Pith Number

pith:5GYU6XLU

pith:2008:5GYU6XLUEF5XMGPHOE7QO4VCBP

not attested not anchored not stored refs pending

Strongly Contracting Geodesics in Outer Space

Yael Algom-Kfir

arxiv:0812.1555 v3 · 2008-12-08 · 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{5GYU6XLUEF5XMGPHOE7QO4VCBP}

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	2026-05-18T02:38:18.971896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9b14f5d74217b7619e7713f0772a20bd3bc3c802c933c6567ef5150e4100145

Aliases

arxiv: 0812.1555 · arxiv_version: 0812.1555v3 · doi: 10.48550/arxiv.0812.1555 · pith_short_12: 5GYU6XLUEF5X · pith_short_16: 5GYU6XLUEF5XMGPH · pith_short_8: 5GYU6XLU

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/5GYU6XLUEF5XMGPHOE7QO4VCBP \
  | 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: e9b14f5d74217b7619e7713f0772a20bd3bc3c802c933c6567ef5150e4100145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d192c122d5731663e80cbc6e54601c11516f060bec840d17c44f86e8af333ce",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-12-08T20:41:31Z",
    "title_canon_sha256": "39c31aa59d2eab240efb92dbd496367118b36c1377b2e90de07b349753f458e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1555",
    "kind": "arxiv",
    "version": 3
  }
}