Pith Number

pith:LTP6YF3R

pith:2026:LTP6YF3RVUXPULW2GSXZ7TQGO4

not attested not anchored not stored refs pending

Commuting Graph of Unitriangular Group UT(4; p)

Miseriya Majeed, Ramkumar P.B

arxiv:2608.09235 v1 · 2026-08-10 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LTP6YF3RVUXPULW2GSXZ7TQGO4}

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	2026-08-11T02:22:08.662343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cdfec1771ad2efa2eda34af9fce06770fc2f806ea94439e12d486efe4598a79

Aliases

arxiv: 2608.09235 · arxiv_version: 2608.09235v1 · doi: 10.48550/arxiv.2608.09235 · pith_short_12: LTP6YF3RVUXP · pith_short_16: LTP6YF3RVUXPULW2 · pith_short_8: LTP6YF3R

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/LTP6YF3RVUXPULW2GSXZ7TQGO4 \
  | 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: 5cdfec1771ad2efa2eda34af9fce06770fc2f806ea94439e12d486efe4598a79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff84f7cb1c149b0021f1c5b1691288cb4aad2a39adda91f9c0ced6fb8d832206",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-08-10T07:59:09Z",
    "title_canon_sha256": "dbc784e5d5d1ebe693c7346bcdbb2dd9f38844fd4440524e17480802c4f20591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09235",
    "kind": "arxiv",
    "version": 1
  }
}