Pith Number

pith:DECT55Q4

pith:2006:DECT55Q4Z5ZVDWGIKX6V74ATKR

not attested not anchored not stored refs pending

On a factorization of graded Hopf algebras using Lyndon words

I. Heckenberger, M. Gra\~na

arxiv:math/0608678 v1 · 2006-08-28 · 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{DECT55Q4Z5ZVDWGIKX6V74ATKR}

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	2026-05-18T01:05:22.574343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19053ef61ccf7351d8c855fd5ff01354508bb47f17785352f61c1203102b8262

Aliases

arxiv: math/0608678 · arxiv_version: math/0608678v1 · doi: 10.48550/arxiv.math/0608678 · pith_short_12: DECT55Q4Z5ZV · pith_short_16: DECT55Q4Z5ZVDWGI · pith_short_8: DECT55Q4

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/DECT55Q4Z5ZVDWGIKX6V74ATKR \
  | 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: 19053ef61ccf7351d8c855fd5ff01354508bb47f17785352f61c1203102b8262

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4627198c4710bb5b380d3013945c04b46ea770d217a57314a9294ac76c87b3e0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2006-08-28T08:38:59Z",
    "title_canon_sha256": "70672299c6e6106a423cff2477580f16e5f64569908cf5ab8b4668d5ea7abd67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608678",
    "kind": "arxiv",
    "version": 1
  }
}