Pith Number

pith:FPMOT5UN

pith:2010:FPMOT5UNYP7VO4HLU6UINTMUJQ

not attested not anchored not stored refs pending

Extremal results regarding $K_6$-minors in graphs of girth at least 5

Elad Aigner-Horev, Roi Krakovski

arxiv:1012.5795 v1 · 2010-12-28 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPMOT5UNYP7VO4HLU6UINTMUJQ}

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	2026-05-18T04:32:21.509581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bd8e9f68dc3ff5770eba7a886cd944c3dcb95c2465dc0b5a19fa48bd4bbe2e3

Aliases

arxiv: 1012.5795 · arxiv_version: 1012.5795v1 · doi: 10.48550/arxiv.1012.5795 · pith_short_12: FPMOT5UNYP7V · pith_short_16: FPMOT5UNYP7VO4HL · pith_short_8: FPMOT5UN

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/FPMOT5UNYP7VO4HLU6UINTMUJQ \
  | 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: 2bd8e9f68dc3ff5770eba7a886cd944c3dcb95c2465dc0b5a19fa48bd4bbe2e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd7427c5a6143a0a38091b677a18cff145cf6b537426af66a94886189d9a167e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-28T17:07:54Z",
    "title_canon_sha256": "457180270137bf54678aa682095b161c906b50625fef7a08491ccbdb619633b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5795",
    "kind": "arxiv",
    "version": 1
  }
}