Pith Number

pith:ZBVTWA64

pith:2026:ZBVTWA64UTU6MS36HXPWMQ7FBJ

not attested not anchored not stored refs pending

A recursive butterfly factorization with optimality guarantees

Christopher Musco, David Persson, Diana Halikias, Paul G. Beckman, Tyler Chen

arxiv:2607.29361 v1 · 2026-07-31 · math.NA · cs.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{ZBVTWA64UTU6MS36HXPWMQ7FBJ}

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	2026-08-03T01:33:16.149211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c86b3b03dca4e9e64b7e3ddf6643e50a5cdbdf6c6bc19b31fc4deb2489554e11

Aliases

arxiv: 2607.29361 · arxiv_version: 2607.29361v1 · doi: 10.48550/arxiv.2607.29361 · pith_short_12: ZBVTWA64UTU6 · pith_short_16: ZBVTWA64UTU6MS36 · pith_short_8: ZBVTWA64

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/ZBVTWA64UTU6MS36HXPWMQ7FBJ \
  | 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: c86b3b03dca4e9e64b7e3ddf6643e50a5cdbdf6c6bc19b31fc4deb2489554e11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d2b75d8505339de025b1bf81469ae503d5e1c43a5a4c75092ace95a600ef67d",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-31T12:49:16Z",
    "title_canon_sha256": "e58967374f97a337c7d9705b43d8b855d22517e44212f366275150fb1c589751"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29361",
    "kind": "arxiv",
    "version": 1
  }
}