Pith Number

pith:V3M5TT6Q

pith:2017:V3M5TT6QGVWJJTMVFZUPKI6DGT

not attested not anchored not stored refs pending

The trivial lower bound for the girth of $S_n$

Sean Eberhard

arxiv:1706.09972 v1 · 2017-06-29 · math.GR · 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{V3M5TT6QGVWJJTMVFZUPKI6DGT}

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	2026-05-18T00:41:11.815252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aed9d9cfd0356c94cd952e68f523c334cc48c88333161cc75636d02a2c9229c2

Aliases

arxiv: 1706.09972 · arxiv_version: 1706.09972v1 · doi: 10.48550/arxiv.1706.09972 · pith_short_12: V3M5TT6QGVWJ · pith_short_16: V3M5TT6QGVWJJTMV · pith_short_8: V3M5TT6Q

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/V3M5TT6QGVWJJTMVFZUPKI6DGT \
  | 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: aed9d9cfd0356c94cd952e68f523c334cc48c88333161cc75636d02a2c9229c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191ffa1df48c2f31ef642aa739f7b38dc5a24a0742a0d0c39c3c1a8ca037ce11",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-06-29T22:26:47Z",
    "title_canon_sha256": "ad2aeecfd0f27c530ffaf73b9c7d05847d4ea92e3cee65eecf9aabb05ab390c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09972",
    "kind": "arxiv",
    "version": 1
  }
}