Pith Number

pith:WCQRD6R4

pith:2017:WCQRD6R42BLRZS6L3CNN5ZXLWW

not attested not anchored not stored refs pending

The discrete yet ubiquitous theorems of Carath\'eodory, Helly, Sperner, Tucker, and Tverberg

Fr\'ed\'eric Meunier, Jesus A. De Loera, Nabil Mustafa, Xavier Goaoc

arxiv:1706.05975 v3 · 2017-06-16 · math.CO · cs.DM · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCQRD6R42BLRZS6L3CNN5ZXLWW}

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	2026-05-18T00:03:56.979692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0a111fa3cd0571ccbcbd89adee6ebb5a61618ff1af83600920e398792a8c6e3

Aliases

arxiv: 1706.05975 · arxiv_version: 1706.05975v3 · doi: 10.48550/arxiv.1706.05975 · pith_short_12: WCQRD6R42BLR · pith_short_16: WCQRD6R42BLRZS6L · pith_short_8: WCQRD6R4

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/WCQRD6R42BLRZS6L3CNN5ZXLWW \
  | 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: b0a111fa3cd0571ccbcbd89adee6ebb5a61618ff1af83600920e398792a8c6e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0748b350272bd07f3926c6815d5d79641d27b01ab8b732e9c52626e5afb141a",
    "cross_cats_sorted": [
      "cs.DM",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-06-16T15:44:50Z",
    "title_canon_sha256": "76fb96a69b5a2a62f09edc5581d8aec046497a93d9e248b1032278c4472ebe1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05975",
    "kind": "arxiv",
    "version": 3
  }
}