Pith Number

pith:S4G2NOAP

pith:2026:S4G2NOAPOTP4A4SKXX7KSGKBP4

not attested not anchored not stored refs pending

Phase transition for weakly interacting focusing Gibbs measures with harmonic potential

Damiano Greco, Yuzhao Wang

arxiv:2607.11608 v1 · 2026-07-13 · math.PR · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S4G2NOAPOTP4A4SKXX7KSGKBP4}

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	2026-07-14T02:22:14.723470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

970da6b80f74dfc0724abdfea919417f147f898e268091ed9b11bdc9e2f65226

Aliases

arxiv: 2607.11608 · arxiv_version: 2607.11608v1 · doi: 10.48550/arxiv.2607.11608 · pith_short_12: S4G2NOAPOTP4 · pith_short_16: S4G2NOAPOTP4A4SK · pith_short_8: S4G2NOAP

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/S4G2NOAPOTP4A4SKXX7KSGKBP4 \
  | 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: 970da6b80f74dfc0724abdfea919417f147f898e268091ed9b11bdc9e2f65226

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4fbc2bdaee154ea4afb842d05df9da5d838d85679af96a48b8c3a9c63e62e8c",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-13T14:30:06Z",
    "title_canon_sha256": "b0ab03e8b27510a27de6f3685b86c0a5a6f9b15d1df7fa54ed79e1e919ce82c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11608",
    "kind": "arxiv",
    "version": 1
  }
}