Pith Number

pith:MZODZ2Q3

pith:2006:MZODZ2Q3GM3WSQ2TIZ7YTQMKIQ

not attested not anchored not stored refs pending

Depth of pleated surfaces in toroidal cusps of hyperbolic 3-manifolds

Ying-Qing Wu

arxiv:math/0610869 v1 · 2006-10-27 · 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{MZODZ2Q3GM3WSQ2TIZ7YTQMKIQ}

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	2026-05-18T02:41:26.709465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

665c3cea1b3337694353467f89c18a4432a432c0c7e9891c639c4f7769c95609

Aliases

arxiv: math/0610869 · arxiv_version: math/0610869v1 · doi: 10.48550/arxiv.math/0610869 · pith_short_12: MZODZ2Q3GM3W · pith_short_16: MZODZ2Q3GM3WSQ2T · pith_short_8: MZODZ2Q3

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/MZODZ2Q3GM3WSQ2TIZ7YTQMKIQ \
  | 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: 665c3cea1b3337694353467f89c18a4432a432c0c7e9891c639c4f7769c95609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d2f791534cbf5c57e4b3f100a85c103adae4fc9dcb3b69c4226b2b3995cabaa",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2006-10-27T22:12:22Z",
    "title_canon_sha256": "fd6fa73073b002ac5141966f53aa571e652d7fe12065cd25d8994e247a52c121"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610869",
    "kind": "arxiv",
    "version": 1
  }
}