Pith Number

pith:CNEDDBU3

pith:2026:CNEDDBU32ZQMWHDU34FMZW2TH3

not attested not anchored not stored refs pending

On zero-sum polytopes: reciprocity, rigidity, and cyclic sieving

Dongchun Han, Hanbin Zhang, Shiwen Zhang, Xuan Wang

arxiv:2606.11005 v1 · 2026-06-09 · 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{CNEDDBU32ZQMWHDU34FMZW2TH3}

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	2026-06-10T01:11:03.209591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

134831869bd660cb1c74df0accdb533ef66395b001fd1b860e59dd91e3704014

Aliases

arxiv: 2606.11005 · arxiv_version: 2606.11005v1 · doi: 10.48550/arxiv.2606.11005 · pith_short_12: CNEDDBU32ZQM · pith_short_16: CNEDDBU32ZQMWHDU · pith_short_8: CNEDDBU3

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/CNEDDBU32ZQMWHDU34FMZW2TH3 \
  | 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: 134831869bd660cb1c74df0accdb533ef66395b001fd1b860e59dd91e3704014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b9fb551b76185e8f609fabf8654467a1e00e0c8c7f84609de8749b47cfa80a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-09T15:39:54Z",
    "title_canon_sha256": "ea432805629b867010715c1e2d2461d98ecd2dd3ed0c4dd983862d67966e11b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11005",
    "kind": "arxiv",
    "version": 1
  }
}