Pith Number

pith:6MLC343R

pith:2007:6MLC343RAR5JFMONX7O2EXJE5B

not attested not anchored not stored refs pending

Hopf Algebras and Congruence Subgroups

Yongchang Zhu, Yorck Sommerhaeuser

arxiv:0710.0705 v2 · 2007-10-03 · math.RA · hep-th · math-ph · math.MP · 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{6MLC343RAR5JFMONX7O2EXJE5B}

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	2026-05-18T03:46:49.596164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3162df371047a92b1cdbfdda25d24e878aeff87d5623fd747a12a64d07b9292

Aliases

arxiv: 0710.0705 · arxiv_version: 0710.0705v2 · doi: 10.48550/arxiv.0710.0705 · pith_short_12: 6MLC343RAR5J · pith_short_16: 6MLC343RAR5JFMON · pith_short_8: 6MLC343R

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/6MLC343RAR5JFMONX7O2EXJE5B \
  | 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: f3162df371047a92b1cdbfdda25d24e878aeff87d5623fd747a12a64d07b9292

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e0161ecf56d090a45fe44a594fe8d0db7f26b75d7aaf698d2e3b42e71e4158e",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "math.QA",
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2007-10-03T04:15:46Z",
    "title_canon_sha256": "f96b3ac84369292c12ce8d6832b24372d247c0f1a7b077e0b44a75f94230a8c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.0705",
    "kind": "arxiv",
    "version": 2
  }
}