Pith Number

pith:WIDKC5QP

pith:2015:WIDKC5QPF4HEKZRP3SVD5JDS5K

not attested not anchored not stored refs pending

Quantum groups, quantum tori, and the Grothendieck-Springer resolution

Alexander Shapiro, Gus Schrader

arxiv:1508.07057 v3 · 2015-08-28 · math.QA · math-ph · math.MP · 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{WIDKC5QPF4HEKZRP3SVD5JDS5K}

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	2026-05-18T00:52:29.458414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b206a1760f2f0e45662fdcaa3ea472eaa99289b32bba1f263593103bcd6808d5

Aliases

arxiv: 1508.07057 · arxiv_version: 1508.07057v3 · doi: 10.48550/arxiv.1508.07057 · pith_short_12: WIDKC5QPF4HE · pith_short_16: WIDKC5QPF4HEKZRP · pith_short_8: WIDKC5QP

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/WIDKC5QPF4HEKZRP3SVD5JDS5K \
  | 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: b206a1760f2f0e45662fdcaa3ea472eaa99289b32bba1f263593103bcd6808d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9e45f637bc75495c1a8e664641431a9f4045d83101a53a9ab37f558df30cb28",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-08-28T00:09:46Z",
    "title_canon_sha256": "528fe2c2f5a3afbb0b8b7b1d521bebfedb615997d9e2438037210e9ee62e3cf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07057",
    "kind": "arxiv",
    "version": 3
  }
}