Pith Number

pith:4HXJHFYC

pith:2025:4HXJHFYCM6D44RTZIAVKRRTOJ3

not attested not anchored not stored refs pending

A rank-based distance for interval modules and Wasserstein stability of persistence landscapes

Peter Bubenik, Wanchen Zhao

arxiv:2509.20921 v3 · 2025-09-25 · math.AT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4HXJHFYCM6D44RTZIAVKRRTOJ3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

A Hilbert space embedding of persistence diagrams and barcodes

Receipt and verification

First computed	2026-08-03T00:09:45.451945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1ee9397026787ce4679402aa8c66e4ed2daf4144f1d829b51015932fa22cc63

Aliases

arxiv: 2509.20921 · arxiv_version: 2509.20921v3 · doi: 10.48550/arxiv.2509.20921 · pith_short_12: 4HXJHFYCM6D4 · pith_short_16: 4HXJHFYCM6D44RTZ · pith_short_8: 4HXJHFYC

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/4HXJHFYCM6D44RTZIAVKRRTOJ3 \
  | 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: e1ee9397026787ce4679402aa8c66e4ed2daf4144f1d829b51015932fa22cc63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d835ea01a81894aeabbccba4b5a4d31a2d09850982c86edf136e852de8d33525",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-09-25T09:02:58Z",
    "title_canon_sha256": "07f0bcb7e2f5b0c49dabd0b3fed6d73cd66d5702aa6948455fe41e19a4cf6c53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.20921",
    "kind": "arxiv",
    "version": 3
  }
}