{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:25I5QMQB6DIJN5GURR5RHAP2DK","short_pith_number":"pith:25I5QMQB","canonical_record":{"source":{"id":"1107.4055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-08T13:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"cc4e8cd908fa8fdd4808d3ceb729814619b1adb389f5d49fd83abe9acfaef689","abstract_canon_sha256":"4e6e0fd4b1d51e910db2ae177f53e530a1fa01a4f2a56d59a7a06a5be046dd0b"},"schema_version":"1.0"},"canonical_sha256":"d751d83201f0d096f4d48c7b1381fa1a856e43f4aeab5cd6db69a43a5d055a58","source":{"kind":"arxiv","id":"1107.4055","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4055","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4055v1","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4055","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"25I5QMQB6DIJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"25I5QMQB6DIJN5GU","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"25I5QMQB","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:25I5QMQB6DIJN5GURR5RHAP2DK","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-08T13:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"cc4e8cd908fa8fdd4808d3ceb729814619b1adb389f5d49fd83abe9acfaef689","abstract_canon_sha256":"4e6e0fd4b1d51e910db2ae177f53e530a1fa01a4f2a56d59a7a06a5be046dd0b"},"schema_version":"1.0"},"canonical_sha256":"d751d83201f0d096f4d48c7b1381fa1a856e43f4aeab5cd6db69a43a5d055a58","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:14.122312Z","signature_b64":"WwUF/vwtzxTMaf5iqRm2DA0mAKW1qJRK7M5XqYiydzkra/kthlxg5WftM1o6H2J5nqDeRJmMlmVwUYvZCuXaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d751d83201f0d096f4d48c7b1381fa1a856e43f4aeab5cd6db69a43a5d055a58","last_reissued_at":"2026-05-18T04:17:14.121503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:14.121503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4055","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrbJjCbKyzc1gvX9/dBeG5YXTG8fH1DRfS4Fa3cQaOKGvQNZ2FW6OmsX/dFslCNwj32PLgqlm2/o57CPn1XBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:34:45.482847Z"},"content_sha256":"3803cbb7488d4ee6e56f24fa57907078c68a27650d2aa82206b5d42ae9c90cf5","schema_version":"1.0","event_id":"sha256:3803cbb7488d4ee6e56f24fa57907078c68a27650d2aa82206b5d42ae9c90cf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:25I5QMQB6DIJN5GURR5RHAP2DK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alternating projections on non-tangential manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fredrik Andersson, Marcus Carlsson","submitted_at":"2011-07-08T13:04:06Z","abstract_excerpt":"We consider sequences $(B_k)_{k=0}^\\infty$ of points obtained by projecting back and forth between two manifolds $\\M_1$ and $\\M_2$, and give conditions guaranteeing that the sequence converge to a limit $B_\\infty\\in\\M_1\\cap\\M_2$. Our motivation is the study of algorithms based on finding the limit of such sequences, which have proven useful in a number of areas. The intersection is typically a set with desirable properties, but for which there is no efficient method of finding the closest point $B_{opt}$ in $\\M_1\\cap\\M_2$. We prove not only that the sequence of alternating projections converge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4055","kind":"arxiv","version":1},"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":"2026-05-18T04:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZaF/bRhHXyj4DfO4YgRcsW+r4BVbBXCca9DGspE0Y7vkN0mClfDjP+TCB1ABPT6uz6l2+MYOhMn4R6ONaR2oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:34:45.483518Z"},"content_sha256":"fa8e7efe6b129e4dba95642b4adda25e1f8cee87e4d0db92e661a829c87fa834","schema_version":"1.0","event_id":"sha256:fa8e7efe6b129e4dba95642b4adda25e1f8cee87e4d0db92e661a829c87fa834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25I5QMQB6DIJN5GURR5RHAP2DK/bundle.json","state_url":"https://pith.science/pith/25I5QMQB6DIJN5GURR5RHAP2DK