Pith Number

pith:MSBBE7IJ

pith:2011:MSBBE7IJ2FUU2BRRDHZWAZD2HS

not attested not anchored not stored refs pending

Formal pseudodifferential operators and Witten's r-spin numbers

Hao Xu, Kefeng Liu, Ravi Vakil

arxiv:1112.4601 v1 · 2011-12-20 · math.AG · math-ph · 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{MSBBE7IJ2FUU2BRRDHZWAZD2HS}

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	2026-05-18T04:05:58.437627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6482127d09d1694d063119f360647a3c90946b92fcd0c838c3bb8e5d65e7c034

Aliases

arxiv: 1112.4601 · arxiv_version: 1112.4601v1 · doi: 10.48550/arxiv.1112.4601 · pith_short_12: MSBBE7IJ2FUU · pith_short_16: MSBBE7IJ2FUU2BRR · pith_short_8: MSBBE7IJ

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/MSBBE7IJ2FUU2BRRDHZWAZD2HS \
  | 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: 6482127d09d1694d063119f360647a3c90946b92fcd0c838c3bb8e5d65e7c034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "201f2f09132d44c490f712bf814074d6729707d69ed05a574ff34ee78827531d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-12-20T08:23:19Z",
    "title_canon_sha256": "4423d66914d29f30f1b245c806e00c676b1007e15791ed6ada27970b92a922c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4601",
    "kind": "arxiv",
    "version": 1
  }
}