{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:I342467FZSFVG4EWS74IEOMBW2","short_pith_number":"pith:I342467F","canonical_record":{"source":{"id":"math/0307251","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T19:51:33Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"7ba01131685ec404bf9e25b44b12a274ba4dbe1cc2720e6f1538cdc7145548e3","abstract_canon_sha256":"3113d7dbb7f026afc0556e30d91dca489840847475829c7287def5d379fc933f"},"schema_version":"1.0"},"canonical_sha256":"46f9ae7be5cc8b53709697f8823981b691094d3f6f540724fef89a11e008126c","source":{"kind":"arxiv","id":"math/0307251","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307251","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307251v3","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307251","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"I342467FZSFV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"I342467FZSFVG4EW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"I342467F","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:I342467FZSFVG4EWS74IEOMBW2","target":"record","payload":{"canonical_record":{"source":{"id":"math/0307251","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T19:51:33Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"7ba01131685ec404bf9e25b44b12a274ba4dbe1cc2720e6f1538cdc7145548e3","abstract_canon_sha256":"3113d7dbb7f026afc0556e30d91dca489840847475829c7287def5d379fc933f"},"schema_version":"1.0"},"canonical_sha256":"46f9ae7be5cc8b53709697f8823981b691094d3f6f540724fef89a11e008126c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:28.925479Z","signature_b64":"EViT+zufcFb4mqi0IQdL1wQRyGUpOS6zBwBoqjWbCXHEr6CwO8xApoPhvNJ/DOkumuXqzpcD1GdqmPHXC4xNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f9ae7be5cc8b53709697f8823981b691094d3f6f540724fef89a11e008126c","last_reissued_at":"2026-05-18T01:38:28.924774Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:28.924774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0307251","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":"2026-05-18T01:38:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIBmmtSis5DP14bo+Hy4xVfYVcVouYgqt5gzZqV8FhhQOvK8KqnNEmhEfy6kHdvye5Kx6O+3RaOHba0nOX3sAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:43:59.106658Z"},"content_sha256":"e60049451f48e1f19c5f8d85f45faf9bce5507350c6db6b441528379b004e865","schema_version":"1.0","event_id":"sha256:e60049451f48e1f19c5f8d85f45faf9bce5507350c6db6b441528379b004e865"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:I342467FZSFVG4EWS74IEOMBW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbations of Dirac operators","license":"","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Igor Prokhorenkov, Ken Richardson","submitted_at":"2003-07-17T19:51:33Z","abstract_excerpt":"We study general conditions under which the computations of the index of a perturbed Dirac operator $D_{s}=D+sZ$ localize to the singular set of the bundle endomorphism $Z$ in the semi-classical limit $s\\to \\infty $. We show how to use Witten's method to compute the index of $D$ by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator $Z$. In particular, we provide examples of novel deformations of the de Rham operator to establish new results relating the Euler characteristic of a spin$^{c}$ manifold to maps between its even and odd spinor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307251","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":"2026-05-18T01:38:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6z7YTpclVltGWcKJf7gAupEtlxYNKKKCdbnC+7mJbRYxmAjhMspieGgAorZ1YwSjVcSrnBWheL1E7Cwblkn8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:43:59.106999Z"},"content_sha256":"072b67f126f31257d32e72b14536ba1335c7d467975d56ca2847089351440560","schema_version":"1.0","event_id":"sha256:072b67f126f31257d32e72b14536ba1335c7d467975d56ca2847089351440560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I342467FZSFVG4EWS74IEOMBW2/bundle.json","state_url":"https://pith.science/pith/I342467FZSFVG4EWS74IEOMBW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I342467FZSFVG4EWS74IEOMBW2/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":"2026-06-09T13:43:59Z","links":{"resolver":"https://pith.science/pith/I342467FZSFVG4EWS74IEOMBW2","bundle":"https://pith.science/pith/I342467FZSFVG4EWS74IEOMBW2/bundle.json","state":"https://pith.science/pith/I342467FZSFVG4EWS74IEOMBW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I342467FZSFVG4EWS74IEOMBW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:I342467FZSFVG4EWS74IEOMBW2","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":"3113d7dbb7f026afc0556e30d91dca489840847475829c7287def5d379fc933f","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T19:51:33Z","title_canon_sha256":"7ba01131685ec404bf9e25b44b12a274ba4dbe1cc2720e6f1538cdc7145548e3"},"schema_version":"1.0","source":{"id":"math/0307251","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307251","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307251v3","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307251","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"I342467FZSFV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"I342467FZSFVG4EW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"I342467F","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:072b67f126f31257d32e72b14536ba1335c7d467975d56ca2847089351440560","target":"graph","created_at":"2026-05-18T01:38:28Z","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 study general conditions under which the computations of the index of a perturbed Dirac operator $D_{s}=D+sZ$ localize to the singular set of the bundle endomorphism $Z$ in the semi-classical limit $s\\to \\infty $. We show how to use Witten's method to compute the index of $D$ by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator $Z$. In particular, we provide examples of novel deformations of the de Rham operator to establish new results relating the Euler characteristic of a spin$^{c}$ manifold to maps between its even and odd spinor","authors_text":"Igor Prokhorenkov, Ken Richardson","cross_cats":["math.SP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T19:51:33Z","title":"Perturbations of Dirac operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307251","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:e60049451f48e1f19c5f8d85f45faf9bce5507350c6db6b441528379b004e865","target":"record","created_at":"2026-05-18T01:38:28Z","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":"3113d7dbb7f026afc0556e30d91dca489840847475829c7287def5d379fc933f","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T19:51:33Z","title_canon_sha256":"7ba01131685ec404bf9e25b44b12a274ba4dbe1cc2720e6f1538cdc7145548e3"},"schema_version":"1.0","source":{"id":"math/0307251","kind":"arxiv","version":3}},"canonical_sha256":"46f9ae7be5cc8b53709697f8823981b691094d3f6f540724fef89a11e008126c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46f9ae7be5cc8b53709697f8823981b691094d3f6f540724fef89a11e008126c","first_computed_at":"2026-05-18T01:38:28.924774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:28.924774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EViT+zufcFb4mqi0IQdL1wQRyGUpOS6zBwBoqjWbCXHEr6CwO8xApoPhvNJ/DOkumuXqzpcD1GdqmPHXC4xNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:28.925479Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307251","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e60049451f48e1f19c5f8d85f45faf9bce5507350c6db6b441528379b004e865","sha256:072b67f126f31257d32e72b14536ba1335c7d467975d56ca2847089351440560"],"state_sha256":"e8bba388af9f4b43bcf8bb67ccf93f28041deef0f6b67dcb7d77e9ad3d14f2d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtuP17ybE1irwE4Y9lN6/QPqf10jZEjnPG8oPiS8H/WwbBntx2cA54VujVt7XyojJbE4fCw6ZPBCwNvRzy+fAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:43:59.108879Z","bundle_sha256":"648f28bc82a5b98a04242bcec32d0d260718d4d80b4d636353acd057df8a65e6"}}