Pith Number

pith:JO6PMB7V

pith:2012:JO6PMB7VCLTY3YYAF6AKNNU2IG

not attested not anchored not stored refs pending

The universal character ring of the (-2,2m+1,2n)-pretzel link

Anh T. Tran

arxiv:1209.0002 v3 · 2012-08-31 · math.GT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JO6PMB7VCLTY3YYAF6AKNNU2IG}

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	2026-05-18T03:19:22.501255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bbcf607f512e78de3002f80a6b69a41b4d6cb4c470ac3e0b2483156eb6a90b6

Aliases

arxiv: 1209.0002 · arxiv_version: 1209.0002v3 · doi: 10.48550/arxiv.1209.0002 · pith_short_12: JO6PMB7VCLTY · pith_short_16: JO6PMB7VCLTY3YYA · pith_short_8: JO6PMB7V

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/JO6PMB7VCLTY3YYAF6AKNNU2IG \
  | 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: 4bbcf607f512e78de3002f80a6b69a41b4d6cb4c470ac3e0b2483156eb6a90b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "384d161edcd4e3b5b0f69705663738637ec92a3ce979301efd1bcb08b6b84b5a",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-08-31T00:55:02Z",
    "title_canon_sha256": "3f7f44c23d92a8a585627842cfcf4225ce02386e88eef80d8bfe93cc438568df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0002",
    "kind": "arxiv",
    "version": 3
  }
}