Pith Number

pith:X5GUYFJB

pith:2017:X5GUYFJBBVDS6S4KTRQIDNJKFA

not attested not anchored not stored refs pending

Rational Ringel-Hall algebras, Hall polynomials of affine type and Canonical bases

Guanglian Zhang

arxiv:1708.06758 v1 · 2017-08-22 · math.RT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X5GUYFJBBVDS6S4KTRQIDNJKFA}

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	2026-05-18T00:36:52.115822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf4d4c15210d472f4b8a9c6081b52a2810ae97d1077108e518abfbb7e843a4a4

Aliases

arxiv: 1708.06758 · arxiv_version: 1708.06758v1 · doi: 10.48550/arxiv.1708.06758 · pith_short_12: X5GUYFJBBVDS · pith_short_16: X5GUYFJBBVDS6S4K · pith_short_8: X5GUYFJB

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/X5GUYFJBBVDS6S4KTRQIDNJKFA \
  | 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: bf4d4c15210d472f4b8a9c6081b52a2810ae97d1077108e518abfbb7e843a4a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a2c9f9154bc5512ff61c40cee8cc23afa8b85545deba15180311d7a0e6346ad",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2017-08-22T11:39:05Z",
    "title_canon_sha256": "50dd9cb7d022f0a86dfc2f98c553d8182965e4dc552b326bdf57d1ad1d48a5d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.06758",
    "kind": "arxiv",
    "version": 1
  }
}