Pith Number

pith:K6ND5RNV

pith:1999:K6ND5RNVIRUZ2BPDTX6BNHCYOJ

not attested not anchored not stored refs pending

Planar algebras, I

Vaughan F. R. Jones (UC Berkeley)

arxiv:math/9909027 v1 · 1999-09-04 · math.QA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K6ND5RNVIRUZ2BPDTX6BNHCYOJ}

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.

Cited by

1 paper in Pith

Irreducibility of the Wysiwyg representations of Thompson's groups

Receipt and verification

First computed	2026-07-04T14:41:18.023477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

579a3ec5b544699d05e39dfc169c58724578b0fc2f49b985c649433972984a70

Aliases

arxiv: math/9909027 · arxiv_version: math/9909027v1 · doi: 10.48550/arxiv.math/9909027 · pith_short_12: K6ND5RNVIRUZ · pith_short_16: K6ND5RNVIRUZ2BPD · pith_short_8: K6ND5RNV

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/K6ND5RNVIRUZ2BPDTX6BNHCYOJ \
  | 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: 579a3ec5b544699d05e39dfc169c58724578b0fc2f49b985c649433972984a70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9db849049aab1d7c98a7f05857034dbb9dd762b690bcaa3060bffb8ee483aea5",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "1999-09-04T06:24:17Z",
    "title_canon_sha256": "bb9435b004f47b95923a53eabefda98bc7a47ee247456f794bdd2444539cf861"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9909027",
    "kind": "arxiv",
    "version": 1
  }
}