{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DE3JRPSAP5QGB2EYGDMU4WYJXJ","short_pith_number":"pith:DE3JRPSA","canonical_record":{"source":{"id":"2405.00963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-02T03:02:05Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"9e89f7d7c708d1161e4da897238f033c9b366fc0916dc56b67b51433fd7517c7","abstract_canon_sha256":"32189fdfb5ab0c4856648ba587e570349752d8728137c91309105378a3a5cb4e"},"schema_version":"1.0"},"canonical_sha256":"193698be407f6060e89830d94e5b09ba7a9b6b177c31aebeff453f941afc49a5","source":{"kind":"arxiv","id":"2405.00963","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.00963","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"2405.00963v2","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.00963","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"DE3JRPSAP5QG","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_16","alias_value":"DE3JRPSAP5QGB2EY","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_8","alias_value":"DE3JRPSA","created_at":"2026-07-05T11:52:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DE3JRPSAP5QGB2EYGDMU4WYJXJ","target":"record","payload":{"canonical_record":{"source":{"id":"2405.00963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-02T03:02:05Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"9e89f7d7c708d1161e4da897238f033c9b366fc0916dc56b67b51433fd7517c7","abstract_canon_sha256":"32189fdfb5ab0c4856648ba587e570349752d8728137c91309105378a3a5cb4e"},"schema_version":"1.0"},"canonical_sha256":"193698be407f6060e89830d94e5b09ba7a9b6b177c31aebeff453f941afc49a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:52:55.339494Z","signature_b64":"i0i2D9fga2CWjy22KtQAbO3ZLn+VO7PJG1QrUSv5Vyx0cwxr8ofhemyqCZXWEbfQcXTuu4rcd05zQuASnqklDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"193698be407f6060e89830d94e5b09ba7a9b6b177c31aebeff453f941afc49a5","last_reissued_at":"2026-07-05T11:52:55.339001Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:52:55.339001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.00963","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":"2026-07-05T11:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MeJoSEFscibfVpR0/NSaaj7GQi6jd0UqpHK8kmjfsSzAzz+Ep+R4BriQikvhAcXEvTbUj8ZGdHivKzaIahkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:26:12.414508Z"},"content_sha256":"863c49195a9dffd4520de0f1917d835f8ea1f74859d3a4fd0750d6b5b872259d","schema_version":"1.0","event_id":"sha256:863c49195a9dffd4520de0f1917d835f8ea1f74859d3a4fd0750d6b5b872259d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DE3JRPSAP5QGB2EYGDMU4WYJXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real spin bordism and orientations of topological $\\mathrm{K}$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Yigal Kamel, Zachary Halladay","submitted_at":"2024-05-02T03:02:05Z","abstract_excerpt":"We construct a commutative orthogonal $C_2$-ring spectrum, $\\mathrm{MSpin}^c_{\\mathbb{R}}$, along with a $C_2$-$E_{\\infty}$-orientation $\\mathrm{MSpin}^c_{\\mathbb{R}} \\to \\mathrm{KU}_{\\mathbb{R}}$ of Atiyah's Real K-theory. Further, we define $E_{\\infty}$-maps $\\mathrm{MSpin} \\to (\\mathrm{MSpin}^c_{\\mathbb{R}})^{C_2}$ and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{MSpin}^c_{\\mathbb{R}}$, which are used to recover the three well-known orientations of topological $\\mathrm{K}$-theory, $\\mathrm{MSpin}^c \\to \\mathrm{KU}$, $\\mathrm{MSpin} \\to \\mathrm{KO}$, and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{KU}_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.00963","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.00963/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":"2026-07-05T11:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/YO1ctcyi4qy7eqpB4N0tClejweALacUJSP79JN7gPT3hVOXR+NUiUjhFL7xoJRRvanzBJFrZ6eqKILCrj1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:26:12.415019Z"},"content_sha256":"3e2eb09c0fbf3845dbccbc367d4cc6ea3f3f6c0473720ec8430792be3978b504","schema_version":"1.0","event_id":"sha256:3e2eb09c0fbf3845dbccbc367d4cc6ea3f3f6c0473720ec8430792be3978b504"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/bundle.json","state_url":