Pith Number

pith:E5P72U42

pith:2009:E5P72U42EFWV6ENL5HTBFQGU7E

not attested not anchored not stored refs pending

Dunkl operator and quantization of $\mathbb{Z}_2$-singularity

Gilles Halbout, Xiang Tang

arxiv:0908.4301 v2 · 2009-08-28 · math.QA · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E5P72U42EFWV6ENL5HTBFQGU7E}

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	2026-05-18T04:40:08.381876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

275ffd539a216d5f11abe9e612c0d4f905702bc2173cb40ab004c331263e2eab

Aliases

arxiv: 0908.4301 · arxiv_version: 0908.4301v2 · doi: 10.48550/arxiv.0908.4301 · pith_short_12: E5P72U42EFWV · pith_short_16: E5P72U42EFWV6ENL · pith_short_8: E5P72U42

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/E5P72U42EFWV6ENL5HTBFQGU7E \
  | 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: 275ffd539a216d5f11abe9e612c0d4f905702bc2173cb40ab004c331263e2eab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdbcd050cd5b0964a0e150f714a9f88bf85e0b1ad62a60b96230c136e0b372c9",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-08-28T22:32:46Z",
    "title_canon_sha256": "73c535963b63e422edc102e3a8696dbcaf9df332526838492ef9a47a8a7ff42d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.4301",
    "kind": "arxiv",
    "version": 2
  }
}