Pith Number

pith:ZTRKLHYK

pith:2026:ZTRKLHYKEBHGYWK3BZQMPYCZYY

not attested not anchored not stored refs pending

No finite level of the NPA hierarchy is exact for the doubly-tilted CHSH functional near the critical tilt

Anton Pakhunov

arxiv:2607.13762 v1 · 2026-07-15 · quant-ph · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTRKLHYKEBHGYWK3BZQMPYCZYY}

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	2026-07-16T01:23:05.047412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca

Aliases

arxiv: 2607.13762 · arxiv_version: 2607.13762v1 · doi: 10.48550/arxiv.2607.13762 · pith_short_12: ZTRKLHYKEBHG · pith_short_16: ZTRKLHYKEBHGYWK3 · pith_short_8: ZTRKLHYK

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/ZTRKLHYKEBHGYWK3BZQMPYCZYY \
  | 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: cce2a59f0a204e6c595b0e60c7e059c634e2e0183e9efd43505578abe274d3ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5f928d3ba63fbecbd3054e9804c3d89a3d9b892cab28b00c8f475195ad18f6a",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-15T12:22:23Z",
    "title_canon_sha256": "af582919be2528511f322c8b1ee8037242dc2b2d169a2ac3023d9d4226aed06e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13762",
    "kind": "arxiv",
    "version": 1
  }
}