{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CQZ6NIOJQWNTWH6FGX7CMT5Z5L","short_pith_number":"pith:CQZ6NIOJ","canonical_record":{"source":{"id":"2411.01646","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2024-11-03T17:52:20Z","cross_cats_sorted":["math.AT","math.DG","math.OA"],"title_canon_sha256":"2b6808e26761cd56ad914c0ced3d20cce814f36e87f8638c5d57645cd0a4c0b2","abstract_canon_sha256":"aec50e9a9fc8ed0285fa7f4d6e47f50bc50fcf6107e8dcade6eee2c7581ad5ae"},"schema_version":"1.0"},"canonical_sha256":"1433e6a1c9859b3b1fc535fe264fb9eac2555db1eb0a99df3167776eb7636139","source":{"kind":"arxiv","id":"2411.01646","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.01646","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.01646v2","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01646","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQZ6NIOJQWNT","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"CQZ6NIOJQWNTWH6F","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"CQZ6NIOJ","created_at":"2026-07-05T09:31:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CQZ6NIOJQWNTWH6FGX7CMT5Z5L","target":"record","payload":{"canonical_record":{"source":{"id":"2411.01646","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2024-11-03T17:52:20Z","cross_cats_sorted":["math.AT","math.DG","math.OA"],"title_canon_sha256":"2b6808e26761cd56ad914c0ced3d20cce814f36e87f8638c5d57645cd0a4c0b2","abstract_canon_sha256":"aec50e9a9fc8ed0285fa7f4d6e47f50bc50fcf6107e8dcade6eee2c7581ad5ae"},"schema_version":"1.0"},"canonical_sha256":"1433e6a1c9859b3b1fc535fe264fb9eac2555db1eb0a99df3167776eb7636139","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:51.086342Z","signature_b64":"S0h1DEJ4GkaCjvUdrMsRFZWRFE2kBJbbnXDlDPN2uFzYICOGWja4oK+aHpRNflEToxgBvdnrclPp9ARBI9evBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1433e6a1c9859b3b1fc535fe264fb9eac2555db1eb0a99df3167776eb7636139","last_reissued_at":"2026-07-05T09:31:51.085812Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:51.085812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.01646","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":"2026-07-05T09:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j1cNre4re5RwIPFR7J3wrTeWWmhq7c+rcVPTNNyVKJtZrjJTOQGJrYnFaxLUGUxqaIVil5b2KPY8Gy2YJRuCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:32:49.092349Z"},"content_sha256":"68e2bbf7fb17646100cf0cd3cc08ed3dc5134b112987a9936d115f08f287b8d8","schema_version":"1.0","event_id":"sha256:68e2bbf7fb17646100cf0cd3cc08ed3dc5134b112987a9936d115f08f287b8d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CQZ6NIOJQWNTWH6FGX7CMT5Z5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coronas and Callias type operators in coarse geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.DG","math.OA"],"primary_cat":"math.KT","authors_text":"Matthias Ludewig, Ulrich Bunke","submitted_at":"2024-11-03T17:52:20Z","abstract_excerpt":"We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\\Psi$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $\\Psi$. Local positivity of $D$ and local invertibility of $\\Psi$ are incorporated in terms of support conditions on the $K$-theoretic level."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01646","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/2411.01646/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":"2026-07-05T09:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LzHvNwGQ+GbqKIDhNd26egN0aUIFc0oiiS20vj8bYsZxR8V5T+C7Igh07sR3a8H3n81Ku0NXeQQgCl7bD2fnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:32:49.092862Z"},"content_sha256":"a275b97bccc053e41919f9ffa72eee3f10a614077c3cafc7101b18c055d8ba82","schema_version":"1.0","event_id":"sha256:a275b97bccc053e41919f9ffa72eee3f10a614077c3cafc7101b18c055d8ba82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/bundle.json","state_url":"https://pith.science/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/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":"2026-08-13T07:32:49Z","links":{"resolver":"https://pith.science/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L","bundle":"https://pith.science/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/bundle.json","state":"https://pith.science/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQZ6NIOJQWNTWH6FGX7CMT5Z5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CQZ6NIOJQWNTWH6FGX7CMT5Z5L","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":"aec50e9a9fc8ed0285fa7f4d6e47f50bc50fcf6107e8dcade6eee2c7581ad5ae","cross_cats_sorted":["math.AT","math.DG","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2024-11-03T17:52:20Z","title_canon_sha256":"2b6808e26761cd56ad914c0ced3d20cce814f36e87f8638c5d57645cd0a4c0b2"},"schema_version":"1.0","source":{"id":"2411.01646","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.01646","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.01646v2","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01646","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQZ6NIOJQWNT","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_16","alias_value":"CQZ6NIOJQWNTWH6F","created_at":"2026-07-05T09:31:51Z"},{"alias_kind":"pith_short_8","alias_value":"CQZ6NIOJ","created_at":"2026-07-05T09:31:51Z"}],"graph_snapshots":[{"event_id":"sha256:a275b97bccc053e41919f9ffa72eee3f10a614077c3cafc7101b18c055d8ba82","target":"graph","created_at":"2026-07-05T09:31:51Z","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/2411.01646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\\Psi$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $\\Psi$. Local positivity of $D$ and local invertibility of $\\Psi$ are incorporated in terms of support conditions on the $K$-theoretic level.","authors_text":"Matthias Ludewig, Ulrich Bunke","cross_cats":["math.AT","math.DG","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2024-11-03T17:52:20Z","title":"Coronas and Callias type operators in coarse geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01646","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":"sha256:68e2bbf7fb17646100cf0cd3cc08ed3dc5134b112987a9936d115f08f287b8d8","target":"record","created_at":"2026-07-05T09:31:51Z","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":"aec50e9a9fc8ed0285fa7f4d6e47f50bc50fcf6107e8dcade6eee2c7581ad5ae","cross_cats_sorted":["math.AT","math.DG","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.KT","submitted_at":"2024-11-03T17:52:20Z","title_canon_sha256":"2b6808e26761cd56ad914c0ced3d20cce814f36e87f8638c5d57645cd0a4c0b2"},"schema_version":"1.0","source":{"id":"2411.01646","kind":"arxiv","version":2}},"canonical_sha256":"1433e6a1c9859b3b1fc535fe264fb9eac2555db1eb0a99df3167776eb7636139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1433e6a1c9859b3b1fc535fe264fb9eac2555db1eb0a99df3167776eb7636139","first_computed_at":"2026-07-05T09:31:51.085812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:31:51.085812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S0h1DEJ4GkaCjvUdrMsRFZWRFE2kBJbbnXDlDPN2uFzYICOGWja4oK+aHpRNflEToxgBvdnrclPp9ARBI9evBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:31:51.086342Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.01646","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68e2bbf7fb17646100cf0cd3cc08ed3dc5134b112987a9936d115f08f287b8d8","sha256:a275b97bccc053e41919f9ffa72eee3f10a614077c3cafc7101b18c055d8ba82"],"state_sha256":"a8fc83b5256ec2481be32d085d3a65b2e31fd67845479a279d46a17957af7adb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWwCe2eny6PIPzoyXavAx9oiF/1KPxf8zRzCTI8BDCAn+ymNOPjRPmJddOFyd2mSTRH0+Zs3WGhy8DgRGDyRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T07:32:49.097969Z","bundle_sha256":"a8641ca7d4e55e8b5812ef1bda720cb6b75b5331da26e46269142f4a38afc135"}}