Pith Number

pith:QUN65XO4

pith:2026:QUN65XO4GP5NSBFNO72MN2J3H7

not attested not anchored not stored refs resolved

It's All About Covers: Persistent Homology of Cover Refinements

Ant\'onio Leit\~ao

Reframing persistent homology around cover refinements produces smaller filtrations with unconditional log-3 interleaving to Vietoris-Rips.

arxiv:2602.22784 v2 · 2026-02-26 · math.AT

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The resulting filtration restores near-linear scaling in the number of data points and enables efficient capture of homology at high degrees while maintaining a log-3 interleaving unconditionally for any metric space.

C2weakest assumption

That the chosen cover refinements and the functors (Nerve, Co-Nerve) that preserve contiguity of refinement maps are sufficient to propagate the interleaving guarantees without additional metric-dependent conditions.

C3one line summary

Cover refinements enable a near-linear-size approximation to the Vietoris-Rips filtration with unconditional log-3 interleaving that preserves persistent homology.

References

54 extracted · 54 resolved · 5 Pith anchors

[1] Dory: Computation of persistence diagrams up to dimension two for Vietoris–Rips filtrations of large data sets 2024

[2] Strong homotopy types, nerves and collapses 2012

[3] Nicolas Bonneel, Julien Rabin, Gabriel Peyr ´e, and Hanspeter Pfister 2021 · doi:10.1007/s41468-021-00071-5

[4] Phat–persistent homology algorithms toolbox 2017

[5] The Vietoris Mapping Theorem for Bicompact Spaces 1950

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

An Algebraic Introduction to Persistence

Receipt and verification

First computed	2026-05-17T23:39:15.936299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

851beedddc33fad904ad77f4c6e93b3ff849ecf394570162833d0223539dad17

Aliases

arxiv: 2602.22784 · arxiv_version: 2602.22784v2 · doi: 10.48550/arxiv.2602.22784 · pith_short_12: QUN65XO4GP5N · pith_short_16: QUN65XO4GP5NSBFN · pith_short_8: QUN65XO4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QUN65XO4GP5NSBFNO72MN2J3H7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 851beedddc33fad904ad77f4c6e93b3ff849ecf394570162833d0223539dad17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a55c35c8f8f6f23589ea0870d46ef68fc23657f8c3af36adbf2910dbad85d9e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-02-26T09:19:26Z",
    "title_canon_sha256": "4e3d2b16e37d21afaa810078ab8f8c54fe2f4f388d28a2acc4cf69b6a40c380e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.22784",
    "kind": "arxiv",
    "version": 2
  }
}