{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XDAHBJKZ5RMMGIG66HF2L3IFQ4","short_pith_number":"pith:XDAHBJKZ","canonical_record":{"source":{"id":"1806.10108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-26T17:00:13Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"e99bdbe5c970276ea9723d678f4806cd0d283fbf8f4440eab8be4e3bc73b142e","abstract_canon_sha256":"2879259095bd165283eb8c5908e217792c47f01a2cb97f6d7f6c684d01f18ddb"},"schema_version":"1.0"},"canonical_sha256":"b8c070a559ec58c320def1cba5ed05872567f99cb552e9df161f863b11ce9d78","source":{"kind":"arxiv","id":"1806.10108","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10108","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10108v2","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10108","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"XDAHBJKZ5RMM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XDAHBJKZ5RMMGIG6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XDAHBJKZ","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XDAHBJKZ5RMMGIG66HF2L3IFQ4","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10108","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-26T17:00:13Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"e99bdbe5c970276ea9723d678f4806cd0d283fbf8f4440eab8be4e3bc73b142e","abstract_canon_sha256":"2879259095bd165283eb8c5908e217792c47f01a2cb97f6d7f6c684d01f18ddb"},"schema_version":"1.0"},"canonical_sha256":"b8c070a559ec58c320def1cba5ed05872567f99cb552e9df161f863b11ce9d78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.029708Z","signature_b64":"tvjFlJgW0sJglsTWsWsPgYmox1YmgKg8gJnnKsgNU6OtTobh4ZPgtFpZAdRm6sM4pM+esm8jOk7PDPmxz8CPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8c070a559ec58c320def1cba5ed05872567f99cb552e9df161f863b11ce9d78","last_reissued_at":"2026-05-17T23:45:53.029217Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.029217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10108","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":"2026-05-17T23:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/dSwkcLDXZl1unRJ3XjNSFU+C0M7tMmC7ZQwmtwDIM8I0vZ9RohQUF+IH+obbI04WC8o6l6OKIllPdI5LBy1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:20:32.516520Z"},"content_sha256":"e6dff8a02b146b8e07d8c9a6f72ade3a8c735e4f7f4ff7762dcb754bd0dcd959","schema_version":"1.0","event_id":"sha256:e6dff8a02b146b8e07d8c9a6f72ade3a8c735e4f7f4ff7762dcb754bd0dcd959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XDAHBJKZ5RMMGIG66HF2L3IFQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motivic Euler characteristics and Witt-valued characteristic classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Marc Levine","submitted_at":"2018-06-26T17:00:13Z","abstract_excerpt":"This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois.\n  Ananyevskiy's splitting principle reduces questions about characteristic classes of vector bundles in $\\text{SL}$-oriented, $\\eta$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\\text{SL}_2$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10108","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":"2026-05-17T23:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G88eeMhCw/E2FRKlnGxKKQMAQ7oKLaL0J3/OF/37asbmMyHX41hYHN840NBu6yS0EVOBP7cRpx3xqepIEYaoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:20:32.516869Z"},"content_sha256":"623a94f71d72eb4f9aec41e8a5f70194ec6d496bc6cc363230e07465777f5e55","schema_version":"1.0","event_id":"sha256:623a94f71d72eb4f9aec41e8a5f70194ec6d496bc6cc363230e07465777f5e55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/bundle.json","state_url":"https://pith.science/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/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":"2026-05-25T22:20:32Z","links":{"resolver":"https://pith.science/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4","bundle":"https://pith.science/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/bundle.json","state":"https://pith.science/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDAHBJKZ5RMMGIG66HF2L3IFQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XDAHBJKZ5RMMGIG66HF2L3IFQ4","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":"2879259095bd165283eb8c5908e217792c47f01a2cb97f6d7f6c684d01f18ddb","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-26T17:00:13Z","title_canon_sha256":"e99bdbe5c970276ea9723d678f4806cd0d283fbf8f4440eab8be4e3bc73b142e"},"schema_version":"1.0","source":{"id":"1806.10108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10108","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10108v2","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10108","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"XDAHBJKZ5RMM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XDAHBJKZ5RMMGIG6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XDAHBJKZ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:623a94f71d72eb4f9aec41e8a5f70194ec6d496bc6cc363230e07465777f5e55","target":"graph","created_at":"2026-05-17T23:45:53Z","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":"This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois.\n  Ananyevskiy's splitting principle reduces questions about characteristic classes of vector bundles in $\\text{SL}$-oriented, $\\eta$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\\text{SL}_2$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, ","authors_text":"Marc Levine","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-26T17:00:13Z","title":"Motivic Euler characteristics and Witt-valued characteristic classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10108","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:e6dff8a02b146b8e07d8c9a6f72ade3a8c735e4f7f4ff7762dcb754bd0dcd959","target":"record","created_at":"2026-05-17T23:45:53Z","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":"2879259095bd165283eb8c5908e217792c47f01a2cb97f6d7f6c684d01f18ddb","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-26T17:00:13Z","title_canon_sha256":"e99bdbe5c970276ea9723d678f4806cd0d283fbf8f4440eab8be4e3bc73b142e"},"schema_version":"1.0","source":{"id":"1806.10108","kind":"arxiv","version":2}},"canonical_sha256":"b8c070a559ec58c320def1cba5ed05872567f99cb552e9df161f863b11ce9d78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8c070a559ec58c320def1cba5ed05872567f99cb552e9df161f863b11ce9d78","first_computed_at":"2026-05-17T23:45:53.029217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:53.029217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tvjFlJgW0sJglsTWsWsPgYmox1YmgKg8gJnnKsgNU6OtTobh4ZPgtFpZAdRm6sM4pM+esm8jOk7PDPmxz8CPBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:53.029708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6dff8a02b146b8e07d8c9a6f72ade3a8c735e4f7f4ff7762dcb754bd0dcd959","sha256:623a94f71d72eb4f9aec41e8a5f70194ec6d496bc6cc363230e07465777f5e55"],"state_sha256":"af9a45c708916e689bfa3b20b4d210e7d62a75cf75b9230429e72e7b4423f8fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gs1WpOvy6TFxW0WY1I5nHy7olx43RuYYvixgpe/YVTeqVzcLFV28AqzLt59/pLC313O6DeWHIfTNH27fGt0hAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:20:32.519016Z","bundle_sha256":"5fe2b6de5931113eee22836d8db6163361b67632b1d9d20b741984d4002d599c"}}