Pith Number

pith:TGFX2XWT

pith:2002:TGFX2XWTHJRKGVOF4QL2CHQX7Q

not attested not anchored not stored refs pending

Virtual crystals and Kleber's algorithm

Anne Schilling, Mark Shimozono, Masato Okado

arxiv:math/0209082 v2 · 2002-09-08 · math.QA · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TGFX2XWTHJRKGVOF4QL2CHQX7Q}

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	2026-05-18T02:54:28.191810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

998b7d5ed33a62a355c5e417a11e17fc3fb34a00fdbc7c725ecdd7d4e0d0b813

Aliases

arxiv: math/0209082 · arxiv_version: math/0209082v2 · doi: 10.48550/arxiv.math/0209082 · pith_short_12: TGFX2XWTHJRK · pith_short_16: TGFX2XWTHJRKGVOF · pith_short_8: TGFX2XWT

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/TGFX2XWTHJRKGVOF4QL2CHQX7Q \
  | 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: 998b7d5ed33a62a355c5e417a11e17fc3fb34a00fdbc7c725ecdd7d4e0d0b813

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56608d0d55c9e9ac43ead99c94f48a19caf31351842dcc03a03eb7b520ec043f",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2002-09-08T10:05:54Z",
    "title_canon_sha256": "ba822d9cb7eefc187675f2e5b093770afb3ff67f36f080063f87771e5e7be0a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209082",
    "kind": "arxiv",
    "version": 2
  }
}