Pith Number

pith:NO67SSTA

pith:2022:NO67SSTAFYPBGR3DBWMQPJTZY3

not attested not anchored not stored refs pending

The Spherical p+s Spin Glass At Zero Temperature

Antonio Auffinger, Yuxin Zhou

arxiv:2209.03866 v1 · 2022-09-08 · 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{NO67SSTAFYPBGR3DBWMQPJTZY3}

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.

Cited by

1 paper in Pith

Superposition of plane waves in high spatial dimensions: from landscape complexity to the deepest minimum value

Receipt and verification

First computed	2026-07-05T04:55:46.591380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bbdf94a602e1e1347630d9907a679c6f3e9c3bc6e06bc595d920f33f6dca821

Aliases

arxiv: 2209.03866 · arxiv_version: 2209.03866v1 · doi: 10.48550/arxiv.2209.03866 · pith_short_12: NO67SSTAFYPB · pith_short_16: NO67SSTAFYPBGR3D · pith_short_8: NO67SSTA

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/NO67SSTAFYPBGR3DBWMQPJTZY3 \
  | 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: 6bbdf94a602e1e1347630d9907a679c6f3e9c3bc6e06bc595d920f33f6dca821

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc6f4aed3724a390587c2e1311616e8fb046f712a441b8ecf06aa481d0fcfee8",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-09-08T15:08:26Z",
    "title_canon_sha256": "05e9fa4c06425080b51b3365a47fd07701770add4a482b5389e14180e06f2a31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.03866",
    "kind": "arxiv",
    "version": 1
  }
}