Pith Number

pith:KR4X4MTB

pith:2020:KR4X4MTBCN4IQQFI5QSYBMYV6L

not attested not anchored not stored refs pending

Multivariate volume, Ehrhart, and $h^*$-polynomials of polytropes

Leon Zhang, Marie-Charlotte Brandenburg, Sophia Elia

arxiv:2006.01920 v2 · 2020-06-02 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KR4X4MTBCN4IQQFI5QSYBMYV6L}

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.

Cited by

1 paper in Pith

Fano and Reflexive Polytopes from Feynman Integrals

Receipt and verification

First computed	2026-07-05T05:48:29.731044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54797e326113788840a8ec2580b315f2f0fd524d2d26a04674945eac055b1666

Aliases

arxiv: 2006.01920 · arxiv_version: 2006.01920v2 · doi: 10.48550/arxiv.2006.01920 · pith_short_12: KR4X4MTBCN4I · pith_short_16: KR4X4MTBCN4IQQFI · pith_short_8: KR4X4MTB

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/KR4X4MTBCN4IQQFI5QSYBMYV6L \
  | 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: 54797e326113788840a8ec2580b315f2f0fd524d2d26a04674945eac055b1666

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "107514ce4c95d68abd9759bb5864c9a66ffec05ac11473e24bacdefabd520d40",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-06-02T20:02:18Z",
    "title_canon_sha256": "3f38bedbc1fd3430566da900458fdd6b3f88e35150d50f02fd276b70058c7c5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.01920",
    "kind": "arxiv",
    "version": 2
  }
}