Pith Number

pith:7ZZKRISZ

pith:2011:7ZZKRISZIHTETX65SQNBFHDNPW

not attested not anchored not stored refs pending

Hyperbolicity of the complex of free factors

Mark Feighn, Mladen Bestvina

arxiv:1107.3308 v4 · 2011-07-17 · 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{7ZZKRISZIHTETX65SQNBFHDNPW}

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	2026-05-18T03:01:33.631609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe72a8a25941e649dfdd941a129c6d7db07dcc484b4635a661442c45e4e67c4f

Aliases

arxiv: 1107.3308 · arxiv_version: 1107.3308v4 · doi: 10.48550/arxiv.1107.3308 · pith_short_12: 7ZZKRISZIHTE · pith_short_16: 7ZZKRISZIHTETX65 · pith_short_8: 7ZZKRISZ

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/7ZZKRISZIHTETX65SQNBFHDNPW \
  | 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: fe72a8a25941e649dfdd941a129c6d7db07dcc484b4635a661442c45e4e67c4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cc5ed37353b4b0dea0e18c45698e6c8f6ed2b0c6d077a4f4a466928b7dd0195",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-17T15:23:15Z",
    "title_canon_sha256": "a50843d1e8d8ec115aa5c84399310b9e784f6c319cdb4ac40e7f6f1c127e90a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3308",
    "kind": "arxiv",
    "version": 4
  }
}