Pith Number

pith:VDGE5LG7

pith:2009:VDGE5LG7U4TVH4KNDMYKYCEXWU

not attested not anchored not stored refs pending

Cross ratios, translation lengths and maximal representations

Tobias Hartnick, Tobias Strubel

arxiv:0908.4101 v2 · 2009-08-27 · math.DG · 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{VDGE5LG7U4TVH4KNDMYKYCEXWU}

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	2026-05-18T04:31:12.024163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8cc4eacdfa72753f14d1b30ac0897b50fc7f2016c6d624c653298af135f3e8c

Aliases

arxiv: 0908.4101 · arxiv_version: 0908.4101v2 · doi: 10.48550/arxiv.0908.4101 · pith_short_12: VDGE5LG7U4TV · pith_short_16: VDGE5LG7U4TVH4KN · pith_short_8: VDGE5LG7

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/VDGE5LG7U4TVH4KNDMYKYCEXWU \
  | 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: a8cc4eacdfa72753f14d1b30ac0897b50fc7f2016c6d624c653298af135f3e8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "569dcde5da43d14a4effb5ab4ef5a67cdb8adae3a0e748c593de2ddb5331f3c0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-08-27T21:29:52Z",
    "title_canon_sha256": "f532f572603f17bd457ef36c747d5f4b69f417cac7180822b08aa7cbae31a4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.4101",
    "kind": "arxiv",
    "version": 2
  }
}