Pith Number

pith:77SJZGEA

pith:2011:77SJZGEAJ7OANLBEC23BMQLBYD

not attested not anchored not stored refs pending

Necessary and sufficient condition for the existence of a Fr\'echet mean on the circle

Benjamin Charlier (IMT)

arxiv:1109.1986 v2 · 2011-09-09 · math.ST · 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{77SJZGEAJ7OANLBEC23BMQLBYD}

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	2026-05-18T04:00:37.901321Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffe49c98804fdc06ac2416b6164161c0da5a2261d5d000aa120b90dc0d975966

Aliases

arxiv: 1109.1986 · arxiv_version: 1109.1986v2 · doi: 10.48550/arxiv.1109.1986 · pith_short_12: 77SJZGEAJ7OA · pith_short_16: 77SJZGEAJ7OANLBE · pith_short_8: 77SJZGEA

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/77SJZGEAJ7OANLBEC23BMQLBYD \
  | 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: ffe49c98804fdc06ac2416b6164161c0da5a2261d5d000aa120b90dc0d975966

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "986e4b033b7fbec6dff617e56591221d270fa0d6475f846c80c455a2080dbed6",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-09-09T12:53:49Z",
    "title_canon_sha256": "e69285bdeb41bfb444045c6a044b0cb865c69137816788dc34f8327a741a4538"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1986",
    "kind": "arxiv",
    "version": 2
  }
}