"https://pith.science/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/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":"2026-08-09T13:26:12Z","links":{"resolver":"https://pith.science/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ","bundle":"https://pith.science/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/bundle.json","state":"https://pith.science/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DE3JRPSAP5QGB2EYGDMU4WYJXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DE3JRPSAP5QGB2EYGDMU4WYJXJ","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":"32189fdfb5ab0c4856648ba587e570349752d8728137c91309105378a3a5cb4e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-02T03:02:05Z","title_canon_sha256":"9e89f7d7c708d1161e4da897238f033c9b366fc0916dc56b67b51433fd7517c7"},"schema_version":"1.0","source":{"id":"2405.00963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.00963","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"2405.00963v2","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.00963","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"DE3JRPSAP5QG","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_16","alias_value":"DE3JRPSAP5QGB2EY","created_at":"2026-07-05T11:52:55Z"},{"alias_kind":"pith_short_8","alias_value":"DE3JRPSA","created_at":"2026-07-05T11:52:55Z"}],"graph_snapshots":[{"event_id":"sha256:3e2eb09c0fbf3845dbccbc367d4cc6ea3f3f6c0473720ec8430792be3978b504","target":"graph","created_at":"2026-07-05T11:52:55Z","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/2405.00963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a commutative orthogonal $C_2$-ring spectrum, $\\mathrm{MSpin}^c_{\\mathbb{R}}$, along with a $C_2$-$E_{\\infty}$-orientation $\\mathrm{MSpin}^c_{\\mathbb{R}} \\to \\mathrm{KU}_{\\mathbb{R}}$ of Atiyah's Real K-theory. Further, we define $E_{\\infty}$-maps $\\mathrm{MSpin} \\to (\\mathrm{MSpin}^c_{\\mathbb{R}})^{C_2}$ and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{MSpin}^c_{\\mathbb{R}}$, which are used to recover the three well-known orientations of topological $\\mathrm{K}$-theory, $\\mathrm{MSpin}^c \\to \\mathrm{KU}$, $\\mathrm{MSpin} \\to \\mathrm{KO}$, and $\\mathrm{MU}_{\\mathbb{R}} \\to \\mathrm{KU}_{\\","authors_text":"Yigal Kamel, Zachary Halladay","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-02T03:02:05Z","title":"Real spin bordism and orientations of topological $\\mathrm{K}$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.00963","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":"sha256:863c49195a9dffd4520de0f1917d835f8ea1f74859d3a4fd0750d6b5b872259d","target":"record","created_at":"2026-07-05T11:52:55Z","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":"32189fdfb5ab0c4856648ba587e570349752d8728137c91309105378a3a5cb4e","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-02T03:02:05Z","title_canon_sha256":"9e89f7d7c708d1161e4da897238f033c9b366fc0916dc56b67b51433fd7517c7"},"schema_version":"1.0","source":{"id":"2405.00963","kind":"arxiv","version":2}},"canonical_sha256":"193698be407f6060e89830d94e5b09ba7a9b6b177c31aebeff453f941afc49a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"193698be407f6060e89830d94e5b09ba7a9b6b177c31aebeff453f941afc49a5","first_computed_at":"2026-07-05T11:52:55.339001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:55.339001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0i2D9fga2CWjy22KtQAbO3ZLn+VO7PJG1QrUSv5Vyx0cwxr8ofhemyqCZXWEbfQcXTuu4rcd05zQuASnqklDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:55.339494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.00963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:863c49195a9dffd4520de0f1917d835f8ea1f74859d3a4fd0750d6b5b872259d","sha256:3e2eb09c0fbf3845dbccbc367d4cc6ea3f3f6c0473720ec8430792be3978b504"],"state_sha256":"821453501fc3f5746ff5c3e4cffdcafe5cc435d9dfeb1252cf52a65b1424eba1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fr28fkd1Ymo/ZJzu3LfyX3eZh+OeY8NAycKOAzudhYgsrpBwcUN+D5u2ZZuFdzPOmuS8ohK+i0+FYODhCLEBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:26:12.420923Z","bundle_sha256":"de9d35ead05d6d15d42accaea7c83889b4c8880c55afe7be0e8de8ff21139adf"}}