Pith Number

pith:T3LH6TLD

pith:2002:T3LH6TLDVZ2EM7TIGQOG6WV53Y

not attested not anchored not stored refs pending

Minimal spheres of arbitrarily high Morse index

J. Hyam Rubinstein, Joel Hass, Paul Norbury

arxiv:math/0206286 v1 · 2002-06-27 · 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{T3LH6TLDVZ2EM7TIGQOG6WV53Y}

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	2026-07-04T14:36:17.726051Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ed67f4d63ae74467e68341c6f5abdde173e3262a497923bb15104f6a48e37c3

Aliases

arxiv: math/0206286 · arxiv_version: math/0206286v1 · doi: 10.48550/arxiv.math/0206286 · pith_short_12: T3LH6TLDVZ2E · pith_short_16: T3LH6TLDVZ2EM7TI · pith_short_8: T3LH6TLD

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/T3LH6TLDVZ2EM7TIGQOG6WV53Y \
  | 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: 9ed67f4d63ae74467e68341c6f5abdde173e3262a497923bb15104f6a48e37c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3a08e1e30880e174ad642f59ee278052fc5860fb38339567028626d2abc88c6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-06-27T07:06:01Z",
    "title_canon_sha256": "8a3481b42b905ddd609ffa93bd387616736103791c6f9a4d69559f93c40576f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206286",
    "kind": "arxiv",
    "version": 1
  }
}