{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MVEFII2VPM7LI72XYWQ6EZDR4W","short_pith_number":"pith:MVEFII2V","canonical_record":{"source":{"id":"1407.8361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-31T11:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"18772ec4a3192dbae27f7ce96a698aeac79ff67f8b06d29bec46538fa48655b4","abstract_canon_sha256":"bf2f3055c7e31b18a722ea34089c21ad40f1d2d250835e718d9f5b8392f72834"},"schema_version":"1.0"},"canonical_sha256":"65485423557b3eb47f57c5a1e26471e5a751130c12f301881345c384c5500dff","source":{"kind":"arxiv","id":"1407.8361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8361","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8361v2","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8361","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"MVEFII2VPM7L","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MVEFII2VPM7LI72X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MVEFII2V","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MVEFII2VPM7LI72XYWQ6EZDR4W","target":"record","payload":{"canonical_record":{"source":{"id":"1407.8361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-31T11:28:13Z","cross_cats_sorted":[],"title_canon_sha256":"18772ec4a3192dbae27f7ce96a698aeac79ff67f8b06d29bec46538fa48655b4","abstract_canon_sha256":"bf2f3055c7e31b18a722ea34089c21ad40f1d2d250835e718d9f5b8392f72834"},"schema_version":"1.0"},"canonical_sha256":"65485423557b3eb47f57c5a1e26471e5a751130c12f301881345c384c5500dff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:58.861085Z","signature_b64":"CCTm7JMoL1R8tYUNkjCewlOnetYdlGb7qE75wakiJxVKm6UU6RN4jCbkWbpxFXM9GzCRgFdAoZdy/2X0KcXYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65485423557b3eb47f57c5a1e26471e5a751130c12f301881345c384c5500dff","last_reissued_at":"2026-05-18T00:56:58.860534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:58.860534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.8361","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":"2026-05-18T00:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNIzGcT51CQHZ4o5HMoCRvlZp0hTzJlRc0xvs+x4KG/ZDuAklhchhTLqnTRqJdjNgnZXcdbPIRwTspX2qn11Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:49.962030Z"},"content_sha256":"83a99d02442918f370e765f0d78b0e30aa8a42cc9bce211983e5bd6d07691b69","schema_version":"1.0","event_id":"sha256:83a99d02442918f370e765f0d78b0e30aa8a42cc9bce211983e5bd6d07691b69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MVEFII2VPM7LI72XYWQ6EZDR4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Manifold-valued subdivision schemes based on geodesic inductive averaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Nira Dyn, Nir Sharon","submitted_at":"2014-07-31T11:28:13Z","abstract_excerpt":"Subdivision schemes have become an important tool for approximation of manifold-valued functions. In this paper, we describe a construction of manifold-valued subdivision schemes for geodesically complete manifolds. Our construction is based upon the adaptation of linear subdivision schemes using the notion of repeated binary averaging, where as a repeated binary average we propose to use the geodesic inductive mean. We derive conditions on the adapted schemes which guarantee convergence from any initial manifold-valued sequence. The definition and analysis of convergence are intrinsic to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8361","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":""},"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":"2026-05-18T00:56:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xT4RwIV0ErXdwJ9G1ncVKf/RkzISN9Ws5CGwnEMLOFV+17wimu0cca4dmlPZWRuZNOjxw4Xuo4dQioKxXfxMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:49.962449Z"},"content_sha256":"25724407d2b54428d1219166cfdf9af81b56521132eaad9c3cae245f63533443","schema_version":"1.0","event_id":"sha256:25724407d2b54428d1219166cfdf9af81b56521132eaad9c3cae245f63533443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/bundle.json","state_url":"https://pith.science/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/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":"2026-06-09T19:22:49Z","links":{"resolver":"https://pith.science/pith/MVEFII2VPM7LI72XYWQ6EZDR4W","bundle":"https://pith.science/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/bundle.json","state":"https://pith.science/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVEFII2VPM7LI72XYWQ6EZDR4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MVEFII2VPM7LI72XYWQ6EZDR4W","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":"bf2f3055c7e31b18a722ea34089c21ad40f1d2d250835e718d9f5b8392f72834","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-31T11:28:13Z","title_canon_sha256":"18772ec4a3192dbae27f7ce96a698aeac79ff67f8b06d29bec46538fa48655b4"},"schema_version":"1.0","source":{"id":"1407.8361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8361","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8361v2","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8361","created_at":"2026-05-18T00:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"MVEFII2VPM7L","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MVEFII2VPM7LI72X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MVEFII2V","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:25724407d2b54428d1219166cfdf9af81b56521132eaad9c3cae245f63533443","target":"graph","created_at":"2026-05-18T00:56:58Z","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":"Subdivision schemes have become an important tool for approximation of manifold-valued functions. In this paper, we describe a construction of manifold-valued subdivision schemes for geodesically complete manifolds. Our construction is based upon the adaptation of linear subdivision schemes using the notion of repeated binary averaging, where as a repeated binary average we propose to use the geodesic inductive mean. We derive conditions on the adapted schemes which guarantee convergence from any initial manifold-valued sequence. The definition and analysis of convergence are intrinsic to the ","authors_text":"Nira Dyn, Nir Sharon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-31T11:28:13Z","title":"Manifold-valued subdivision schemes based on geodesic inductive averaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8361","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":"sha256:83a99d02442918f370e765f0d78b0e30aa8a42cc9bce211983e5bd6d07691b69","target":"record","created_at":"2026-05-18T00:56:58Z","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":"bf2f3055c7e31b18a722ea34089c21ad40f1d2d250835e718d9f5b8392f72834","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-31T11:28:13Z","title_canon_sha256":"18772ec4a3192dbae27f7ce96a698aeac79ff67f8b06d29bec46538fa48655b4"},"schema_version":"1.0","source":{"id":"1407.8361","kind":"arxiv","version":2}},"canonical_sha256":"65485423557b3eb47f57c5a1e26471e5a751130c12f301881345c384c5500dff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65485423557b3eb47f57c5a1e26471e5a751130c12f301881345c384c5500dff","first_computed_at":"2026-05-18T00:56:58.860534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:58.860534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCTm7JMoL1R8tYUNkjCewlOnetYdlGb7qE75wakiJxVKm6UU6RN4jCbkWbpxFXM9GzCRgFdAoZdy/2X0KcXYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:58.861085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83a99d02442918f370e765f0d78b0e30aa8a42cc9bce211983e5bd6d07691b69","sha256:25724407d2b54428d1219166cfdf9af81b56521132eaad9c3cae245f63533443"],"state_sha256":"bc9d7484d3def301217ac16a4da212b5ed5c3e5206d679fd22f356b768ee098f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cSHisLHjgVKtlWgw1FP9vuPaVfY0lfkKXWn3KiknlbCSo2ngXglGj4nYPHbsJMtVvYcph9ISYItvLNIFpT2jDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:22:49.965310Z","bundle_sha256":"fc3a98df49504bc193864e80df8a96c4be5f80f4fafe0ab2941c3d7e19dbf51b"}}