Pith Number

pith:BE6BNBBI

pith:2010:BE6BNBBI5SOWJPC5XKCN4X7W4Y

not attested not anchored not stored refs pending

The Dehn functions of Out(F_n) and Aut(F_n)

Karen Vogtmann, Martin R. Bridson

arxiv:1011.1506 v2 · 2010-11-05 · math.GR · 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{BE6BNBBI5SOWJPC5XKCN4X7W4Y}

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	2026-05-18T04:07:40.633048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

093c168428ec9d64bc5dba84de5ff6e602ceb2f75f1949f450b4cba4c3176659

Aliases

arxiv: 1011.1506 · arxiv_version: 1011.1506v2 · doi: 10.48550/arxiv.1011.1506 · pith_short_12: BE6BNBBI5SOW · pith_short_16: BE6BNBBI5SOWJPC5 · pith_short_8: BE6BNBBI

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/BE6BNBBI5SOWJPC5XKCN4X7W4Y \
  | 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: 093c168428ec9d64bc5dba84de5ff6e602ceb2f75f1949f450b4cba4c3176659

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f63e7e1a0a165dd100db384fa5c08effa4dc0056b4ab25576144610d97deaa43",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-11-05T20:18:26Z",
    "title_canon_sha256": "ad5e7ef5d3ef7cf10098eecdc0b2da286a27683a4f27dc3f385a8b5ba2124667"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1506",
    "kind": "arxiv",
    "version": 2
  }
}