Pith Number

pith:T6Y57QRN

pith:2026:T6Y57QRNF2AKQ3O3KBJB7QQUHI

not attested not anchored not stored refs pending

Derivation of the focusing $\Phi^6_1$ measure in the optimal mass regime from many-body quantum Gibbs states

Lin L\"u, Phan Th\`anh Nam, Rongchan Zhu

arxiv:2605.25755 v1 · 2026-05-25 · math-ph · math.AP · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T6Y57QRNF2AKQ3O3KBJB7QQUHI}

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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	2026-05-26T02:04:53.417521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fb1dfc22d2e80a86ddb50521fc2143a338d4347632fdae73169e74788ef37d8

Aliases

arxiv: 2605.25755 · arxiv_version: 2605.25755v1 · doi: 10.48550/arxiv.2605.25755 · pith_short_12: T6Y57QRNF2AK · pith_short_16: T6Y57QRNF2AKQ3O3 · pith_short_8: T6Y57QRN

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/T6Y57QRNF2AKQ3O3KBJB7QQUHI \
  | 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: 9fb1dfc22d2e80a86ddb50521fc2143a338d4347632fdae73169e74788ef37d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "376e3f89fa6344bc9563a084c82baaff47290d12cab55b5ff902d039390f36dc",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-25T12:07:10Z",
    "title_canon_sha256": "eec6aea061d76fd9e2c96c199ab3c6d0816e1310ec117db4fd9c6e68e6ded83a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25755",
    "kind": "arxiv",
    "version": 1
  }
}