{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SPMU3K6M4BB5LULM6JZHINDZTZ","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":"a0f79e33296c04fe50b1ff11812faa55392a2c6b6ccf676df90e10357abeeaa3","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-01-12T05:27:41Z","title_canon_sha256":"4eefc55ba55976def460023fff26d3425be0b7af36f067d3543631d803b75e0a"},"schema_version":"1.0","source":{"id":"1601.02732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02732","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02732v2","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02732","created_at":"2026-05-18T01:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"SPMU3K6M4BB5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SPMU3K6M4BB5LULM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SPMU3K6M","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:d4bb73f43db9c19720da74a7d9ef7db56b80a20a7fce82eef5878c31d61aeefd","target":"graph","created_at":"2026-05-18T01:17:55Z","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":"Classical methods to model topological properties of point clouds, such as the Vietoris-Rips complex, suffer from the combinatorial explosion of complex sizes. We propose a novel technique to approximate a multi-scale filtration of the Rips complex with improved bounds for size: precisely, for $n$ points in $\\mathbb{R}^d$, we obtain a $O(d)$-approximation with at most $n2^{O(d \\log k)}$ simplices of dimension $k$ or lower. In conjunction with dimension reduction techniques, our approach yields a $O(\\mathrm{polylog} (n))$-approximation of size $n^{O(1)}$ for Rips filtrations on arbitrary metric","authors_text":"Aruni Choudhary, Michael Kerber, Sharath Raghvendra","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-01-12T05:27:41Z","title":"Polynomial-Sized Topological Approximations Using The Permutahedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02732","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:f2309468bfe288e3c88da97a5a2d8eaa2238eb22b10b9d9dc3f926a441870f08","target":"record","created_at":"2026-05-18T01:17:55Z","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":"a0f79e33296c04fe50b1ff11812faa55392a2c6b6ccf676df90e10357abeeaa3","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-01-12T05:27:41Z","title_canon_sha256":"4eefc55ba55976def460023fff26d3425be0b7af36f067d3543631d803b75e0a"},"schema_version":"1.0","source":{"id":"1601.02732","kind":"arxiv","version":2}},"canonical_sha256":"93d94dabcce043d5d16cf2727434799e58e7f6d935e11f952a0fdbe496ad92c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93d94dabcce043d5d16cf2727434799e58e7f6d935e11f952a0fdbe496ad92c4","first_computed_at":"2026-05-18T01:17:55.198103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:55.198103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M3S2u2+13jC+05Z+yEmgYZZGPgwTTDxvQYv68kz47ICyVEHUdHftaembM+OQTv1smwhX924evlKQV1ZOunZVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:55.198850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2309468bfe288e3c88da97a5a2d8eaa2238eb22b10b9d9dc3f926a441870f08","sha256:d4bb73f43db9c19720da74a7d9ef7db56b80a20a7fce82eef5878c31d61aeefd"],"state_sha256":"871dd7ae0eb5cd078494ea8ba85d80a5b88c4d7d293e8704bf2896d267656619"}