{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NMP6IMFHOA7V5AR47GP7M5IO56","short_pith_number":"pith:NMP6IMFH","canonical_record":{"source":{"id":"1708.04710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:47:44Z","cross_cats_sorted":[],"title_canon_sha256":"14c124f18da152706e3b12867d5e4253366f1ea255e1cec8467fe8d46fff5ad3","abstract_canon_sha256":"840dd921312a51bdaa6f67ec1ed9ec60489192e7a47da8565aed781f96341f4c"},"schema_version":"1.0"},"canonical_sha256":"6b1fe430a7703f5e823cf99ff6750eef943aa4f92c1aff973cd82e343e918afd","source":{"kind":"arxiv","id":"1708.04710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04710","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04710v1","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04710","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"NMP6IMFHOA7V","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NMP6IMFHOA7V5AR4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NMP6IMFH","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NMP6IMFHOA7V5AR47GP7M5IO56","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:47:44Z","cross_cats_sorted":[],"title_canon_sha256":"14c124f18da152706e3b12867d5e4253366f1ea255e1cec8467fe8d46fff5ad3","abstract_canon_sha256":"840dd921312a51bdaa6f67ec1ed9ec60489192e7a47da8565aed781f96341f4c"},"schema_version":"1.0"},"canonical_sha256":"6b1fe430a7703f5e823cf99ff6750eef943aa4f92c1aff973cd82e343e918afd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:58.120718Z","signature_b64":"+fDiQUNMOIiyiLJOVSmRYLbnmnEGfZh1yatwQdDkAmwJoY3odPkxN8bt62ppp8igmQMIj3nu9lwfgxTTbfJyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b1fe430a7703f5e823cf99ff6750eef943aa4f92c1aff973cd82e343e918afd","last_reissued_at":"2026-05-18T00:37:58.120205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:58.120205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04710","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":"2026-05-18T00:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86Q5XlFxNdhK1rA5RDlu1yUMze4H0oVhvnm2ZZclYpIGcIX1XJfjwjSHmAtjyUEEBrpj/XBFgn6SzeUsla6XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:36:41.827603Z"},"content_sha256":"0477564ffc14e70fd19114b78963655bfc4d851a0253b7224cba3f5657f9769a","schema_version":"1.0","event_id":"sha256:0477564ffc14e70fd19114b78963655bfc4d851a0253b7224cba3f5657f9769a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NMP6IMFHOA7V5AR47GP7M5IO56","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel multi-scale reduction of persistent homology filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jared Tanner, Rodrigo Mendoza-Smith","submitted_at":"2017-08-15T22:47:44Z","abstract_excerpt":"The persistent homology pipeline includes the reduction of a, so-called, boundary matrix. We extend the work of Bauer et al. (2014) and Chen et al. (2011) where they show how to use dependencies in the boundary matrix to adapt the reduction algorithm presented in Edelsbrunner et al. (2002) in such a way as to reduce its computational cost. Herein we present a number of additional dependencies in the boundary matrices and propose a novel parallel algorithms for the reduction of boundary matrices. In particular, we show: that part of the reduction is immediately apparent, give bounds on the redu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04710","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":"2026-05-18T00:37:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t2ZwQR1v4MrREgDsJtconRN/OGpwRPC12YqXOEK868SKMAg4kOf0J202yy/65wqGpMpsfks6UpNIYycH6UBgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:36:41.827988Z"},"content_sha256":"0f310d50c7df5ff35e8eda72b8c73c985d246aeec307f44ab51ea479eddd73dc","schema_version":"1.0","event_id":"sha256:0f310d50c7df5ff35e8eda72b8c73c985d246aeec307f44ab51ea479eddd73dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMP6IMFHOA7V5AR47GP7M5IO56/bundle.json","state_url":"https://pith.science/pith/NMP6IMFHOA7V5AR47GP7M5IO56/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMP6IMFHOA7V5AR47GP7M5IO56/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":"2026-06-23T12:36:41Z","links":{"resolver":"https://pith.science/pith/NMP6IMFHOA7V5AR47GP7M5IO56","bundle":"https://pith.science/pith/NMP6IMFHOA7V5AR47GP7M5IO56/bundle.json","state":"https://pith.science/pith/NMP6IMFHOA7V5AR47GP7M5IO56/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMP6IMFHOA7V5AR47GP7M5IO56/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NMP6IMFHOA7V5AR47GP7M5IO56","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":"840dd921312a51bdaa6f67ec1ed9ec60489192e7a47da8565aed781f96341f4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:47:44Z","title_canon_sha256":"14c124f18da152706e3b12867d5e4253366f1ea255e1cec8467fe8d46fff5ad3"},"schema_version":"1.0","source":{"id":"1708.04710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04710","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04710v1","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04710","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"NMP6IMFHOA7V","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NMP6IMFHOA7V5AR4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NMP6IMFH","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:0f310d50c7df5ff35e8eda72b8c73c985d246aeec307f44ab51ea479eddd73dc","target":"graph","created_at":"2026-05-18T00:37:58Z","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":"The persistent homology pipeline includes the reduction of a, so-called, boundary matrix. We extend the work of Bauer et al. (2014) and Chen et al. (2011) where they show how to use dependencies in the boundary matrix to adapt the reduction algorithm presented in Edelsbrunner et al. (2002) in such a way as to reduce its computational cost. Herein we present a number of additional dependencies in the boundary matrices and propose a novel parallel algorithms for the reduction of boundary matrices. In particular, we show: that part of the reduction is immediately apparent, give bounds on the redu","authors_text":"Jared Tanner, Rodrigo Mendoza-Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:47:44Z","title":"Parallel multi-scale reduction of persistent homology filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04710","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":"sha256:0477564ffc14e70fd19114b78963655bfc4d851a0253b7224cba3f5657f9769a","target":"record","created_at":"2026-05-18T00:37:58Z","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":"840dd921312a51bdaa6f67ec1ed9ec60489192e7a47da8565aed781f96341f4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:47:44Z","title_canon_sha256":"14c124f18da152706e3b12867d5e4253366f1ea255e1cec8467fe8d46fff5ad3"},"schema_version":"1.0","source":{"id":"1708.04710","kind":"arxiv","version":1}},"canonical_sha256":"6b1fe430a7703f5e823cf99ff6750eef943aa4f92c1aff973cd82e343e918afd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b1fe430a7703f5e823cf99ff6750eef943aa4f92c1aff973cd82e343e918afd","first_computed_at":"2026-05-18T00:37:58.120205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:58.120205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+fDiQUNMOIiyiLJOVSmRYLbnmnEGfZh1yatwQdDkAmwJoY3odPkxN8bt62ppp8igmQMIj3nu9lwfgxTTbfJyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:58.120718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0477564ffc14e70fd19114b78963655bfc4d851a0253b7224cba3f5657f9769a","sha256:0f310d50c7df5ff35e8eda72b8c73c985d246aeec307f44ab51ea479eddd73dc"],"state_sha256":"b48ab938d241621ac38378877ab640b22c5f37674fa01065f999437d0e555f4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2pXLaf8iYf25CVqKlq6ZzSTV42QTPLic78nvvpUFk4AutPoBvt3pbtlLpg49yUphzeXB+PqXfc4FHhgIeM1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:36:41.830287Z","bundle_sha256":"ae0a9a1fbde59665e13c534d3ec39fb997434b759df9c9531e53bceda848d56a"}}