Pith Number

pith:FYDRTDDI

pith:2013:FYDRTDDIR7PSJFQZZBL5W64NR2

not attested not anchored not stored refs pending

Random Currents and Continuity of Ising Model's Spontaneous Magnetization

Hugo Duminil-Copin, Michael Aizenman, Vladas Sidoravicius

arxiv:1311.1937 v3 · 2013-11-08 · 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{FYDRTDDIR7PSJFQZZBL5W64NR2}

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	2026-05-18T00:34:58.282583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e07198c688fdf249619c857db7b8d8e8195166e19ad780e86cd24c11abe4733

Aliases

arxiv: 1311.1937 · arxiv_version: 1311.1937v3 · doi: 10.48550/arxiv.1311.1937 · pith_short_12: FYDRTDDIR7PS · pith_short_16: FYDRTDDIR7PSJFQZ · pith_short_8: FYDRTDDI

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/FYDRTDDIR7PSJFQZZBL5W64NR2 \
  | 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: 2e07198c688fdf249619c857db7b8d8e8195166e19ad780e86cd24c11abe4733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63d5c2b48083291ca9aa4f6e1d056445869608ddbdaa33e87d9582e1b32fbbfb",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-11-08T11:24:56Z",
    "title_canon_sha256": "d38fa3482ede31e4569b808e92ed20c924850ce8c819268325d2501fb5fb07c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1937",
    "kind": "arxiv",
    "version": 3
  }
}