Pith Number

pith:KCRI5DP5

pith:2016:KCRI5DP5NMVCW2YBL7UDJ2YOMJ

not attested not anchored not stored refs pending

Proving Tucker's Lemma with a Volume Argument

Beauttie Kuture, Christopher Loa, Francis Edward Su, Mutiara Sondjaja, Oscar Leong

arxiv:1604.02395 v1 · 2016-04-08 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCRI5DP5NMVCW2YBL7UDJ2YOMJ}

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	2026-05-18T01:17:26.654360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50a28e8dfd6b2a2b6b015fe834eb0e624c649f82f89721af95917191e674ae3d

Aliases

arxiv: 1604.02395 · arxiv_version: 1604.02395v1 · doi: 10.48550/arxiv.1604.02395 · pith_short_12: KCRI5DP5NMVC · pith_short_16: KCRI5DP5NMVCW2YB · pith_short_8: KCRI5DP5

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/KCRI5DP5NMVCW2YBL7UDJ2YOMJ \
  | 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: 50a28e8dfd6b2a2b6b015fe834eb0e624c649f82f89721af95917191e674ae3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9df4364511ce9e387b0a71246786d16cca979fdffd4a4ba8d28ae367f7ebbfe",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-08T16:41:54Z",
    "title_canon_sha256": "eb26cc809c6e7183b0a68e2f90a9e8cf3445ac5cfe295cbfc8d9f613d2b56e8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02395",
    "kind": "arxiv",
    "version": 1
  }
}