Pith Number

pith:YK4SZAIC

pith:2011:YK4SZAICBKCXRZBLSB5HDIPTFV

not attested not anchored not stored refs pending

Outer automorphism groups of free groups: linear and free representations

Dawid Kielak

arxiv:1103.1624 v2 · 2011-03-08 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YK4SZAICBKCXRZBLSB5HDIPTFV}

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	2026-05-18T01:56:00.220031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2b92c81020a8578e42b907a71a1f32d669ebefc167ddef8ffab759f5ae798b9

Aliases

arxiv: 1103.1624 · arxiv_version: 1103.1624v2 · doi: 10.48550/arxiv.1103.1624 · pith_short_12: YK4SZAICBKCX · pith_short_16: YK4SZAICBKCXRZBL · pith_short_8: YK4SZAIC

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/YK4SZAICBKCXRZBLSB5HDIPTFV \
  | 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: c2b92c81020a8578e42b907a71a1f32d669ebefc167ddef8ffab759f5ae798b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4734aeea23129f6a88671234ba05fe6a67ce99b46139cf97f7f99e62c680a47",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-03-08T20:47:01Z",
    "title_canon_sha256": "648773a51366032059b9bcb2cc2241839760edebc3888e5d2e60122c42f59fe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1624",
    "kind": "arxiv",
    "version": 2
  }
}