Pith Number

pith:AOH3BDCI

pith:2010:AOH3BDCISFFFYQ2YBH6MQ3ZZK4

not attested not anchored not stored refs pending

Margulis numbers for Haken manifolds

Marc Culler, Peter B. Shalen

arxiv:1006.3467 v3 · 2010-06-17 · 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{AOH3BDCISFFFYQ2YBH6MQ3ZZK4}

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	2026-05-18T04:19:22.229948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

038fb08c48914a5c435809fcc86f39570e5ceab1067b98675bd037d7c72183c2

Aliases

arxiv: 1006.3467 · arxiv_version: 1006.3467v3 · doi: 10.48550/arxiv.1006.3467 · pith_short_12: AOH3BDCISFFF · pith_short_16: AOH3BDCISFFFYQ2Y · pith_short_8: AOH3BDCI

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/AOH3BDCISFFFYQ2YBH6MQ3ZZK4 \
  | 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: 038fb08c48914a5c435809fcc86f39570e5ceab1067b98675bd037d7c72183c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3221769c1d1e99d9a488df89005d81517b74b54d7b6bc1355f7ce8a3dff95b08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-06-17T13:47:53Z",
    "title_canon_sha256": "a3d60a25a32172ef56627d1a8f5bc0194edbc9597918d818e2fb185cb345c440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3467",
    "kind": "arxiv",
    "version": 3
  }
}