Pith Number

pith:ULBSCPSQ

pith:2002:ULBSCPSQYP52D5IX7JXUBTQZZL

not attested not anchored not stored refs pending

Dual canonical bases, quantum shuffles and q-characters

Bernard Leclerc

arxiv:math/0209133 v3 · 2002-09-11 · math.QA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULBSCPSQYP52D5IX7JXUBTQZZL}

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	2026-07-04T14:36:26.141889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2c3213e50c3fba1f517fa6f40ce19cacf8c89fcd7900a788ab221614e5c26cb

Aliases

arxiv: math/0209133 · arxiv_version: math/0209133v3 · doi: 10.48550/arxiv.math/0209133 · pith_short_12: ULBSCPSQYP52 · pith_short_16: ULBSCPSQYP52D5IX · pith_short_8: ULBSCPSQ

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/ULBSCPSQYP52D5IX7JXUBTQZZL \
  | 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: a2c3213e50c3fba1f517fa6f40ce19cacf8c89fcd7900a788ab221614e5c26cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941e87d05ba26a24a62f6181f34f7f0792310ebd398c0819e209094e1c80e84a",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-09-11T18:23:08Z",
    "title_canon_sha256": "42076cb1cb43c191c9aeb39f808c931a5ce6bd9284369154a08f13b7f897ce02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209133",
    "kind": "arxiv",
    "version": 3
  }
}