Pith Number

pith:UVALQKQT

pith:2026:UVALQKQTE6C62JYOGOT5TTADKX

not attested not anchored not stored refs pending

A phase transition in the exactness of the NPA hierarchy at the critical doubly-tilted CHSH functional

Anton Pakhunov

arxiv:2607.13774 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{UVALQKQTE6C62JYOGOT5TTADKX}

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	2026-07-16T01:23:05.902567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a540b82a132785ed270e33a7d9cc0355f379f92124cc26211610b567c274ea42

Aliases

arxiv: 2607.13774 · arxiv_version: 2607.13774v1 · doi: 10.48550/arxiv.2607.13774 · pith_short_12: UVALQKQTE6C6 · pith_short_16: UVALQKQTE6C62JYO · pith_short_8: UVALQKQT

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/UVALQKQTE6C62JYOGOT5TTADKX \
  | 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: a540b82a132785ed270e33a7d9cc0355f379f92124cc26211610b567c274ea42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dd48bf37c7a8b6bbb394e861e9b35cf8e83439228bca25330999cac320c7720",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-15T12:34:25Z",
    "title_canon_sha256": "f64fd537b36c0617a7da2d6d0af08105b22d1589ff55fd31bb13599d17be0438"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13774",
    "kind": "arxiv",
    "version": 1
  }
}