Pith Number

pith:PU4SQCD4

pith:2026:PU4SQCD4SSKB5YLXIYY7H6YOMB

not attested not anchored not stored refs pending

Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions

Hao Liang

arxiv:2607.23041 v1 · 2026-07-25 · 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{PU4SQCD4SSKB5YLXIYY7H6YOMB}

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	2026-07-28T00:22:09.024953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d3928087c94941ee1774631f3fb0e60563588bbaa5c0c9fdaa824f1ace8af06

Aliases

arxiv: 2607.23041 · arxiv_version: 2607.23041v1 · doi: 10.48550/arxiv.2607.23041 · pith_short_12: PU4SQCD4SSKB · pith_short_16: PU4SQCD4SSKB5YLX · pith_short_8: PU4SQCD4

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/PU4SQCD4SSKB5YLXIYY7H6YOMB \
  | 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: 7d3928087c94941ee1774631f3fb0e60563588bbaa5c0c9fdaa824f1ace8af06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1d2ec1f4b0ea52852a621fe7047860fe87aa1400eceb52f54d77a542cb8c3ab",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-25T04:52:58Z",
    "title_canon_sha256": "1e754643dc907dc771a1050cfdf186bfa36b4aac13991380d72612e5430a154d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23041",
    "kind": "arxiv",
    "version": 1
  }
}