Pith Number

pith:7S7JQQ2N

pith:2026:7S7JQQ2NQEQSDNHMR7WGHAFA25

not attested not anchored not stored refs pending

On the Gardner Transition in the Ising Pure $p$-Spin Glass II

Yuxin Zhou

arxiv:2608.06523 v1 · 2026-08-06 · math.PR · math-ph · 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{7S7JQQ2NQEQSDNHMR7WGHAFA25}

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	2026-08-10T01:10:55.923898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcbe98434d812121b4ec8fec6380a0d7731fe51c9f0c17bf8fd5ab838e4cb667

Aliases

arxiv: 2608.06523 · arxiv_version: 2608.06523v1 · doi: 10.48550/arxiv.2608.06523 · pith_short_12: 7S7JQQ2NQEQS · pith_short_16: 7S7JQQ2NQEQSDNHM · pith_short_8: 7S7JQQ2N

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/7S7JQQ2NQEQSDNHMR7WGHAFA25 \
  | 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: fcbe98434d812121b4ec8fec6380a0d7731fe51c9f0c17bf8fd5ab838e4cb667

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9036d02991b7b554cded9245e2e34904eae3db8dc1e493da903de80afe08f32",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-06T19:08:04Z",
    "title_canon_sha256": "7cb7804c9530efd945b5c1ab8aba6416e10cd46414400a74bd61cdc8c2586953"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06523",
    "kind": "arxiv",
    "version": 1
  }
}