Pith Number

pith:KN7YIHQS

pith:2021:KN7YIHQS2ISXZWDEMWR2UP2Q7Q

not attested not anchored not stored refs pending

A geometric perspective on the scaling limits of critical Ising and $\varphi^4_d$ models

Michael Aizenman

arxiv:2112.04248 v3 · 2021-12-08 · math-ph · cond-mat.stat-mech · hep-th · 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{KN7YIHQS2ISXZWDEMWR2UP2Q7Q}

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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

The supercritical phase of the $\varphi^4$ model is well behaved

Receipt and verification

First computed	2026-07-05T05:02:40.052883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

537f841e12d2257cd86465a3aa3f50fc2ad152fd80ebe93bed61a8a62b031467

Aliases

arxiv: 2112.04248 · arxiv_version: 2112.04248v3 · doi: 10.48550/arxiv.2112.04248 · pith_short_12: KN7YIHQS2ISX · pith_short_16: KN7YIHQS2ISXZWDE · pith_short_8: KN7YIHQS

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/KN7YIHQS2ISXZWDEMWR2UP2Q7Q \
  | 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: 537f841e12d2257cd86465a3aa3f50fc2ad152fd80ebe93bed61a8a62b031467

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87524f2aabebc3dd2dea961735a29be47c3f8d36d64bfaa03c819c8e9ddfb384",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "hep-th",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2021-12-08T11:49:22Z",
    "title_canon_sha256": "7c44da81fd7d215a141c3a07bb125faf1152e199e48e2338a28e06dc63842c32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.04248",
    "kind": "arxiv",
    "version": 3
  }
}