Pith Number

pith:QE64YPBU

pith:2002:QE64YPBUQ3HQSUIT3EG7NTPYFP

not attested not anchored not stored refs pending

Unusual formulae for the Euler characteristic

Justin Roberts

arxiv:math/0201178 v1 · 2002-01-18 · 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{QE64YPBUQ3HQSUIT3EG7NTPYFP}

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	2026-07-04T14:35:52.430469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

813dcc3c3486cf095113d90df6cdf82bf40aa451bd66cbbfe163bb033429467d

Aliases

arxiv: math/0201178 · arxiv_version: math/0201178v1 · doi: 10.48550/arxiv.math/0201178 · pith_short_12: QE64YPBUQ3HQ · pith_short_16: QE64YPBUQ3HQSUIT · pith_short_8: QE64YPBU

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/QE64YPBUQ3HQSUIT3EG7NTPYFP \
  | 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: 813dcc3c3486cf095113d90df6cdf82bf40aa451bd66cbbfe163bb033429467d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "addd135bb45fe480f94b76a059e1570ede342ccb4c71b7dc9161f1d39fbc9618",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-01-18T20:38:59Z",
    "title_canon_sha256": "9d90bd75742e05e40a13d8c1b38791a8b72547296cf5633bf9492e3822b63178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0201178",
    "kind": "arxiv",
    "version": 1
  }
}