Pith Number

pith:QMIKBNKB

pith:2019:QMIKBNKB5KMHVQG3ESOUOTJ44R

not attested not anchored not stored refs pending

Volume of the Minkowski sums of star-shaped sets

Artem Zvavitch, Matthieu Fradelizi, Zsolt L\'angi

arxiv:1910.06146 v2 · 2019-10-14 · math.MG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QMIKBNKB5KMHVQG3ESOUOTJ44R}

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	2026-07-05T02:51:35.454967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8310a0b541ea987ac0db249d474d3ce47ac1a560552753e9548bac8e49fee594

Aliases

arxiv: 1910.06146 · arxiv_version: 1910.06146v2 · doi: 10.48550/arxiv.1910.06146 · pith_short_12: QMIKBNKB5KMH · pith_short_16: QMIKBNKB5KMHVQG3 · pith_short_8: QMIKBNKB

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/QMIKBNKB5KMHVQG3ESOUOTJ44R \
  | 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: 8310a0b541ea987ac0db249d474d3ce47ac1a560552753e9548bac8e49fee594

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90818b8f4147047f32fd81daa121201269b30c0db9f98c1e884ef2918409fba2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-10-14T13:59:29Z",
    "title_canon_sha256": "ec191e59271fb99455ca023833af2afb6a71bcb4cec5673b4bc5040cc1b01bf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.06146",
    "kind": "arxiv",
    "version": 2
  }
}