{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MW6QTHHTWFI4MKQQMWSMSOS24G","short_pith_number":"pith:MW6QTHHT","canonical_record":{"source":{"id":"1705.01954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-04T18:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"c15bcb1decc07d098e50cb178af4b650deb78f0fae7f08709bc60badd4cd1a4f","abstract_canon_sha256":"4a6da22bba5bb07ac8dcea9852d11930874261a98acc57c820f18da36cb2bdad"},"schema_version":"1.0"},"canonical_sha256":"65bd099cf3b151c62a1065a4c93a5ae191a0b17d1ce72e7b808e5f6ab2b0d676","source":{"kind":"arxiv","id":"1705.01954","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01954","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01954v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01954","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"MW6QTHHTWFI4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MW6QTHHTWFI4MKQQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MW6QTHHT","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MW6QTHHTWFI4MKQQMWSMSOS24G","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-04T18:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"c15bcb1decc07d098e50cb178af4b650deb78f0fae7f08709bc60badd4cd1a4f","abstract_canon_sha256":"4a6da22bba5bb07ac8dcea9852d11930874261a98acc57c820f18da36cb2bdad"},"schema_version":"1.0"},"canonical_sha256":"65bd099cf3b151c62a1065a4c93a5ae191a0b17d1ce72e7b808e5f6ab2b0d676","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:45.354014Z","signature_b64":"DaSvUbrjC9VSAo1JxIhKZQGzvSUx498Puu2bdGxMkQbEiPraPKsK8qGU1WWwg8tTnE9JXs4ExEXE8KQrpKMzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65bd099cf3b151c62a1065a4c93a5ae191a0b17d1ce72e7b808e5f6ab2b0d676","last_reissued_at":"2026-05-18T00:16:45.353366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:45.353366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01954","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":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AfiFYiMPgqyDq3jj9mbnRPPRldZqmJnIxiR7d8p74Hlnm0DQofpw8CxRL76myN3+XQtgMQnE5PGCLnB417fJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:05:06.496118Z"},"content_sha256":"cd6d7e55a4237d57df15c807421a92104017e2537dc72613930b37c3115aa9ca","schema_version":"1.0","event_id":"sha256:cd6d7e55a4237d57df15c807421a92104017e2537dc72613930b37c3115aa9ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MW6QTHHTWFI4MKQQMWSMSOS24G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Index theorem for Z/2-harmonic spinors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ryosuke Takahashi","submitted_at":"2017-05-04T18:00:57Z","abstract_excerpt":"In my previous paper, I prove the existence of the Kuranishi structure for the moduli space $\\mathfrak{M}$ of zero loci of $\\mathbb{Z}/2$-harmonic spinors on a 3-manifold. So a nature question we can ask is to compute the virtual dimension for this moduli space $\\mathfrak{M}_{g_0}:=\\mathfrak{M}\\cap\\{g=g_0\\}$. In this paper, I will first prove that $v-dim(\\mathfrak{M}_{g_0})=0$. Secondly, I will generalize this formula on 4-manifolds by using a special type of index developed by Jochen Bruning, Robert Seeley, and Fangyun Yang."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01954","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":""},"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":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JkOBH4ZxR3HPJ3llzpDg1kzgqG9q4iejCJoblcpV/PDeZpyThDAdHLrYeDEUtkRir88PfP/ZQPHrbH2MobHMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:05:06.496771Z"},"content_sha256":"abcdf26b09cf5be7f2c8927aef4a2e37a1464a110b5e9509f8dc5b64a7b2fc3c","schema_version":"1.0","event_id":"sha256:abcdf26b09cf5be7f2c8927aef4a2e37a1464a110b5e9509f8dc5b64a7b2fc3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/bundle.json","state_url":"https://pith.science/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/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":"2026-06-01T12:05:06Z","links":{"resolver":"https://pith.science/pith/MW6QTHHTWFI4MKQQMWSMSOS24G","bundle":"https://pith.science/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/bundle.json","state":"https://pith.science/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MW6QTHHTWFI4MKQQMWSMSOS24G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MW6QTHHTWFI4MKQQMWSMSOS24G","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":"4a6da22bba5bb07ac8dcea9852d11930874261a98acc57c820f18da36cb2bdad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-04T18:00:57Z","title_canon_sha256":"c15bcb1decc07d098e50cb178af4b650deb78f0fae7f08709bc60badd4cd1a4f"},"schema_version":"1.0","source":{"id":"1705.01954","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01954","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01954v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01954","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"MW6QTHHTWFI4","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MW6QTHHTWFI4MKQQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MW6QTHHT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:abcdf26b09cf5be7f2c8927aef4a2e37a1464a110b5e9509f8dc5b64a7b2fc3c","target":"graph","created_at":"2026-05-18T00:16:45Z","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":"In my previous paper, I prove the existence of the Kuranishi structure for the moduli space $\\mathfrak{M}$ of zero loci of $\\mathbb{Z}/2$-harmonic spinors on a 3-manifold. So a nature question we can ask is to compute the virtual dimension for this moduli space $\\mathfrak{M}_{g_0}:=\\mathfrak{M}\\cap\\{g=g_0\\}$. In this paper, I will first prove that $v-dim(\\mathfrak{M}_{g_0})=0$. Secondly, I will generalize this formula on 4-manifolds by using a special type of index developed by Jochen Bruning, Robert Seeley, and Fangyun Yang.","authors_text":"Ryosuke Takahashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-04T18:00:57Z","title":"Index theorem for Z/2-harmonic spinors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01954","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:cd6d7e55a4237d57df15c807421a92104017e2537dc72613930b37c3115aa9ca","target":"record","created_at":"2026-05-18T00:16:45Z","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":"4a6da22bba5bb07ac8dcea9852d11930874261a98acc57c820f18da36cb2bdad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-04T18:00:57Z","title_canon_sha256":"c15bcb1decc07d098e50cb178af4b650deb78f0fae7f08709bc60badd4cd1a4f"},"schema_version":"1.0","source":{"id":"1705.01954","kind":"arxiv","version":3}},"canonical_sha256":"65bd099cf3b151c62a1065a4c93a5ae191a0b17d1ce72e7b808e5f6ab2b0d676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65bd099cf3b151c62a1065a4c93a5ae191a0b17d1ce72e7b808e5f6ab2b0d676","first_computed_at":"2026-05-18T00:16:45.353366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:45.353366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DaSvUbrjC9VSAo1JxIhKZQGzvSUx498Puu2bdGxMkQbEiPraPKsK8qGU1WWwg8tTnE9JXs4ExEXE8KQrpKMzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:45.354014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01954","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6d7e55a4237d57df15c807421a92104017e2537dc72613930b37c3115aa9ca","sha256:abcdf26b09cf5be7f2c8927aef4a2e37a1464a110b5e9509f8dc5b64a7b2fc3c"],"state_sha256":"93c9d84e46cbd2d6547bf77b5f8650eb270248d4fc642cf719c92b28ec1929ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXdtj4UBGE56iZD+xlQK4q0xzIjcodUNuy/S+6K4DwRpJLpoZ77SBnL5ubjUDZyZXthvBkwu77KswNFDn+fyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:05:06.499775Z","bundle_sha256":"193cf357ec4f177176021408ed5c08a982ee789e5e5d9c9d5deb133cf0d2bd38"}}