Pith Number

pith:XEUQOQ32

pith:2011:XEUQOQ32RAZKYS7FJL3IH7NZCE

not attested not anchored not stored refs pending

Crystals and D-modules

Dennis Gaitsgory, Nick Rozenblyum

arxiv:1111.2087 v4 · 2011-11-09 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XEUQOQ32RAZKYS7FJL3IH7NZCE}

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	2026-05-18T02:41:18.973514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b92907437a8832ac4be54af683fdb91108ffb22185760ab05a9513f0d86c7c2c

Aliases

arxiv: 1111.2087 · arxiv_version: 1111.2087v4 · doi: 10.48550/arxiv.1111.2087 · pith_short_12: XEUQOQ32RAZK · pith_short_16: XEUQOQ32RAZKYS7F · pith_short_8: XEUQOQ32

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/XEUQOQ32RAZKYS7FJL3IH7NZCE \
  | 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: b92907437a8832ac4be54af683fdb91108ffb22185760ab05a9513f0d86c7c2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02a4487bbb9606443e728864e0e4eeeaed67cc1f4603e6d1c5081b68139d2fbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-09T02:10:50Z",
    "title_canon_sha256": "9371ff3f6587fe034caf16e7cf7120103ff6a35a466f5bf4aca11f629c7fab59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2087",
    "kind": "arxiv",
    "version": 4
  }
}