Pith Number

pith:RWWIXXOX

pith:2026:RWWIXXOXOJGEM3EQX75NEKXMPJ

not attested not anchored not stored refs pending

The Switching Lemma shows what the Switching Lemma cannot prove: an unconditional natural-proofs barrier

Bruno Loff, Francesca Ugazio, Navid Talebanfard, Suhail Sherif

arxiv:2606.12631 v1 · 2026-06-10 · 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{RWWIXXOXOJGEM3EQX75NEKXMPJ}

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	2026-06-12T01:08:41.590751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dac8bddd7724c466c90bffad22aec7a6d502df2b02183ccbe725519a2d37819

Aliases

arxiv: 2606.12631 · arxiv_version: 2606.12631v1 · doi: 10.48550/arxiv.2606.12631 · pith_short_12: RWWIXXOXOJGE · pith_short_16: RWWIXXOXOJGEM3EQ · pith_short_8: RWWIXXOX

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/RWWIXXOXOJGEM3EQX75NEKXMPJ \
  | 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: 8dac8bddd7724c466c90bffad22aec7a6d502df2b02183ccbe725519a2d37819

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b770d7b071baa5bd278af649c5aeb8f85a8b63c980205efaa5446c86f9eb5d7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-06-10T19:38:26Z",
    "title_canon_sha256": "b5c0c8a6564d8a4ce06d42682d9ceef650ced8fa343e35ed2b579ad1bd943f61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12631",
    "kind": "arxiv",
    "version": 1
  }
}