Pith Number

pith:47XFWXSY

pith:2011:47XFWXSYFBNKOMI2GFTIDOXWAL

not attested not anchored not stored refs pending

The deformation theory of sheaves of commutative rings

Jonathan Wise

arxiv:1101.4069 v3 · 2011-01-21 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{47XFWXSYFBNKOMI2GFTIDOXWAL}

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	2026-05-18T04:18:33.099697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7ee5b5e58285aa7311a316681baf602faeb142291736149c6b3522eb0db4795

Aliases

arxiv: 1101.4069 · arxiv_version: 1101.4069v3 · doi: 10.48550/arxiv.1101.4069 · pith_short_12: 47XFWXSYFBNK · pith_short_16: 47XFWXSYFBNKOMI2 · pith_short_8: 47XFWXSY

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/47XFWXSYFBNKOMI2GFTIDOXWAL \
  | 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: e7ee5b5e58285aa7311a316681baf602faeb142291736149c6b3522eb0db4795

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "821725c9aa834bd806284b5fa688e6526fbd315d7ffb7a58b5a0e736567b97a3",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-01-21T04:21:52Z",
    "title_canon_sha256": "e104c5ab3c90cee6e941f084f6ad5481c2a2b48ac7d017c353f60174b0fb7b06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4069",
    "kind": "arxiv",
    "version": 3
  }
}