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25I5QMQB6DIJN5GURR5RHAP2DK/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":"2026-06-06T15:34:45Z","links":{"resolver":"https://pith.science/pith/25I5QMQB6DIJN5GURR5RHAP2DK","bundle":"https://pith.science/pith/25I5QMQB6DIJN5GURR5RHAP2DK/bundle.json","state":"https://pith.science/pith/25I5QMQB6DIJN5GURR5RHAP2DK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25I5QMQB6DIJN5GURR5RHAP2DK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:25I5QMQB6DIJN5GURR5RHAP2DK","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":"4e6e0fd4b1d51e910db2ae177f53e530a1fa01a4f2a56d59a7a06a5be046dd0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-08T13:04:06Z","title_canon_sha256":"cc4e8cd908fa8fdd4808d3ceb729814619b1adb389f5d49fd83abe9acfaef689"},"schema_version":"1.0","source":{"id":"1107.4055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4055","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4055v1","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4055","created_at":"2026-05-18T04:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"25I5QMQB6DIJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"25I5QMQB6DIJN5GU","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"25I5QMQB","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:fa8e7efe6b129e4dba95642b4adda25e1f8cee87e4d0db92e661a829c87fa834","target":"graph","created_at":"2026-05-18T04:17:14Z","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 consider sequences $(B_k)_{k=0}^\\infty$ of points obtained by projecting back and forth between two manifolds $\\M_1$ and $\\M_2$, and give conditions guaranteeing that the sequence converge to a limit $B_\\infty\\in\\M_1\\cap\\M_2$. Our motivation is the study of algorithms based on finding the limit of such sequences, which have proven useful in a number of areas. The intersection is typically a set with desirable properties, but for which there is no efficient method of finding the closest point $B_{opt}$ in $\\M_1\\cap\\M_2$. We prove not only that the sequence of alternating projections converge","authors_text":"Fredrik Andersson, Marcus Carlsson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-08T13:04:06Z","title":"Alternating projections on non-tangential manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4055","kind":"arxiv","version":1},"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":"sha256:3803cbb7488d4ee6e56f24fa57907078c68a27650d2aa82206b5d42ae9c90cf5","target":"record","created_at":"2026-05-18T04:17:14Z","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":"4e6e0fd4b1d51e910db2ae177f53e530a1fa01a4f2a56d59a7a06a5be046dd0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-08T13:04:06Z","title_canon_sha256":"cc4e8cd908fa8fdd4808d3ceb729814619b1adb389f5d49fd83abe9acfaef689"},"schema_version":"1.0","source":{"id":"1107.4055","kind":"arxiv","version":1}},"canonical_sha256":"d751d83201f0d096f4d48c7b1381fa1a856e43f4aeab5cd6db69a43a5d055a58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d751d83201f0d096f4d48c7b1381fa1a856e43f4aeab5cd6db69a43a5d055a58","first_computed_at":"2026-05-18T04:17:14.121503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:14.121503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WwUF/vwtzxTMaf5iqRm2DA0mAKW1qJRK7M5XqYiydzkra/kthlxg5WftM1o6H2J5nqDeRJmMlmVwUYvZCuXaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:14.122312Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3803cbb7488d4ee6e56f24fa57907078c68a27650d2aa82206b5d42ae9c90cf5","sha256:fa8e7efe6b129e4dba95642b4adda25e1f8cee87e4d0db92e661a829c87fa834"],"state_sha256":"b6c5c64f8cd341cf6142a3b3b0e06aec1e0f33d05c102a859901311b8c2c44de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c0xhKlWSftHT/wggCmKnz3FN2DUvt5by5O2YFXBvtstMSHNMkN6hVMwfMdb3ffy7GIVDwhnabCns3MchgOU/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:34:45.486825Z","bundle_sha256":"609b3f4d7193abefcce0af7749f5c05a7e797d423bbc0b7a7b2ba4662da1e5de"}}