Pith Number

pith:SJGEZP2Y

pith:2018:SJGEZP2YKCOAZFGQDM5IC7F7KL

not attested not anchored not stored refs pending

Critical two-point function for long-range models with power-law couplings: The marginal case for $d\ge d_c$

Akira Sakai, Lung-Chi Chen

arxiv:1808.06789 v3 · 2018-08-21 · 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{SJGEZP2YKCOAZFGQDM5IC7F7KL}

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	2026-05-17T23:50:24.346208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

924c4cbf58509c0c94d01b3a817cbf52e7516edb69603ab4469ffd102ee11293

Aliases

arxiv: 1808.06789 · arxiv_version: 1808.06789v3 · doi: 10.48550/arxiv.1808.06789 · pith_short_12: SJGEZP2YKCOA · pith_short_16: SJGEZP2YKCOAZFGQ · pith_short_8: SJGEZP2Y

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/SJGEZP2YKCOAZFGQDM5IC7F7KL \
  | 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: 924c4cbf58509c0c94d01b3a817cbf52e7516edb69603ab4469ffd102ee11293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e54a61c530b24ada827e953af24447f52fdcfd32c3cefb30f80687ed17857c4",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-08-21T07:13:31Z",
    "title_canon_sha256": "955ff88c76405a7105f436ee9b398cb94235ebf0878ec890c912e0ffa0519c58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.06789",
    "kind": "arxiv",
    "version": 3
  }
}