Pith Number

pith:FXMURKSC

pith:2017:FXMURKSCUV2DGN3STTYGFOSNPJ

not attested not anchored not stored refs pending

Mean value property and harmonicity on Carnot-Carath\'eodory groups

Ben Warhurst, Tomasz Adamowicz

arxiv:1702.07642 v1 · 2017-02-24 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FXMURKSCUV2DGN3STTYGFOSNPJ}

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	2026-05-18T00:50:02.662619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dd948aa42a5743337729cf062ba4d7a71c4ade8cf38713b24b6e401994cc267

Aliases

arxiv: 1702.07642 · arxiv_version: 1702.07642v1 · doi: 10.48550/arxiv.1702.07642 · pith_short_12: FXMURKSCUV2D · pith_short_16: FXMURKSCUV2DGN3S · pith_short_8: FXMURKSC

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/FXMURKSCUV2DGN3STTYGFOSNPJ \
  | 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: 2dd948aa42a5743337729cf062ba4d7a71c4ade8cf38713b24b6e401994cc267

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2152b768fd0fcdcb2556a2e12cd029ba03e15dd33f3f5f742ae17aab7534e605",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-24T16:09:18Z",
    "title_canon_sha256": "8a2ef26d5d5a4e42c5bb4d09eddddecaf2fa581baa1c73388f2773cae596b235"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.07642",
    "kind": "arxiv",
    "version": 1
  }
}