Pith Number

pith:5WIEWD4D

pith:2026:5WIEWD4D7ZSLULDGF7UM6W4MFH

not attested not anchored not stored refs pending

Partition Rank and Algebraic Circuit Lower Bounds

Cornelius Brand, Jiaheng Wang, Petteri Kaski

arxiv:2607.02241 v1 · 2026-07-02 · cs.CC · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5WIEWD4D7ZSLULDGF7UM6W4MFH}

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	2026-07-03T01:17:46.170670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed904b0f83fe64ba2c662fe8cf5b8c29c51cd2f342deb36e88389f449342186e

Aliases

arxiv: 2607.02241 · arxiv_version: 2607.02241v1 · doi: 10.48550/arxiv.2607.02241 · pith_short_12: 5WIEWD4D7ZSL · pith_short_16: 5WIEWD4D7ZSLULDG · pith_short_8: 5WIEWD4D

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/5WIEWD4D7ZSLULDGF7UM6W4MFH \
  | 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: ed904b0f83fe64ba2c662fe8cf5b8c29c51cd2f342deb36e88389f449342186e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1a32a8f6a7bf633af64a8358f46e1348b61cd0f5034d0bae3d996b21b1a8d02",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-07-02T14:37:35Z",
    "title_canon_sha256": "b9f68f6902d8bc6b9224b9d03cb6dd6f0f18309b41b5e0900bf8e996414a2a90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02241",
    "kind": "arxiv",
    "version": 1
  }
}