{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OJEKZMY6W4U5SE2ZI35QMXJHBK","short_pith_number":"pith:OJEKZMY6","canonical_record":{"source":{"id":"1810.02149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcfe15c12d65a2d870e22cdb9f8eab4e3377a749001b46cedcbcc52c259e2678","abstract_canon_sha256":"9bf66c4f2851a7857c1c00f20ccb0ae218181d6b2f8071c9f70efbe0b0354aa0"},"schema_version":"1.0"},"canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","source":{"kind":"arxiv","id":"1810.02149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02149","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02149v2","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02149","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"OJEKZMY6W4U5","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OJEKZMY6W4U5SE2Z","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OJEKZMY6","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OJEKZMY6W4U5SE2ZI35QMXJHBK","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcfe15c12d65a2d870e22cdb9f8eab4e3377a749001b46cedcbcc52c259e2678","abstract_canon_sha256":"9bf66c4f2851a7857c1c00f20ccb0ae218181d6b2f8071c9f70efbe0b0354aa0"},"schema_version":"1.0"},"canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:53.855037Z","signature_b64":"pYi2QJcrQjvOjYXNpvwmj+PuLvPElvCYEoPfxG5sbDHR3hHH/YX3BU2+ACfNxBkBpZ5KLyAnr6Yy2rwN7M9mCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","last_reissued_at":"2026-05-17T23:47:53.854376Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:53.854376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02149","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":"2026-05-17T23:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxSFRT510JPDpviAAiPiHsYwrQD3qgoeostRA/+7/+L+X+fTc5zZVT61965LB0z5AuBi0lAvE/jeUUD4AqKeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:04:21.192681Z"},"content_sha256":"c0e9182afb1f65cd1af9f32619d9eadd49dc02a4e745ba599f9f023276d5995f","schema_version":"1.0","event_id":"sha256:c0e9182afb1f65cd1af9f32619d9eadd49dc02a4e745ba599f9f023276d5995f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OJEKZMY6W4U5SE2ZI35QMXJHBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Filtered Nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Morten Brun, Nello Blaser","submitted_at":"2018-10-04T11:29:42Z","abstract_excerpt":"Given a point cloud $P$ in Euclidean space and a positive parameter $t$ we can consider the $t$-neighborhood $P^{t}$ of $P$ consisting of points at distance less than $t$ to $P$. Homology of $P^{t}$ gives information about components, holes, voids etc. in $P^{t}$. The idea of persistent homology is that it may happen that we are interested in some of holes in the spaces $P^t$ that are not detected simultaneously in homology for a single value of $t$, but where each of these holes is detected for $t$ in a wide range.\n  When the dimension of the ambient Euclidean space is small, persistent homol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02149","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":"2026-05-17T23:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9zncpCD94X52Y53O7WHo7wFjz/MP1NysIIYnOWmgULWooczLN1Wl4U/us2XAu7bD8fy23Hr/SD/FieyrJoJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:04:21.193034Z"},"content_sha256":"a700841ae435059b7d407bd4295b6cf99a1170d18b3be24773d63887afc2e879","schema_version":"1.0","event_id":"sha256:a700841ae435059b7d407bd4295b6cf99a1170d18b3be24773d63887afc2e879"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/bundle.json","state_url":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/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":"2026-06-10T20:04:21Z","links":{"resolver":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK","bundle":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/bundle.json","state":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OJEKZMY6W4U5SE2ZI35QMXJHBK","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":"9bf66c4f2851a7857c1c00f20ccb0ae218181d6b2f8071c9f70efbe0b0354aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","title_canon_sha256":"bcfe15c12d65a2d870e22cdb9f8eab4e3377a749001b46cedcbcc52c259e2678"},"schema_version":"1.0","source":{"id":"1810.02149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02149","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02149v2","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02149","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"OJEKZMY6W4U5","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OJEKZMY6W4U5SE2Z","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OJEKZMY6","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:a700841ae435059b7d407bd4295b6cf99a1170d18b3be24773d63887afc2e879","target":"graph","created_at":"2026-05-17T23:47:53Z","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":"Given a point cloud $P$ in Euclidean space and a positive parameter $t$ we can consider the $t$-neighborhood $P^{t}$ of $P$ consisting of points at distance less than $t$ to $P$. Homology of $P^{t}$ gives information about components, holes, voids etc. in $P^{t}$. The idea of persistent homology is that it may happen that we are interested in some of holes in the spaces $P^t$ that are not detected simultaneously in homology for a single value of $t$, but where each of these holes is detected for $t$ in a wide range.\n  When the dimension of the ambient Euclidean space is small, persistent homol","authors_text":"Morten Brun, Nello Blaser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","title":"Sparse Filtered Nerves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02149","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:c0e9182afb1f65cd1af9f32619d9eadd49dc02a4e745ba599f9f023276d5995f","target":"record","created_at":"2026-05-17T23:47:53Z","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":"9bf66c4f2851a7857c1c00f20ccb0ae218181d6b2f8071c9f70efbe0b0354aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","title_canon_sha256":"bcfe15c12d65a2d870e22cdb9f8eab4e3377a749001b46cedcbcc52c259e2678"},"schema_version":"1.0","source":{"id":"1810.02149","kind":"arxiv","version":2}},"canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","first_computed_at":"2026-05-17T23:47:53.854376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:53.854376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYi2QJcrQjvOjYXNpvwmj+PuLvPElvCYEoPfxG5sbDHR3hHH/YX3BU2+ACfNxBkBpZ5KLyAnr6Yy2rwN7M9mCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:53.855037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0e9182afb1f65cd1af9f32619d9eadd49dc02a4e745ba599f9f023276d5995f","sha256:a700841ae435059b7d407bd4295b6cf99a1170d18b3be24773d63887afc2e879"],"state_sha256":"3f18df434bcc5a1cd8f742205631395a81c81e217f0cc4bc944920ff181cb5ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Za52ACOfHfAS+XONFNTTKsVWHe2rGA1+MVmx82iLYeOFPwhZxRhYPG1CB5X48JLXIyh0rPk0291tDACzfQCrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:04:21.195060Z","bundle_sha256":"4456f7a04df02f2c3e9e804668b305a88305d8e3d5484cb47959bfed5c22dfb0"}}