Pith Number

pith:PTSZUTKW

pith:2025:PTSZUTKWZRKKFNOE5J6JHWYW6K

not attested not anchored not stored refs pending

Robust Representation and Estimation of Barycenters and Modes of Probability Measures on Metric Spaces

Tom Needham, Washington Mio

arxiv:2505.09609 v2 · 2025-05-14 · math.ST · math.MG · stat.ME · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTSZUTKWZRKKFNOE5J6JHWYW6K}

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

Observable Covariance and Principal Observable Analysis for Data on Metric Spaces

Receipt and verification

First computed	2026-07-05T11:10:56.489017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ce59a4d56cc54a2b5c4ea7c93db16f297d036ed57630a42780cf7884dc2fca6

Aliases

arxiv: 2505.09609 · arxiv_version: 2505.09609v2 · doi: 10.48550/arxiv.2505.09609 · pith_short_12: PTSZUTKWZRKK · pith_short_16: PTSZUTKWZRKKFNOE · pith_short_8: PTSZUTKW

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/PTSZUTKWZRKKFNOE5J6JHWYW6K \
  | 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: 7ce59a4d56cc54a2b5c4ea7c93db16f297d036ed57630a42780cf7884dc2fca6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31da1ad987f762f1a0b564559e216a30ae211a9d0ce94c3f7e33282b282acd82",
    "cross_cats_sorted": [
      "math.MG",
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-05-14T17:58:22Z",
    "title_canon_sha256": "81f77e85f23ac0ee6f0187322c50fa3e9e4e01159b393ce545638a08bc23db9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.09609",
    "kind": "arxiv",
    "version": 2
  }
}