Pith Number

pith:GWL6P22O

pith:2011:GWL6P22ON72RIAUC4XIFN5UWEK

not attested not anchored not stored refs pending

A product integral representation of mixed volumes of two convex bodies

Daniel Hug, Jan Rataj, Wolfgang Weil

arxiv:1112.0955 v3 · 2011-11-30 · 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{GWL6P22ON72RIAUC4XIFN5UWEK}

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	2026-05-18T03:02:59.775622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3597e7eb4e6ff5140282e5d056f69622a89a79e0f199c2854fa87de99a1f87ed

Aliases

arxiv: 1112.0955 · arxiv_version: 1112.0955v3 · doi: 10.48550/arxiv.1112.0955 · pith_short_12: GWL6P22ON72R · pith_short_16: GWL6P22ON72RIAUC · pith_short_8: GWL6P22O

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/GWL6P22ON72RIAUC4XIFN5UWEK \
  | 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: 3597e7eb4e6ff5140282e5d056f69622a89a79e0f199c2854fa87de99a1f87ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "def5b70b6e653cb3e2a17125cf1dac090846ea156e0665d113246d88ff5caa9d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-11-30T09:03:53Z",
    "title_canon_sha256": "69248d48d3c3b2c1787fcb7a96ffbaa6ee0dea365b7943e2ee50ccb907e00977"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0955",
    "kind": "arxiv",
    "version": 3
  }
}