Pith Number

pith:FECBK6CD

pith:2011:FECBK6CDKAAZHA4UJSMXTMW4RJ

not attested not anchored not stored refs pending

Isometric endomorphisms of free groups

Alden Walker, Danny Calegari

arxiv:1101.4055 v2 · 2011-01-21 · 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{FECBK6CDKAAZHA4UJSMXTMW4RJ}

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	2026-05-18T02:22:50.825525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

290415784350019383944c9979b2dc8a52a1e33e1d0cf518b6665add78dfe8a3

Aliases

arxiv: 1101.4055 · arxiv_version: 1101.4055v2 · doi: 10.48550/arxiv.1101.4055 · pith_short_12: FECBK6CDKAAZ · pith_short_16: FECBK6CDKAAZHA4U · pith_short_8: FECBK6CD

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/FECBK6CDKAAZHA4UJSMXTMW4RJ \
  | 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: 290415784350019383944c9979b2dc8a52a1e33e1d0cf518b6665add78dfe8a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cb3563186671f3c7b33d749ec6d8533e234bb43bd8ce683df5a73a6e0c0997c",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-01-21T00:36:08Z",
    "title_canon_sha256": "edc179d30d15740ef68e2406447594b6978c56e9d3387212a7888c77f40b8dae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4055",
    "kind": "arxiv",
    "version": 2
  }
}