Pith Number

pith:FROTKTGO

pith:2021:FROTKTGOGBDDWX4RTYOWRU5C72

not attested not anchored not stored refs pending

Percolation and $O(1)$ loop model

Mikhail Khristoforov, Stanislav Smirnov

arxiv:2111.15612 v1 · 2021-11-30 · math.PR · math-ph · math.CV · 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{FROTKTGOGBDDWX4RTYOWRU5C72}

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

On loops in the complement to dimers

Receipt and verification

First computed	2026-07-05T03:36:28.080706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c5d354cce30463b5f919e1d68d3a2feaa873aecdbf7061578645a5b4ddb84d6

Aliases

arxiv: 2111.15612 · arxiv_version: 2111.15612v1 · doi: 10.48550/arxiv.2111.15612 · pith_short_12: FROTKTGOGBDD · pith_short_16: FROTKTGOGBDDWX4R · pith_short_8: FROTKTGO

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/FROTKTGOGBDDWX4RTYOWRU5C72 \
  | 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: 2c5d354cce30463b5f919e1d68d3a2feaa873aecdbf7061578645a5b4ddb84d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "589364fb13d5a36e3e3a7fab05723343de747489d530299cd790214b14db2cc8",
    "cross_cats_sorted": [
      "math-ph",
      "math.CV",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-11-30T18:03:19Z",
    "title_canon_sha256": "ae16651414bd3cc7549e13e41fda3c118b384375f390196097ae015e40a4a2b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.15612",
    "kind": "arxiv",
    "version": 1
  }
}