Pith Number

pith:QU4OIHYK

pith:2006:QU4OIHYKYBTAGVDDSO7C4ZWKRU

not attested not anchored not stored refs pending

Algebraic Structures on Grothendieck Groups of a Tower of Algebras

Huilan Li, Nantel Bergeron

arxiv:math/0612170 v1 · 2006-12-06 · math.RA · math.CO · 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{QU4OIHYKYBTAGVDDSO7C4ZWKRU}

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	2026-05-18T01:00:03.402530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8538e41f0ac06603546393be2e66ca8d18350c240f77430c893a73b7f4a5664c

Aliases

arxiv: math/0612170 · arxiv_version: math/0612170v1 · doi: 10.48550/arxiv.math/0612170 · pith_short_12: QU4OIHYKYBTA · pith_short_16: QU4OIHYKYBTAGVDD · pith_short_8: QU4OIHYK

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/QU4OIHYKYBTAGVDDSO7C4ZWKRU \
  | 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: 8538e41f0ac06603546393be2e66ca8d18350c240f77430c893a73b7f4a5664c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94273996ca0a74e56025d1b0e3014346ae9f74baeae33cdac90f83ab8532b811",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.RA",
    "submitted_at": "2006-12-06T21:59:05Z",
    "title_canon_sha256": "2ecd0a2f8f771203f7bfc1e6dad40ce0eae459fab3e18d83191af89f73aef912"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612170",
    "kind": "arxiv",
    "version": 1
  }
}