Pith Number

pith:SNTGPFDE

pith:2004:SNTGPFDEJQJHTQVUSP6V3JRFAP

not attested not anchored not stored refs pending

The obstructions for toroidal graphs with no $K_{3,3}$'s

Andrei Gagarin, John Chambers, Wendy Myrvold

arxiv:math/0411488 v2 · 2004-11-22 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SNTGPFDEJQJHTQVUSP6V3JRFAP}

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	2026-05-18T04:32:53.676061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93666794644c1279c2b493fd5da62503d990ec3387d27f542cc6020d3493a604

Aliases

arxiv: math/0411488 · arxiv_version: math/0411488v2 · doi: 10.48550/arxiv.math/0411488 · pith_short_12: SNTGPFDEJQJH · pith_short_16: SNTGPFDEJQJHTQVU · pith_short_8: SNTGPFDE

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/SNTGPFDEJQJHTQVUSP6V3JRFAP \
  | 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: 93666794644c1279c2b493fd5da62503d990ec3387d27f542cc6020d3493a604

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e92295cf2aee3561b7e0a578d358a714299405f3443130324622594e2e3c7c79",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-11-22T20:33:28Z",
    "title_canon_sha256": "dc80922b54d5fa554b493c0ca3fde8d09256529735b7c7582b9d5e29e5ba92a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411488",
    "kind": "arxiv",
    "version": 2
  }
}