Pith Number

pith:2TTJMISZ

pith:1998:2TTJMISZ4EGXWUMJQWL43CPVV7

not attested not anchored not stored refs pending

Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds

Nathan M. Dunfield

arxiv:math/9802022 v3 · 1998-02-04 · 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{2TTJMISZ4EGXWUMJQWL43CPVV7}

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	2026-07-04T16:10:08.875391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4e6962259e10d7b51898597cd89f5afc5518494179f406faae1d7dd346bc7a2

Aliases

arxiv: math/9802022 · arxiv_version: math/9802022v3 · doi: 10.48550/arxiv.math/9802022 · pith_short_12: 2TTJMISZ4EGX · pith_short_16: 2TTJMISZ4EGXWUMJ · pith_short_8: 2TTJMISZ

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/2TTJMISZ4EGXWUMJQWL43CPVV7 \
  | 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: d4e6962259e10d7b51898597cd89f5afc5518494179f406faae1d7dd346bc7a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc33069a15178dab63bbe720017d013260946d4e73c6c13295435c6130fddcee",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-02-04T20:00:13Z",
    "title_canon_sha256": "cb2c4ad646ddb8c779ed2e84c73a74469e1d65e92abc4f9163de0f676c85c216"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9802022",
    "kind": "arxiv",
    "version": 3
  }
}