Pith Number

pith:K4TLLU5U

pith:2012:K4TLLU5UGYSKHM7GARIAVQKOLO

not attested not anchored not stored refs pending

On hyperbolicity of free splitting and free factor complexes

Ilya Kapovich, Kasra Rafi

arxiv:1206.3626 v3 · 2012-06-16 · 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{K4TLLU5UGYSKHM7GARIAVQKOLO}

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	2026-05-18T02:48:02.902950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5726b5d3b43624a3b3e604500ac14e5b8a3e7fd61ecbb2e4b32b61f905f98837

Aliases

arxiv: 1206.3626 · arxiv_version: 1206.3626v3 · doi: 10.48550/arxiv.1206.3626 · pith_short_12: K4TLLU5UGYSK · pith_short_16: K4TLLU5UGYSKHM7G · pith_short_8: K4TLLU5U

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/K4TLLU5UGYSKHM7GARIAVQKOLO \
  | 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: 5726b5d3b43624a3b3e604500ac14e5b8a3e7fd61ecbb2e4b32b61f905f98837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56c848da8f7ca682d0db3d9bbb187d863050b6f25f5fb65db21fb336ddf3cb6c",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-16T03:22:50Z",
    "title_canon_sha256": "7a9dee7179a35dd136e40363c9c2ff3d96986a3bd088af89d168d7ec4455042b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3626",
    "kind": "arxiv",
    "version": 3
  }
}