Pith Number

pith:GILE4ITU

pith:2010:GILE4ITUCZRXCX3RBMDOIKYTN4

not attested not anchored not stored refs pending

Hall Algebras as Hopf Objects

Christopher D. Walker

arxiv:1011.5446 v1 · 2010-11-24 · 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{GILE4ITUCZRXCX3RBMDOIKYTN4}

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	2026-05-18T04:34:47.290797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32164e22741663715f710b06e42b136f2c27b038c8683ad07c23bf842d162312

Aliases

arxiv: 1011.5446 · arxiv_version: 1011.5446v1 · doi: 10.48550/arxiv.1011.5446 · pith_short_12: GILE4ITUCZRX · pith_short_16: GILE4ITUCZRXCX3R · pith_short_8: GILE4ITU

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/GILE4ITUCZRXCX3RBMDOIKYTN4 \
  | 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: 32164e22741663715f710b06e42b136f2c27b038c8683ad07c23bf842d162312

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a31b867aa3eb048fb45f16b21b65075fb5ad850553bca1d94fb1a0548a189a84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-11-24T18:06:01Z",
    "title_canon_sha256": "8656aac7f52070982578b2a02d7e274c94cf57cae67f82846eb1531c5cc8d640"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5446",
    "kind": "arxiv",
    "version": 1
  }
}