Pith Number

pith:POLGBPDP

pith:2010:POLGBPDPMFHLGB6OKILDAKRE3I

not attested not anchored not stored refs pending

A Bers-like proof of the existence of train tracks for free group automorphisms

Mladen Bestvina

arxiv:1001.0325 v2 · 2010-01-02 · 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{POLGBPDPMFHLGB6OKILDAKRE3I}

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	2026-05-18T04:30:12.700186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b9660bc6f614eb307ce5216302a24da29ab2201e28f8c26011f43fb5b136480

Aliases

arxiv: 1001.0325 · arxiv_version: 1001.0325v2 · doi: 10.48550/arxiv.1001.0325 · pith_short_12: POLGBPDPMFHL · pith_short_16: POLGBPDPMFHLGB6O · pith_short_8: POLGBPDP

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/POLGBPDPMFHLGB6OKILDAKRE3I \
  | 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: 7b9660bc6f614eb307ce5216302a24da29ab2201e28f8c26011f43fb5b136480

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "531da9d6eee8e78d09425539ea395ee47e36191cceba9639c4a65188469007e1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-01-02T18:36:38Z",
    "title_canon_sha256": "07c0ccc9c3c1e9f608c8eaf9a06a434710b100e2694ffd4ece0961f7dd056eac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0325",
    "kind": "arxiv",
    "version": 2
  }
}