{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C5WHWOOXPFFAO2YMG6IBGQINZY","short_pith_number":"pith:C5WHWOOX","canonical_record":{"source":{"id":"1108.1056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-04T12:12:24Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"1d0fbddf59cb34b3219afa8dd5b7463f73739d0b589a6598024493791812a7d6","abstract_canon_sha256":"d3edadadd4a260191cd1e582e0a05cf7b903425eb068d5b3777726414834fc69"},"schema_version":"1.0"},"canonical_sha256":"176c7b39d7794a076b0c379013410dce3080b62c59e05af94bdcd7339b3c4b5a","source":{"kind":"arxiv","id":"1108.1056","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1056","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1056v2","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1056","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"C5WHWOOXPFFA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5WHWOOXPFFAO2YM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5WHWOOX","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C5WHWOOXPFFAO2YMG6IBGQINZY","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1056","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-04T12:12:24Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"1d0fbddf59cb34b3219afa8dd5b7463f73739d0b589a6598024493791812a7d6","abstract_canon_sha256":"d3edadadd4a260191cd1e582e0a05cf7b903425eb068d5b3777726414834fc69"},"schema_version":"1.0"},"canonical_sha256":"176c7b39d7794a076b0c379013410dce3080b62c59e05af94bdcd7339b3c4b5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:50.454438Z","signature_b64":"OZAmASusYGaawIOhtqbiqn39M07O+XltUhh3VjvoEUsde+sXl1AesYI1NH/0GelpKEiSqSIXe+m8hwEjzWeYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"176c7b39d7794a076b0c379013410dce3080b62c59e05af94bdcd7339b3c4b5a","last_reissued_at":"2026-05-18T02:41:50.453952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:50.453952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1056","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":"2026-05-18T02:41:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPa49hMfHiH0irun9iZZsgwBUlcrgRBVoF+mzqvwKXw8tB3LQ7pHIxkvbWiYK61mr+YMJ0ffKVBpCFAEzN3tAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:03:44.137657Z"},"content_sha256":"61d50b1c8ac046f5e2f988f821bc7344ef4bb318abf6b4923d4697629aa711e9","schema_version":"1.0","event_id":"sha256:61d50b1c8ac046f5e2f988f821bc7344ef4bb318abf6b4923d4697629aa711e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C5WHWOOXPFFAO2YMG6IBGQINZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac-operators and symmetries of quasitoric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Michael Wiemeler","submitted_at":"2011-08-04T12:12:24Z","abstract_excerpt":"We establish a vanishing result for indices of certain twisted Dirac operators on $\\text{Spin}^c$-manifolds with non-abelian Lie-group actions. We apply this result to study non-abelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1056","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:41:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/dQQbyy/YjKIeAOMrs64+9wx01DXs/6ZelTzLOoOh2kbX9UzpYHGh7tmj1gxLwspG1L9ShSmTzP9favDA2BWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:03:44.137997Z"},"content_sha256":"bf80be5ce643f475b66dfd4fc47cd3959abfcb101c829840f51a256dd3e55351","schema_version":"1.0","event_id":"sha256:bf80be5ce643f475b66dfd4fc47cd3959abfcb101c829840f51a256dd3e55351"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/bundle.json","state_url":"https://pith.science/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/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":"2026-06-21T22:03:44Z","links":{"resolver":"https://pith.science/pith/C5WHWOOXPFFAO2YMG6IBGQINZY","bundle":"https://pith.science/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/bundle.json","state":"https://pith.science/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5WHWOOXPFFAO2YMG6IBGQINZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C5WHWOOXPFFAO2YMG6IBGQINZY","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":"d3edadadd4a260191cd1e582e0a05cf7b903425eb068d5b3777726414834fc69","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-04T12:12:24Z","title_canon_sha256":"1d0fbddf59cb34b3219afa8dd5b7463f73739d0b589a6598024493791812a7d6"},"schema_version":"1.0","source":{"id":"1108.1056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1056","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1056v2","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1056","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"C5WHWOOXPFFA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5WHWOOXPFFAO2YM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5WHWOOX","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:bf80be5ce643f475b66dfd4fc47cd3959abfcb101c829840f51a256dd3e55351","target":"graph","created_at":"2026-05-18T02:41:50Z","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"},"paper":{"abstract_excerpt":"We establish a vanishing result for indices of certain twisted Dirac operators on $\\text{Spin}^c$-manifolds with non-abelian Lie-group actions. We apply this result to study non-abelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds.","authors_text":"Michael Wiemeler","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-04T12:12:24Z","title":"Dirac-operators and symmetries of quasitoric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1056","kind":"arxiv","version":2},"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":"sha256:61d50b1c8ac046f5e2f988f821bc7344ef4bb318abf6b4923d4697629aa711e9","target":"record","created_at":"2026-05-18T02:41:50Z","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":"d3edadadd4a260191cd1e582e0a05cf7b903425eb068d5b3777726414834fc69","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-04T12:12:24Z","title_canon_sha256":"1d0fbddf59cb34b3219afa8dd5b7463f73739d0b589a6598024493791812a7d6"},"schema_version":"1.0","source":{"id":"1108.1056","kind":"arxiv","version":2}},"canonical_sha256":"176c7b39d7794a076b0c379013410dce3080b62c59e05af94bdcd7339b3c4b5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"176c7b39d7794a076b0c379013410dce3080b62c59e05af94bdcd7339b3c4b5a","first_computed_at":"2026-05-18T02:41:50.453952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:50.453952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OZAmASusYGaawIOhtqbiqn39M07O+XltUhh3VjvoEUsde+sXl1AesYI1NH/0GelpKEiSqSIXe+m8hwEjzWeYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:50.454438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61d50b1c8ac046f5e2f988f821bc7344ef4bb318abf6b4923d4697629aa711e9","sha256:bf80be5ce643f475b66dfd4fc47cd3959abfcb101c829840f51a256dd3e55351"],"state_sha256":"2fb8e158f23bf5005416a25481bcd72f2caf2ca43bfc9a6c370009219d806691"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndLEQ5h7hwddzU1UZCMySEEBVScz4MZgpHtNTWBki/y9t7Cg5bTCm9M6Fz/ygO2AH54Kmn+hQa52QRumpQg0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:03:44.139867Z","bundle_sha256":"6138d1cb47fba46b3d2568544f569df204b3e4573492c779b23313b5d230b385"}}