Pith Number

pith:ID57PCWP

pith:2007:ID57PCWPHGOWAELTAVFBSL2QEQ

not attested not anchored not stored refs pending

Lectures on two-dimensional critical percolation

Wendelin Werner

arxiv:0710.0856 v3 · 2007-10-03 · 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{ID57PCWPHGOWAELTAVFBSL2QEQ}

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	2026-05-18T00:40:08.916325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40fbf78acf399d601173054a192f50243d97791c042bc7fb002a64145a6d971c

Aliases

arxiv: 0710.0856 · arxiv_version: 0710.0856v3 · doi: 10.48550/arxiv.0710.0856 · pith_short_12: ID57PCWPHGOW · pith_short_16: ID57PCWPHGOWAELT · pith_short_8: ID57PCWP

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/ID57PCWPHGOWAELTAVFBSL2QEQ \
  | 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: 40fbf78acf399d601173054a192f50243d97791c042bc7fb002a64145a6d971c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55d91644a12b9d3e9e0c30d3ed6243ab10fae71aabb74085db457d1495600b74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-10-03T18:06:51Z",
    "title_canon_sha256": "9cd9712961894d1afc79cf19f39c9a487963998ffe055c2de09b09047e45a75d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.0856",
    "kind": "arxiv",
    "version": 3
  }
}