Pith Number

pith:SM3SZV5U

pith:2024:SM3SZV5UOD7GCBSPSYZUFZLRGK

not attested not anchored not stored refs pending

Triviality proof for mean-field $\varphi_4^4$-theories

Christoph Kopper, Pierre Wang

arxiv:2407.01309 v3 · 2024-07-01 · 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{SM3SZV5UOD7GCBSPSYZUFZLRGK}

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

Triviality in a Non-Perturbative Second-Order Mean-Field Theory for $\phi^4_4$

Receipt and verification

First computed	2026-07-05T10:20:13.411768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93372cd7b470fe61064f963342e571328eeb4f7f8c8fc5d728c58ea30f33a004

Aliases

arxiv: 2407.01309 · arxiv_version: 2407.01309v3 · doi: 10.48550/arxiv.2407.01309 · pith_short_12: SM3SZV5UOD7G · pith_short_16: SM3SZV5UOD7GCBSP · pith_short_8: SM3SZV5U

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/SM3SZV5UOD7GCBSPSYZUFZLRGK \
  | 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: 93372cd7b470fe61064f963342e571328eeb4f7f8c8fc5d728c58ea30f33a004

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35155e004c30dc93088fe009d97bd54758de9554101b70845cb3e18834888053",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2024-07-01T14:16:55Z",
    "title_canon_sha256": "6213bf5c47e41ea8b2c693309c2cbd8f44122894c2f1126dacc28056b4aa4472"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.01309",
    "kind": "arxiv",
    "version": 3
  }
}