Pith Number

pith:GWWDF4X3

pith:2011:GWWDF4X3YUY2V4DQFUSX7LYJ4N

not attested not anchored not stored refs pending

Discrete spherical means of directional derivatives and Veronese maps

Alexander Belyaev, Boris Khesin, Serge Tabachnikov

arxiv:1106.3691 v2 · 2011-06-18 · math.NA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWWDF4X3YUY2V4DQFUSX7LYJ4N}

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	2026-05-18T02:01:35.198749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35ac32f2fbc531aaf0702d257faf09e37f49133c0a6ab1f3f948ff737bff73a8

Aliases

arxiv: 1106.3691 · arxiv_version: 1106.3691v2 · doi: 10.48550/arxiv.1106.3691 · pith_short_12: GWWDF4X3YUY2 · pith_short_16: GWWDF4X3YUY2V4DQ · pith_short_8: GWWDF4X3

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/GWWDF4X3YUY2V4DQFUSX7LYJ4N \
  | 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: 35ac32f2fbc531aaf0702d257faf09e37f49133c0a6ab1f3f948ff737bff73a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baf8ea5a79eb8bad279b3b3afd697b9ddfc4151253252b96d82e90422791fef5",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-06-18T21:30:31Z",
    "title_canon_sha256": "7617564f0650335f1457db703535807c9d4f8e4e7de3f307bfd3f98a1a035f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3691",
    "kind": "arxiv",
    "version": 2
  }
}