Pith Number

pith:4WFMJMFT

pith:2007:4WFMJMFTNXNS2FTJQDGEHY4IRI

not attested not anchored not stored refs pending

Local torus actions modeled on the standard representation

Takahiko Yoshida

arxiv:0710.2166 v3 · 2007-10-11 · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WFMJMFTNXNS2FTJQDGEHY4IRI}

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	2026-05-18T04:20:51.454411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e58ac4b0b36ddb2d166980cc43e3888a3242988199e33fbadeac47e52b04fa5b

Aliases

arxiv: 0710.2166 · arxiv_version: 0710.2166v3 · doi: 10.48550/arxiv.0710.2166 · pith_short_12: 4WFMJMFTNXNS · pith_short_16: 4WFMJMFTNXNS2FTJ · pith_short_8: 4WFMJMFT

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/4WFMJMFTNXNS2FTJQDGEHY4IRI \
  | 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: e58ac4b0b36ddb2d166980cc43e3888a3242988199e33fbadeac47e52b04fa5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "110a69d119ab5e9af91259184bad04f70bbcbb18a2d2d91bd26f88ecff99e112",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-10-11T05:08:40Z",
    "title_canon_sha256": "276bd2605080d1964a187c3a9e643018d386ecc16c3df608cbab7e3266a6de84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2166",
    "kind": "arxiv",
    "version": 3
  }
}