Pith Number

pith:FWZQSFMT

pith:2013:FWZQSFMTOHQOKGL6G7N2WLCJKP

not attested not anchored not stored refs pending

Geometric complexity of embeddings in ${\mathbb R}^d$

Michael Freedman, Vyacheslav Krushkal

arxiv:1311.2667 v2 · 2013-11-12 · math.MG · cs.CG · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FWZQSFMTOHQOKGL6G7N2WLCJKP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T02:41:42.079033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2db309159371e0e5197e37dbab2c4953c76bde32deb98c0043f72f000989bc22

Aliases

arxiv: 1311.2667 · arxiv_version: 1311.2667v2 · doi: 10.48550/arxiv.1311.2667 · pith_short_12: FWZQSFMTOHQO · pith_short_16: FWZQSFMTOHQOKGL6 · pith_short_8: FWZQSFMT

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/FWZQSFMTOHQOKGL6G7N2WLCJKP \
  | 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: 2db309159371e0e5197e37dbab2c4953c76bde32deb98c0043f72f000989bc22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "843670d18819792f96cc96f4eece3665f922778715e0811efe932e08046c0a85",
    "cross_cats_sorted": [
      "cs.CG",
      "math.CO",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-11-12T03:50:41Z",
    "title_canon_sha256": "2e572896a9c8f9a4c6a8d651efd7a093f6dee0950dd475a11d9362daacc0edfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2667",
    "kind": "arxiv",
    "version": 2
  }
}