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We equip the tangent blow-up with a product metric and define discretized differential operators, such as the gradient, divergence, and Laplacian, directly in the lifted domain.","weakest_assumption":"The discretization of the product metric and differential operators on the lifted space preserves the separation property and yields stable numerical results without introducing new artifacts at the original singularities (implicit in the demonstration claims across geodesic computation, segmentation, parameterization, and curvature estimation)."}},"verdict_id":"66a93857-d715-43e0-bffb-37111a89fa97"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5fdc7cf4d7e8bdd879f34eeec796bb77d9f50af675e7a70da45fdf88afc23b0a","target":"record","created_at":"2026-05-20T00:05:50Z","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":"b86e1c9b510b6fb42c40dacae45227ee5e229ccac6db28c9b334e1a1e1cc227f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.GR","submitted_at":"2026-05-18T11:00:42Z","title_canon_sha256":"c7f98a30f8c0b27d3de3e068110e25345f0b14c6467873a250d7c7c4b5b34007"},"schema_version":"1.0","source":{"id":"2605.18215","kind":"arxiv","version":1}},"canonical_sha256":"59f5f3255879e9dc05d8d3bfaadcf6903283b6c3d8a9dade1005a43265a6443d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59f5f3255879e9dc05d8d3bfaadcf6903283b6c3d8a9dade1005a43265a6443d","first_computed_at":"2026-05-20T00:05:50.871243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:50.871243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09bC++IyGQEbYJqmeaqKDsp+5MpQsQHQcKksZ3TT3T1pjPORctvxtwAfaDO2/R2PjTVPX+dcjkxLvj9rjFRRCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:50.871814Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fdc7cf4d7e8bdd879f34eeec796bb77d9f50af675e7a70da45fdf88afc23b0a","sha256:58b961e08b29db6cd70f1c53dfb3abaae2c6bffba0da8d82eb61139c71f46dd6"],"state_sha256":"b6cfd052a5eeeb78998d5a3f0cadb28d100067b5077d4d938192938f1b7995d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+abaloTtuHyZ/PPrwOkknTBWGcI6+81fIIg3azGSDBP4BogY/Mpe0E2kXpnPM+2gbtljIJ264Kf0Hmhb+tpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T19:10:14.760580Z","bundle_sha256":"bb9e100311d42d353cd2c01eddc45682624d482ef1c724b5e086a3580d6b48c2"}}