Pith Number

pith:UPGYGCZW

pith:2012:UPGYGCZWZ4FTD7ZWPKNTM6I2LZ

not attested not anchored not stored refs pending

On subsets of $S^n$ whose $(n+1)$-point subsets are contained in open hemisheres

Brendan Owens, Peter Kropholler, Robert Bieri

arxiv:1208.5041 v1 · 2012-08-24 · math.GR · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPGYGCZWZ4FTD7ZWPKNTM6I2LZ}

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	2026-05-18T03:47:52.034706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3cd830b36cf0b31ff367a9b36791a5e7104d40001d5a466b4c6ea7346cb0ae7

Aliases

arxiv: 1208.5041 · arxiv_version: 1208.5041v1 · doi: 10.48550/arxiv.1208.5041 · pith_short_12: UPGYGCZWZ4FT · pith_short_16: UPGYGCZWZ4FTD7ZW · pith_short_8: UPGYGCZW

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/UPGYGCZWZ4FTD7ZWPKNTM6I2LZ \
  | 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: a3cd830b36cf0b31ff367a9b36791a5e7104d40001d5a466b4c6ea7346cb0ae7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76b7f6a61bf272e2650882da48c5c81a2964a0c920c7c37b595bcfbff38778f4",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-08-24T19:39:20Z",
    "title_canon_sha256": "35c2e5862bd66b182de25443aa39c33c5c8604dd11d461a1fdf524ea60fff1cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5041",
    "kind": "arxiv",
    "version": 1
  }
}