Pith Number

pith:PMBG4YP3

pith:2012:PMBG4YP32DJYRTOC2SZ7CCQXPG

not attested not anchored not stored refs pending

Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases

Toshiki Nakashima

arxiv:1203.2112 v1 · 2012-03-09 · 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{PMBG4YP32DJYRTOC2SZ7CCQXPG}

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	2026-05-18T04:00:27.490758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b026e61fbd0d388cdc2d4b3f10a17799fe1e727339d7236da1dc6da044a7560

Aliases

arxiv: 1203.2112 · arxiv_version: 1203.2112v1 · doi: 10.48550/arxiv.1203.2112 · pith_short_12: PMBG4YP32DJY · pith_short_16: PMBG4YP32DJYRTOC · pith_short_8: PMBG4YP3

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/PMBG4YP32DJYRTOC2SZ7CCQXPG \
  | 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: 7b026e61fbd0d388cdc2d4b3f10a17799fe1e727339d7236da1dc6da044a7560

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c6e4f745f1e4d10f868ca94b2e664ef294004dd51c65e005ef62733ea62e4bd",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-03-09T15:38:32Z",
    "title_canon_sha256": "ea50fdf8df4fc4f7641dde2eaeacba2da01fd61ab2dd450aeefe87b4020c9002"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2112",
    "kind": "arxiv",
    "version": 1
  }
}