Pith Number

pith:72LQH5WL

pith:2005:72LQH5WLHR24OPHENT7VV66NTP

not attested not anchored not stored refs pending

Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure

Dubravko Ivansic, John G. Ratcliffe, Steven T. Tschantz

arxiv:math/0502293 v2 · 2005-02-14 · 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{72LQH5WLHR24OPHENT7VV66NTP}

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	2026-05-18T02:41:32.096540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe9703f6cb3c75c73ce46cff5afbcd9bec9bdd4abc97428976facc6097a4177f

Aliases

arxiv: math/0502293 · arxiv_version: math/0502293v2 · doi: 10.48550/arxiv.math/0502293 · pith_short_12: 72LQH5WLHR24 · pith_short_16: 72LQH5WLHR24OPHE · pith_short_8: 72LQH5WL

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/72LQH5WLHR24OPHENT7VV66NTP \
  | 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: fe9703f6cb3c75c73ce46cff5afbcd9bec9bdd4abc97428976facc6097a4177f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b1c254d3d85528825bb10e68b14283fc6052d2f4e57e89aabd1c80eec440499",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-02-14T17:30:47Z",
    "title_canon_sha256": "def1a933b90e0823f57f812597f4b4603e14cea04cf72395a316c7b8bd2362f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502293",
    "kind": "arxiv",
    "version": 2
  }
}