Pith Number

pith:Y65GMBHW

pith:1998:Y65GMBHWOFEA3ZIKJ54T6YMCRR

not attested not anchored not stored refs pending

Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

William P. Thurston

arxiv:math/9801045 v1 · 1998-01-10 · math.GT · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y65GMBHWOFEA3ZIKJ54T6YMCRR}

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.

Cited by

3 papers in Pith

Mostow rigidity for skew solenoidal manifolds

Geometrisation of 3-manifolds

CaTherine wheels

Receipt and verification

First computed	2026-07-04T14:40:25.029145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7ba6604f671480de50a4f793f61828c4f27f2251f78123b6f4210cead205f92

Aliases

arxiv: math/9801045 · arxiv_version: math/9801045v1 · doi: 10.48550/arxiv.math/9801045 · pith_short_12: Y65GMBHWOFEA · pith_short_16: Y65GMBHWOFEA3ZIK · pith_short_8: Y65GMBHW

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/Y65GMBHWOFEA3ZIKJ54T6YMCRR \
  | 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: c7ba6604f671480de50a4f793f61828c4f27f2251f78123b6f4210cead205f92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b096c98fc9f30173476f6826c50fd6488c0168819f290a8ec9ac68ad2507510",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-01-10T22:16:57Z",
    "title_canon_sha256": "1db57f1a49873d55b1df37222da5187e17114eee0de1710c57d331159213b10c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9801045",
    "kind": "arxiv",
    "version": 1
  }
}