Pith Number

pith:GPWMOAQD

pith:2012:GPWMOAQDJY6CUG7YOTOQ77T73L

not attested not anchored not stored refs pending

Hadwiger's Theorem for Definable Functions

Matthew Wright, Robert Ghrist, Yuliy Baryshnikov

arxiv:1203.6120 v3 · 2012-03-28 · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPWMOAQDJY6CUG7YOTOQ77T73L}

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	2026-05-18T03:19:35.375264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33ecc702034e3c2a1bf874dd0ffe7fdae3bf4291b89676a0dafd7b4a294be15b

Aliases

arxiv: 1203.6120 · arxiv_version: 1203.6120v3 · doi: 10.48550/arxiv.1203.6120 · pith_short_12: GPWMOAQDJY6C · pith_short_16: GPWMOAQDJY6CUG7Y · pith_short_8: GPWMOAQD

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/GPWMOAQDJY6CUG7YOTOQ77T73L \
  | 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: 33ecc702034e3c2a1bf874dd0ffe7fdae3bf4291b89676a0dafd7b4a294be15b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fde3318be4060de44dd4ce710da84552621a2bad1e886eed43031e5ff2d115bb",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-03-28T00:44:46Z",
    "title_canon_sha256": "a148115f172b94c97afac3f07b40864ae9c611c5e0e99f46777f6de50d5c6420"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6120",
    "kind": "arxiv",
    "version": 3
  }
}