{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NWJSRNUEFZXGX3CCLECDN2ZDUJ","short_pith_number":"pith:NWJSRNUE","canonical_record":{"source":{"id":"2210.14359","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-10-25T21:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"e398464c451c4caeabbbce1560632519c643eda84a64fe8bd3f22f2f837a1836","abstract_canon_sha256":"b6e166a447ee0b7ba1b51673e082ca1e9abb3cf31f6d70ebc59a6761c93e68e4"},"schema_version":"1.0"},"canonical_sha256":"6d9328b6842e6e6bec42590436eb23a2767d3f3df8e86fae086afe5e967dccb6","source":{"kind":"arxiv","id":"2210.14359","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.14359","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"2210.14359v2","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.14359","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"NWJSRNUEFZXG","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_16","alias_value":"NWJSRNUEFZXGX3CC","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_8","alias_value":"NWJSRNUE","created_at":"2026-07-05T05:13:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NWJSRNUEFZXGX3CCLECDN2ZDUJ","target":"record","payload":{"canonical_record":{"source":{"id":"2210.14359","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-10-25T21:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"e398464c451c4caeabbbce1560632519c643eda84a64fe8bd3f22f2f837a1836","abstract_canon_sha256":"b6e166a447ee0b7ba1b51673e082ca1e9abb3cf31f6d70ebc59a6761c93e68e4"},"schema_version":"1.0"},"canonical_sha256":"6d9328b6842e6e6bec42590436eb23a2767d3f3df8e86fae086afe5e967dccb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:57.934125Z","signature_b64":"B/ZqOHWtCiD8xYhLrf+cC4mvI35h8O1EaUMwXIk/CnvWimQVY/QOZVGLFOA7PsdbCMnp4OWh9a6GWT3PPR7YDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d9328b6842e6e6bec42590436eb23a2767d3f3df8e86fae086afe5e967dccb6","last_reissued_at":"2026-07-05T05:13:57.933692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:57.933692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.14359","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":"2026-07-05T05:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmS61onYw5kE1bA0KlXs9zIKy8fymJa3KFrX4KTM1/Z4eXBkmwi2Tcu/5Yqq5mY2AjVUbFsSzeBMcelvUkSOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:49:36.167582Z"},"content_sha256":"5ee2a205cec283dcd827003c83f4928887e849e6b88e76c9261bdbabcaf1a0be","schema_version":"1.0","event_id":"sha256:5ee2a205cec283dcd827003c83f4928887e849e6b88e76c9261bdbabcaf1a0be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NWJSRNUEFZXGX3CCLECDN2ZDUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation Spaces, Rescaled Bundles and the Kirillov Character Formula","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ahmad Reza Haj Saeedi Sadegh, Maxim Braverman","submitted_at":"2022-10-25T21:57:27Z","abstract_excerpt":"In this paper, we construct a smooth vector bundle over the deformation to the normal cone $\\text{DNC}(V,M)$ through a rescaling of a vector bundle $E\\to V$, which generalizes the construction of the spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin Yi. We also provide an equivariant version of their construction. As the main application, we recover the Kirillov character formula for the equivariant index of Dirac-type operators. As another application, we get an equivariant generalization of the description of the Witten and the Novikov deformations of the de Rham-Dir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.14359","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/2210.14359/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":"2026-07-05T05:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ce1RDGUNhAdalWvkrlDA4Q9V4coA19kTCP/inoVPhVpfSTFZRRRFC9/lgxPAK3ppMxigGLxm1jBRCxJdp7BIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:49:36.168139Z"},"content_sha256":"ef52c034972e4c7ae4eb242db6eab4e9f1937a8c4ce095e2ffb11287c23e00f7","schema_version":"1.0","event_id":"sha256:ef52c034972e4c7ae4eb242db6eab4e9f1937a8c4ce095e2ffb11287c23e00f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/bundle.json","state_url":"https://pith.science/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/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":"2026-08-13T12:49:36Z","links":{"resolver":"https://pith.science/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ","bundle":"https://pith.science/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/bundle.json","state":"https://pith.science/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWJSRNUEFZXGX3CCLECDN2ZDUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NWJSRNUEFZXGX3CCLECDN2ZDUJ","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":"b6e166a447ee0b7ba1b51673e082ca1e9abb3cf31f6d70ebc59a6761c93e68e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-10-25T21:57:27Z","title_canon_sha256":"e398464c451c4caeabbbce1560632519c643eda84a64fe8bd3f22f2f837a1836"},"schema_version":"1.0","source":{"id":"2210.14359","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.14359","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"2210.14359v2","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.14359","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"NWJSRNUEFZXG","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_16","alias_value":"NWJSRNUEFZXGX3CC","created_at":"2026-07-05T05:13:57Z"},{"alias_kind":"pith_short_8","alias_value":"NWJSRNUE","created_at":"2026-07-05T05:13:57Z"}],"graph_snapshots":[{"event_id":"sha256:ef52c034972e4c7ae4eb242db6eab4e9f1937a8c4ce095e2ffb11287c23e00f7","target":"graph","created_at":"2026-07-05T05:13:57Z","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/2210.14359/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct a smooth vector bundle over the deformation to the normal cone $\\text{DNC}(V,M)$ through a rescaling of a vector bundle $E\\to V$, which generalizes the construction of the spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin Yi. We also provide an equivariant version of their construction. As the main application, we recover the Kirillov character formula for the equivariant index of Dirac-type operators. As another application, we get an equivariant generalization of the description of the Witten and the Novikov deformations of the de Rham-Dir","authors_text":"Ahmad Reza Haj Saeedi Sadegh, Maxim Braverman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-10-25T21:57:27Z","title":"Deformation Spaces, Rescaled Bundles and the Kirillov Character Formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.14359","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":"sha256:5ee2a205cec283dcd827003c83f4928887e849e6b88e76c9261bdbabcaf1a0be","target":"record","created_at":"2026-07-05T05:13:57Z","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":"b6e166a447ee0b7ba1b51673e082ca1e9abb3cf31f6d70ebc59a6761c93e68e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-10-25T21:57:27Z","title_canon_sha256":"e398464c451c4caeabbbce1560632519c643eda84a64fe8bd3f22f2f837a1836"},"schema_version":"1.0","source":{"id":"2210.14359","kind":"arxiv","version":2}},"canonical_sha256":"6d9328b6842e6e6bec42590436eb23a2767d3f3df8e86fae086afe5e967dccb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d9328b6842e6e6bec42590436eb23a2767d3f3df8e86fae086afe5e967dccb6","first_computed_at":"2026-07-05T05:13:57.933692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:57.933692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B/ZqOHWtCiD8xYhLrf+cC4mvI35h8O1EaUMwXIk/CnvWimQVY/QOZVGLFOA7PsdbCMnp4OWh9a6GWT3PPR7YDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:57.934125Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.14359","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee2a205cec283dcd827003c83f4928887e849e6b88e76c9261bdbabcaf1a0be","sha256:ef52c034972e4c7ae4eb242db6eab4e9f1937a8c4ce095e2ffb11287c23e00f7"],"state_sha256":"f1a74de1b861edc6cf23f88682f60cdedf9ba53bfa95cb9448254c970148339d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TiW/zYEWXHqiO0O7KRyQwzhJwBwSL4loGGM8UJlpBltU7udnVTO2nDRHDcH4UDAGWN1A+rC8+OhuzzS2KIpCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:49:36.176022Z","bundle_sha256":"3d4f054744c5a5174458f2521f24e1fa82ea9c032433bcd65055667928e656fa"}}