Pith Number

pith:UPKFD5UL

pith:2010:UPKFD5ULUQ4XBDC3DZVREF4HYI

not attested not anchored not stored refs pending

Volume formula for a $\mathbb{Z}_2$-symmetric spherical tetrahedron through its edge lengths

Alexander Kolpakov, Alexander Mednykh, Marina Pashkevich

arxiv:1007.3948 v8 · 2010-07-22 · math.MG · math.CV · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPKFD5ULUQ4XBDC3DZVREF4HYI}

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	2026-05-18T04:16:32.183911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3d451f68ba439708c5b1e6b121787c217b71aeb9e23e6fa5136ba36cbd59c11

Aliases

arxiv: 1007.3948 · arxiv_version: 1007.3948v8 · doi: 10.48550/arxiv.1007.3948 · pith_short_12: UPKFD5ULUQ4X · pith_short_16: UPKFD5ULUQ4XBDC3 · pith_short_8: UPKFD5UL

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/UPKFD5ULUQ4XBDC3DZVREF4HYI \
  | 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: a3d451f68ba439708c5b1e6b121787c217b71aeb9e23e6fa5136ba36cbd59c11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb8274711b261829add14e353456f5f66971dd87b23fb930326be2711339a018",
    "cross_cats_sorted": [
      "math.CV",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-07-22T17:22:47Z",
    "title_canon_sha256": "00a2c0833a3e7780942d60fe9ed174e5502c598471c9aa131a545751152f654a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3948",
    "kind": "arxiv",
    "version": 8
  }
}