Pith Number

pith:LO76PM2G

pith:2026:LO76PM2G34DJ5TOU2J5HNDNR5T

not attested not anchored not stored refs pending

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update

Maxim Rakhuba, Mikhail Solonko, Molozhavenko Alexander

arxiv:2608.06218 v1 · 2026-08-06 · math.OC · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LO76PM2G34DJ5TOU2J5HNDNR5T}

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	2026-08-07T01:40:58.496650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bbfe7b346df069ecdd4d27a768db1ecd0b9cc6de6bc1fd1532c3351af5fa4c6

Aliases

arxiv: 2608.06218 · arxiv_version: 2608.06218v1 · doi: 10.48550/arxiv.2608.06218 · pith_short_12: LO76PM2G34DJ · pith_short_16: LO76PM2G34DJ5TOU · pith_short_8: LO76PM2G

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/LO76PM2G34DJ5TOU2J5HNDNR5T \
  | 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: 5bbfe7b346df069ecdd4d27a768db1ecd0b9cc6de6bc1fd1532c3351af5fa4c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b01c0659d29dc7e5fceb89db523b47f8c60ae9a89e9d0ace9bd9ec972c25c0d",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-06T16:09:56Z",
    "title_canon_sha256": "1e67327fca74bde3feadc33f9f313e088b0a839cc79c488cbc491cc0f5b10b7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06218",
    "kind": "arxiv",
    "version": 1
  }
}