Pith Number

pith:MEPCKAWM

pith:2026:MEPCKAWMUBR5TPIBRE5XKGXXW2

not attested not anchored not stored refs pending

Near-Maximum Circuit Lower Bounds for Exponential Time with Merlin-Arthur Queries

Hanlin Ren, Ryan Williams

arxiv:2607.09963 v1 · 2026-07-10 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MEPCKAWMUBR5TPIBRE5XKGXXW2}

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	2026-07-14T00:18:45.059163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

611e2502cca063d9bd01893b751af7b6a7aeac34fc7ad1b6b7d5761ab1c26145

Aliases

arxiv: 2607.09963 · arxiv_version: 2607.09963v1 · doi: 10.48550/arxiv.2607.09963 · pith_short_12: MEPCKAWMUBR5 · pith_short_16: MEPCKAWMUBR5TPIB · pith_short_8: MEPCKAWM

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/MEPCKAWMUBR5TPIBRE5XKGXXW2 \
  | 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: 611e2502cca063d9bd01893b751af7b6a7aeac34fc7ad1b6b7d5761ab1c26145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47e9734049b956769bcd6e56ab5aeff08c219e58e5449d7aafc4ea8bf120fae2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-07-10T20:33:08Z",
    "title_canon_sha256": "2e27cee5114b4a9c03f360f6a671b625523d744ecc881295afa38d2537f17ebf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09963",
    "kind": "arxiv",
    "version": 1
  }
}