Pith Number

pith:VMFCW2ZV

pith:2006:VMFCW2ZVXHKRNICDW7VFSJMQ2M

not attested not anchored not stored refs pending

Dobrushin states in the \phi^4_1 model

L. Bertini, P. Butt\`a, S. Brassesco

arxiv:math-ph/0611077 v1 · 2006-11-27 · 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{VMFCW2ZVXHKRNICDW7VFSJMQ2M}

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	2026-05-18T01:20:59.729172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab0a2b6b35b9d516a043b7ea592590d330a0572a5568863e76c077a5689d9b7b

Aliases

arxiv: math-ph/0611077 · arxiv_version: math-ph/0611077v1 · doi: 10.48550/arxiv.math-ph/0611077 · pith_short_12: VMFCW2ZVXHKR · pith_short_16: VMFCW2ZVXHKRNICD · pith_short_8: VMFCW2ZV

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/VMFCW2ZVXHKRNICDW7VFSJMQ2M \
  | 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: ab0a2b6b35b9d516a043b7ea592590d330a0572a5568863e76c077a5689d9b7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6581763fb34abfc30a989fbd6c9a01b80a6cbcc618f65a1ff75b688cb34c507b",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-11-27T18:05:47Z",
    "title_canon_sha256": "4754c53e1d6023a93f9fb80b8173edf81c2651e4d8ca594fde62861a82ef812d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0611077",
    "kind": "arxiv",
    "version": 1
  }
}