Pith Number

pith:LEA37XIW

pith:2015:LEA37XIWDJ57PKBWMG4XBVSHQ2

not attested not anchored not stored refs pending

Coupling and an application to level-set percolation of the Gaussian free field

Alain-Sol Sznitman

arxiv:1509.02251 v2 · 2015-09-08 · math.PR · 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{LEA37XIWDJ57PKBWMG4XBVSHQ2}

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	2026-05-18T01:15:38.635270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5901bfdd161a7bf7a83661b970d64786b3c3435316cf1f63d7f97c11455bd84e

Aliases

arxiv: 1509.02251 · arxiv_version: 1509.02251v2 · doi: 10.48550/arxiv.1509.02251 · pith_short_12: LEA37XIWDJ57 · pith_short_16: LEA37XIWDJ57PKBW · pith_short_8: LEA37XIW

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/LEA37XIWDJ57PKBWMG4XBVSHQ2 \
  | 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: 5901bfdd161a7bf7a83661b970d64786b3c3435316cf1f63d7f97c11455bd84e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b118edf8f97204ed1b01271038641838490ecb27a315edc3b253183426351d91",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-08T04:21:05Z",
    "title_canon_sha256": "7f26f573ee7861202eb9ba4bc5774fd627be2042ca8a457932f6721d193ac0c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02251",
    "kind": "arxiv",
    "version": 2
  }
}