Pith Number

pith:SRH35XEW

pith:2026:SRH35XEW343MRY443SMZZW5DWY

not attested anchored not stored refs pending

A counterexample to the Kato conjecture for positive commutators

Paata Ivanisvili, Rupert L. Frank

arxiv:2608.07805 v1 · 2026-08-07 · math.FA · math-ph · math.MP · math.OA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SRH35XEW343MRY443SMZZW5DWY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

✓ Bitcoin timestamp 1 stamp

2026-08-11 04:46:05 · pending_bitcoin · .ots proof (pending)

verify this Bitcoin timestamp

Fastest: click any block number above. The block's timestamp on the public Bitcoin chain is your independent proof that the canonical hash 944fbedc96df36c8e39cdc99… existed by that time.

Rigorous: download the .ots proof and verify locally:

pip install opentimestamps-client
echo -n '944fbedc96df36c8e39cdc999cdba3b632ef3758565d5c9d9dc0039dbbfebaa1' | xxd -r -p > canon.bin
ots verify -f canon.bin pith_*.ots

Output Success! Bitcoin block N attests data existed as of T confirms the chain anchor.

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	2026-08-11T01:18:17.564803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

944fbedc96df36c8e39cdc999cdba3b632ef3758565d5c9d9dc0039dbbfebaa1

Aliases

arxiv: 2608.07805 · arxiv_version: 2608.07805v1 · doi: 10.48550/arxiv.2608.07805 · pith_short_12: SRH35XEW343M · pith_short_16: SRH35XEW343MRY44 · pith_short_8: SRH35XEW

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/SRH35XEW343MRY443SMZZW5DWY \
  | 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: 944fbedc96df36c8e39cdc999cdba3b632ef3758565d5c9d9dc0039dbbfebaa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64bee119b41bb72774e53c21884e6b05542a983654ff17ba88e25a2041bf092d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-07T23:03:56Z",
    "title_canon_sha256": "4d551ac6a4887233f99f3b2314c8ba84d374a266e2ded7a6ddb6a38632803799"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07805",
    "kind": "arxiv",
    "version": 1
  }
}