Pith Number

pith:XIYZ6OIY

pith:2026:XIYZ6OIY5LAEEPWTKTW46VS56C

not attested not anchored not stored refs pending

The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups

Przemyslaw Musialski

arxiv:2606.20547 v1 · 2026-06-18 · cs.LG · cs.CV · cs.GR · cs.RO · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XIYZ6OIY5LAEEPWTKTW46VS56C}

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	2026-06-19T16:13:14.992950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba319f3918eac0423ed354edcf565df09f00551c3d212221aee6f1690fe61554

Aliases

arxiv: 2606.20547 · arxiv_version: 2606.20547v1 · doi: 10.48550/arxiv.2606.20547 · pith_short_12: XIYZ6OIY5LAE · pith_short_16: XIYZ6OIY5LAEEPWT · pith_short_8: XIYZ6OIY

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/XIYZ6OIY5LAEEPWTKTW46VS56C \
  | 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: ba319f3918eac0423ed354edcf565df09f00551c3d212221aee6f1690fe61554

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27588cb01691aecf6da0b2b5d8b13c27e540f064ff4898e080966c91b5660bcb",
    "cross_cats_sorted": [
      "cs.CV",
      "cs.GR",
      "cs.RO",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-18T17:56:17Z",
    "title_canon_sha256": "3d45ee421e48f2c38f795819b85b8722f0e61bf24a8ef8364f8d0ba1d039d583"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20547",
    "kind": "arxiv",
    "version": 1
  }
}