Pith Number

pith:F3BR6US3

pith:2016:F3BR6US3S2QTUJQARETK4AZUSK

not attested not anchored not stored refs pending

Critical exponents for long-range O(n) models below the upper critical dimension

Gordon Slade

arxiv:1611.06169 v4 · 2016-11-18 · math-ph · 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{F3BR6US3S2QTUJQARETK4AZUSK}

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	2026-05-18T00:28:47.031224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ec31f525b96a13a26008926ae033492b3f6b3fb4bd6476a89f7ecf411f37654

Aliases

arxiv: 1611.06169 · arxiv_version: 1611.06169v4 · doi: 10.48550/arxiv.1611.06169 · pith_short_12: F3BR6US3S2QT · pith_short_16: F3BR6US3S2QTUJQA · pith_short_8: F3BR6US3

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/F3BR6US3S2QTUJQARETK4AZUSK \
  | 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: 2ec31f525b96a13a26008926ae033492b3f6b3fb4bd6476a89f7ecf411f37654

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "495e89052f939aa467fce288abdcede2aef2c18f6c3f9d220e599e601b1d5df1",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-11-18T17:34:32Z",
    "title_canon_sha256": "027d2bf62608d2540154d5d3129df0fdc9c036ce46d01dbe098ad7e6d0ff9a7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06169",
    "kind": "arxiv",
    "version": 4
  }
}