We prove its torsion freeness in Borel-Moore homology. In K-theory we find an analog of wheel conditions verified by the image of restriction map to the fixed point and consider examples.","authors_text":"Danil Gubarevich","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2025-12-31T21:58:20Z","title":"Hall induction for cotangent representations and wheel conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.00124","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":"sha256:2e8ea0756dcd6030a0ed13c50d64d87a1403d111ee800325d03da5dc24293960","target":"record","created_at":"2026-06-30T01:16:27Z","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":"229a27c4a8b31109eead9cb2c2148b7377ade37c0ad4cbd3d9f1a72f1e7cea18","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2025-12-31T21:58:20Z","title_canon_sha256":"a25564d2280f3cd0f965d6ac31b936a3c9b70b3345803c22c52508ce7df3325d"},"schema_version":"1.0","source":{"id":"2601.00124","kind":"arxiv","version":3}},"canonical_sha256":"da8d763c172b2d561a51e5836060b60ce04134a7213fb2bf931d606330f8c0c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da8d763c172b2d561a51e5836060b60ce04134a7213fb2bf931d606330f8c0c4","first_computed_at":"2026-06-30T01:16:27.472010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:16:27.472010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7EHwG+EudwpbturjRQFmGuwvM8EgFFHinRYmMn2OM8/l/sKjZx496iJk1hL9HeeAsl6tZNI4bNrj6YEvDRT5DQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:16:27.472567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.00124","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e8ea0756dcd6030a0ed13c50d64d87a1403d111ee800325d03da5dc24293960","sha256:f61efdff3ddfd545b36321cef26bb3f73634eed5ced91b4086337c4f8bf48650"],"state_sha256":"f925d04601454a029cda6c7471eeb710f6f99b0f7a38ac69b11a79866101df75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UhF0esqbqE6WSAPGNxEkQNCDUJOvjsyrIIN19mu6qwsUnkudBW3eMQC6ccgCwt3/0WLEsUMN4LLBS5x489qIBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:13:29.080884Z","bundle_sha256":"bb84b4261b5e20848bd155996f8346b2a56c727b4fa47698dfd256d6f7df77ac"}}