Pith Number

pith:FA337BJJ

pith:2011:FA337BJJRL2PQB6KN4OQOCAD5G

not attested not anchored not stored refs pending

Spheres and Projections for $\mathrm{Out}(F_n)$

Sebastian Hensel, Ursula Hamenst\"adt

arxiv:1109.2687 v3 · 2011-09-13 · math.GT · 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{FA337BJJRL2PQB6KN4OQOCAD5G}

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	2026-05-18T00:44:30.529574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839

Aliases

arxiv: 1109.2687 · arxiv_version: 1109.2687v3 · doi: 10.48550/arxiv.1109.2687 · pith_short_12: FA337BJJRL2P · pith_short_16: FA337BJJRL2PQB6K · pith_short_8: FA337BJJ

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/FA337BJJRL2PQB6KN4OQOCAD5G \
  | 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: 2837bf85298af4f807ca6f1d070803e98522e2e80b04f27f77c7114a526e5839

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb6c7e68318eb89065c6dfb519ea9cf79a14da1bf922590b7726a13a562a22f0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-13T07:28:59Z",
    "title_canon_sha256": "455e23a24d4d7656c401c3b5a035c6e9319d02c7ffbede1fcb8b14250a9aa15e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2687",
    "kind": "arxiv",
    "version": 3
  }
}