Pith Number

pith:5L3E3V7D

pith:2013:5L3E3V7DM37X4IZHWXDU7GDPZI

not attested not anchored not stored refs pending

Systems of Differential Operators and Generalized Verma Modules

Toshihisa Kubo

arxiv:1304.1646 v5 · 2013-04-05 · 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{5L3E3V7DM37X4IZHWXDU7GDPZI}

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	2026-05-18T03:01:13.763898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaf64dd7e366ff7e2327b5c74f986fca04083c3204894637c53ec5bb2fb48fe0

Aliases

arxiv: 1304.1646 · arxiv_version: 1304.1646v5 · doi: 10.48550/arxiv.1304.1646 · pith_short_12: 5L3E3V7DM37X · pith_short_16: 5L3E3V7DM37X4IZH · pith_short_8: 5L3E3V7D

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/5L3E3V7DM37X4IZHWXDU7GDPZI \
  | 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: eaf64dd7e366ff7e2327b5c74f986fca04083c3204894637c53ec5bb2fb48fe0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50b2fea839b1fc650b2de4b4c4f19c55d470b8d9b1cf7a8243c08170a854ad68",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2013-04-05T08:58:45Z",
    "title_canon_sha256": "769158f38ae5d7d860c4589b0a7769e779218b8f4f0c913c742254948bf3e6fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1646",
    "kind": "arxiv",
    "version": 5
  }
}