Pith Number

pith:MHKR5NJY

pith:2015:MHKR5NJYR6KHPH25QYJRQWUHO5

not attested not anchored not stored refs pending

Bernstein components via Bernstein center

Alexander Braverman, David Kazhdan, Roman Bezrukavnikov

arxiv:1512.08637 v3 · 2015-12-29 · 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{MHKR5NJYR6KHPH25QYJRQWUHO5}

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	2026-05-18T00:03:34.618168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61d51eb5388f94779f5d8613185a8777534068e328d8a16a19ff9410d26130a3

Aliases

arxiv: 1512.08637 · arxiv_version: 1512.08637v3 · doi: 10.48550/arxiv.1512.08637 · pith_short_12: MHKR5NJYR6KH · pith_short_16: MHKR5NJYR6KHPH25 · pith_short_8: MHKR5NJY

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/MHKR5NJYR6KHPH25QYJRQWUHO5 \
  | 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: 61d51eb5388f94779f5d8613185a8777534068e328d8a16a19ff9410d26130a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06e337ff51ee3fcb67d277bec4c7131bd835a261a4f4f990cbe5f9f49eac0b89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-12-29T09:50:15Z",
    "title_canon_sha256": "34d4b59c311baa2ba39e6ae0cabaf0465d401b118efc54359eac4347745050ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08637",
    "kind": "arxiv",
    "version": 3
  }
}