Pith Number

pith:7ABUDN3Y

pith:2024:7ABUDN3YCXCISB4GRWVNVIUXU6

not attested not anchored not stored refs pending

Averaging operators on groups and Hopf algebras

Huhu Zhang, Xing Gao

arxiv:2412.11600 v3 · 2024-12-16 · math.RA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ABUDN3YCXCISB4GRWVNVIUXU6}

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	2026-07-05T10:53:50.112042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f80341b77815c48907868daadaa297a79829be0fbb2aa396346848d3b8dc9572

Aliases

arxiv: 2412.11600 · arxiv_version: 2412.11600v3 · doi: 10.48550/arxiv.2412.11600 · pith_short_12: 7ABUDN3YCXCI · pith_short_16: 7ABUDN3YCXCISB4G · pith_short_8: 7ABUDN3Y

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/7ABUDN3YCXCISB4GRWVNVIUXU6 \
  | 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: f80341b77815c48907868daadaa297a79829be0fbb2aa396346848d3b8dc9572

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "659f52af87851f2478a972784bf6d4c93ba2297832ebed1d58bc594c47d5bd12",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2024-12-16T09:38:24Z",
    "title_canon_sha256": "5c1be021612462a00a3b46e00798923024053d641582bca45f1002e76cd355d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11600",
    "kind": "arxiv",
    "version": 3
  }
}