Pith Number

pith:32SAY22N

pith:2006:32SAY22NJVBPTP2RCXSLW4TA4I

not attested not anchored not stored refs pending

Co-contractions of Graphs and Right-angled Artin Groups

Sang-hyun Kim

arxiv:math/0611588 v1 · 2006-11-19 · 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{32SAY22NJVBPTP2RCXSLW4TA4I}

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	2026-05-18T01:22:19.328116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dea40c6b4d4d42f9bf5115e4bb7260e223dcf439097c7cf8a006826589784482

Aliases

arxiv: math/0611588 · arxiv_version: math/0611588v1 · doi: 10.48550/arxiv.math/0611588 · pith_short_12: 32SAY22NJVBP · pith_short_16: 32SAY22NJVBPTP2R · pith_short_8: 32SAY22N

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/32SAY22NJVBPTP2RCXSLW4TA4I \
  | 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: dea40c6b4d4d42f9bf5115e4bb7260e223dcf439097c7cf8a006826589784482

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd0248e2fb3e3ec1643ddbce57cec55ec70d27fde8e357fc9dfaa28ba86204fd",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-11-19T22:51:42Z",
    "title_canon_sha256": "849a9061c93f1611c39f14efbd388f9a470b88b1c6eb67368caaaef4c1962522"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611588",
    "kind": "arxiv",
    "version": 1
  }
}