Pith Number

pith:UGB22HAC

pith:2012:UGB22HACGPNPBADP3SPNBGVDF7

not attested not anchored not stored refs pending

Primitively generated Hall algebras

Arkady Berenstein, Jacob Greenstein

arxiv:1209.2770 v5 · 2012-09-13 · math.QA · 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{UGB22HACGPNPBADP3SPNBGVDF7}

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	2026-05-18T01:20:12.632950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a183ad1c0233daf0806fdc9ed09aa32ff4891e2f74eb551cb5cc05cb7b17ab2b

Aliases

arxiv: 1209.2770 · arxiv_version: 1209.2770v5 · doi: 10.48550/arxiv.1209.2770 · pith_short_12: UGB22HACGPNP · pith_short_16: UGB22HACGPNPBADP · pith_short_8: UGB22HAC

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/UGB22HACGPNPBADP3SPNBGVDF7 \
  | 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: a183ad1c0233daf0806fdc9ed09aa32ff4891e2f74eb551cb5cc05cb7b17ab2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51ee3039b955dfde3a970d432d6c861baa3e110790cc2d0f5bb1229d243a03de",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-09-13T03:15:07Z",
    "title_canon_sha256": "37f03d9a3adfc34e651cc08c7cb2c96dd926f0e3994e4cf9a5ff3ddad41f53de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2770",
    "kind": "arxiv",
    "version": 5
  }
}