Pith Number

pith:FOTOLT5B

pith:2015:FOTOLT5BLUQKE3M7GEPNXDON3M

not attested not anchored not stored refs pending

Invariable generation of the symmetric group

Ben Green, Kevin Ford, Sean Eberhard

arxiv:1508.01870 v2 · 2015-08-08 · math.GR · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FOTOLT5BLUQKE3M7GEPNXDON3M}

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	2026-05-18T00:32:44.941950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ba6e5cfa15d20a26d9f311edb8dcddb2ad5edacbb893d80226984d0ceb88bcb

Aliases

arxiv: 1508.01870 · arxiv_version: 1508.01870v2 · doi: 10.48550/arxiv.1508.01870 · pith_short_12: FOTOLT5BLUQK · pith_short_16: FOTOLT5BLUQKE3M7 · pith_short_8: FOTOLT5B

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/FOTOLT5BLUQKE3M7GEPNXDON3M \
  | 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: 2ba6e5cfa15d20a26d9f311edb8dcddb2ad5edacbb893d80226984d0ceb88bcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "656d1442bd2396d0b7280320fcaa55d154e3e42d9697c82c08b1b94ddf6c8c7f",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-08-08T08:36:02Z",
    "title_canon_sha256": "e8b124466eac8429b650f7dda41db70cadc6bf6ef577d85e790969a19c992107"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01870",
    "kind": "arxiv",
    "version": 2
  }
}