Pith Number

pith:SZXTEM4V

pith:2026:SZXTEM4VIUWVQBTT7LFY4RQRPL

not attested not anchored not stored refs pending

A Quadratic Lower Bound for Noncommutative Circuits

Pratik Shastri

Every fan-in 2 noncommutative arithmetic circuit for the palindrome polynomial requires size Omega of n squared.

arxiv:2604.20575 v3 · 2026-04-22 · cs.CC

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SZXTEM4VIUWVQBTT7LFY4RQRPL}

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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.

Claims

C1strongest claim

every fan-in 2 noncommutative arithmetic circuit computing the palindrome polynomial has size Ω(n^2)

C2weakest assumption

The proof relies on refining techniques from the author's prior work; without the full text the precise load-bearing assumptions in the refinement step cannot be identified.

C3one line summary

Every fan-in 2 noncommutative arithmetic circuit computing the palindrome polynomial has size Ω(n²).

Receipt and verification

First computed	2026-05-20T01:04:30.543681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

966f323395452d580673facb8e46117ac956794376765c35a9ecb02fc5ab47f7

Aliases

arxiv: 2604.20575 · arxiv_version: 2604.20575v3 · doi: 10.48550/arxiv.2604.20575 · pith_short_12: SZXTEM4VIUWV · pith_short_16: SZXTEM4VIUWVQBTT · pith_short_8: SZXTEM4V

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/SZXTEM4VIUWVQBTT7LFY4RQRPL \
  | 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: 966f323395452d580673facb8e46117ac956794376765c35a9ecb02fc5ab47f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "134bb6ee22375244ff5c011179820a87cbe0e49439aa0608415d18c96e18b5ab",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-04-22T13:55:01Z",
    "title_canon_sha256": "deb285c1e2158ffa4bac66a8f676b682971b6f9dde02def7c9f3996d69f95abf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20575",
    "kind": "arxiv",
    "version": 3
  }
}