Pith Number

pith:H2ZZ5UIA

pith:2011:H2ZZ5UIAQ7CD6B3P4HZD4VU5T7

not attested not anchored not stored refs pending

The free splitting complex of a free group I: Hyperbolicity

Lee Mosher, Michael Handel

arxiv:1111.1994 v2 · 2011-11-08 · 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{H2ZZ5UIAQ7CD6B3P4HZD4VU5T7}

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	2026-05-18T02:38:18.007737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3eb39ed10087c43f076fe1f23e569d9fd97f95d79aed28288eba80b66120e495

Aliases

arxiv: 1111.1994 · arxiv_version: 1111.1994v2 · doi: 10.48550/arxiv.1111.1994 · pith_short_12: H2ZZ5UIAQ7CD · pith_short_16: H2ZZ5UIAQ7CD6B3P · pith_short_8: H2ZZ5UIA

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/H2ZZ5UIAQ7CD6B3P4HZD4VU5T7 \
  | 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: 3eb39ed10087c43f076fe1f23e569d9fd97f95d79aed28288eba80b66120e495

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48bb3c312b547ca725f49a4a2070d03c0a417b5909688a50083f114d29c99d91",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-11-08T17:52:02Z",
    "title_canon_sha256": "4d946e260ea99fe49eec3fea9effdd31a698193ec15a3c7e3bc816dc7fee52c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1994",
    "kind": "arxiv",
    "version": 2
  }
}