{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PWP5EGRNF43EGJW3EH4OCC75NU","short_pith_number":"pith:PWP5EGRN","canonical_record":{"source":{"id":"1701.08395","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-29T16:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"bedfc4a5170895f9f108b78b40e4bfd8b2a65ede995334b2cd8c07752ed81e2a","abstract_canon_sha256":"9cd39928e4d9e14ca6e3ed3b15f2903f8e6bab7da20b91f44476051d877d8626"},"schema_version":"1.0"},"canonical_sha256":"7d9fd21a2d2f364326db21f8e10bfd6d02cfb4c8e975fef581f200d60df10017","source":{"kind":"arxiv","id":"1701.08395","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08395","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08395v5","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08395","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"PWP5EGRNF43E","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PWP5EGRNF43EGJW3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PWP5EGRN","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PWP5EGRNF43EGJW3EH4OCC75NU","target":"record","payload":{"canonical_record":{"source":{"id":"1701.08395","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-29T16:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"bedfc4a5170895f9f108b78b40e4bfd8b2a65ede995334b2cd8c07752ed81e2a","abstract_canon_sha256":"9cd39928e4d9e14ca6e3ed3b15f2903f8e6bab7da20b91f44476051d877d8626"},"schema_version":"1.0"},"canonical_sha256":"7d9fd21a2d2f364326db21f8e10bfd6d02cfb4c8e975fef581f200d60df10017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:57.140003Z","signature_b64":"XjdUx/tbyVHksfHG/AB3+dkAt0p7XP2Ux2jqap8YqiRdqjtLNFwknCtaYCPUZ4KeFN+G6A1jeDbwcT9PDHr+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d9fd21a2d2f364326db21f8e10bfd6d02cfb4c8e975fef581f200d60df10017","last_reissued_at":"2026-05-18T00:03:57.139331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:57.139331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.08395","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8JD5vFILL1Yspp149yNUNCbqckF1zwhoyvnkZjSKA0XMnlejPkZqkDGI8dxeLybhnznlGZIt8Iv+HHDnBV8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:49:04.022002Z"},"content_sha256":"31be688271bfcec48ae9cd36ec07bf1a79108e1b986be277a2d46fa09c0f56a3","schema_version":"1.0","event_id":"sha256:31be688271bfcec48ae9cd36ec07bf1a79108e1b986be277a2d46fa09c0f56a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PWP5EGRNF43EGJW3EH4OCC75NU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Higher-Dimensional Skeletonization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Davorin Lesnik, Sara Kalisnik Verovsek, Vitaliy Kurlin","submitted_at":"2017-01-29T16:14:47Z","abstract_excerpt":"Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional non-linear subspace such as an embedded graph or a simplicial complex. Classical clustering methods and principal component analysis work well when given data points split into well-separated clusters or lie near linear subspaces of a Euclidean space. Methods from topological data analysis in general metric spaces detect more complicated patterns such as hol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08395","kind":"arxiv","version":5},"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":"2026-05-18T00:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qSIEdR33OQFEtvtaBgYmg+0aqbaGtPW8AN+9WnXAxvcfvxPMMLRjwMdw7aFf2Fm5f0hDisEP56SELJRSXfAkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:49:04.022387Z"},"content_sha256":"17c4549deff5cb56687d1946d4cca483f8d44e405009d1f7d1adfdeb553abf9e","schema_version":"1.0","event_id":"sha256:17c4549deff5cb56687d1946d4cca483f8d44e405009d1f7d1adfdeb553abf9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWP5EGRNF43EGJW3EH4OCC75NU/bundle.json","state_url":"https://pith.science/pith/PWP5EGRNF43EGJW3EH4OCC75NU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWP5EGRNF43EGJW3EH4OCC75NU/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":"2026-05-30T10:49:04Z","links":{"resolver":"https://pith.science/pith/PWP5EGRNF43EGJW3EH4OCC75NU","bundle":"https://pith.science/pith/PWP5EGRNF43EGJW3EH4OCC75NU/bundle.json","state":"https://pith.science/pith/PWP5EGRNF43EGJW3EH4OCC75NU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWP5EGRNF43EGJW3EH4OCC75NU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PWP5EGRNF43EGJW3EH4OCC75NU","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":"9cd39928e4d9e14ca6e3ed3b15f2903f8e6bab7da20b91f44476051d877d8626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-29T16:14:47Z","title_canon_sha256":"bedfc4a5170895f9f108b78b40e4bfd8b2a65ede995334b2cd8c07752ed81e2a"},"schema_version":"1.0","source":{"id":"1701.08395","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08395","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08395v5","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08395","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"PWP5EGRNF43E","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PWP5EGRNF43EGJW3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PWP5EGRN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:17c4549deff5cb56687d1946d4cca483f8d44e405009d1f7d1adfdeb553abf9e","target":"graph","created_at":"2026-05-18T00:03:57Z","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"},"paper":{"abstract_excerpt":"Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional non-linear subspace such as an embedded graph or a simplicial complex. Classical clustering methods and principal component analysis work well when given data points split into well-separated clusters or lie near linear subspaces of a Euclidean space. Methods from topological data analysis in general metric spaces detect more complicated patterns such as hol","authors_text":"Davorin Lesnik, Sara Kalisnik Verovsek, Vitaliy Kurlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-29T16:14:47Z","title":"The Higher-Dimensional Skeletonization Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08395","kind":"arxiv","version":5},"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":"sha256:31be688271bfcec48ae9cd36ec07bf1a79108e1b986be277a2d46fa09c0f56a3","target":"record","created_at":"2026-05-18T00:03:57Z","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":"9cd39928e4d9e14ca6e3ed3b15f2903f8e6bab7da20b91f44476051d877d8626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-29T16:14:47Z","title_canon_sha256":"bedfc4a5170895f9f108b78b40e4bfd8b2a65ede995334b2cd8c07752ed81e2a"},"schema_version":"1.0","source":{"id":"1701.08395","kind":"arxiv","version":5}},"canonical_sha256":"7d9fd21a2d2f364326db21f8e10bfd6d02cfb4c8e975fef581f200d60df10017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d9fd21a2d2f364326db21f8e10bfd6d02cfb4c8e975fef581f200d60df10017","first_computed_at":"2026-05-18T00:03:57.139331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:57.139331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XjdUx/tbyVHksfHG/AB3+dkAt0p7XP2Ux2jqap8YqiRdqjtLNFwknCtaYCPUZ4KeFN+G6A1jeDbwcT9PDHr+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:57.140003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08395","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31be688271bfcec48ae9cd36ec07bf1a79108e1b986be277a2d46fa09c0f56a3","sha256:17c4549deff5cb56687d1946d4cca483f8d44e405009d1f7d1adfdeb553abf9e"],"state_sha256":"968cb2a597df27444d7914bc9de050aa755b361ba3aa304408a912e271800650"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRmq2Y0wueaqzMrT95/7x8eXpWY7+2a5lxtdSbNUhor7JI5/iLLKu2Y79pQillmEF3unIQGF20OMWYogiMbuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:49:04.024756Z","bundle_sha256":"9509964921ec0e906fa762efec92b8b0576756a939e587e9129e0d2fbd070ab8"}}