Pith Number

pith:AFWXMPFF

pith:2015:AFWXMPFFYFL4IP62KROYQO6YNJ

not attested not anchored not stored refs pending

Fr\'echet Barycenters and a Law of Large Numbers for Measures on the Real Line

Alexey Kroshnin, Andrei Sobolevski

arxiv:1512.08421 v2 · 2015-12-28 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFWXMPFFYFL4IP62KROYQO6YNJ}

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.

Receipt and verification

First computed	2026-05-18T01:08:45.289959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

016d763ca5c157c43fda545d883bd86a4625b010f9573051b7cc44013e88ca36

Aliases

arxiv: 1512.08421 · arxiv_version: 1512.08421v2 · doi: 10.48550/arxiv.1512.08421 · pith_short_12: AFWXMPFFYFL4 · pith_short_16: AFWXMPFFYFL4IP62 · pith_short_8: AFWXMPFF

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/AFWXMPFFYFL4IP62KROYQO6YNJ \
  | 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: 016d763ca5c157c43fda545d883bd86a4625b010f9573051b7cc44013e88ca36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2fe1578ac3853bfeeb2773c7ac68975d038438b1c9835ff7fe87bccdf99c036",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-28T14:16:23Z",
    "title_canon_sha256": "614f1a94fa40148d974bed19e9d168e2fc2f7ab4e6eb45b966c918b392b3af85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08421",
    "kind": "arxiv",
    "version": 2
  }
}