Pith Number

pith:IBMFXDX6

pith:2024:IBMFXDX6RIFCEXV7T3NJ4NON4M

not attested not anchored not stored refs pending

Annulus crossing formulae for critical planar percolation

Shengjing Xu, Xin Sun, Zijie Zhuang

arxiv:2410.04767 v2 · 2024-10-07 · math.PR · math-ph · math.MP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBMFXDX6RIFCEXV7T3NJ4NON4M}

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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

Mixing rate exponent of planar Fortuin-Kasteleyn percolation

Receipt and verification

First computed	2026-07-05T10:11:25.306183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40585b8efe8a0a225ebf9eda9e35cde33fc09d847e8ff759547958c9727aaa15

Aliases

arxiv: 2410.04767 · arxiv_version: 2410.04767v2 · doi: 10.48550/arxiv.2410.04767 · pith_short_12: IBMFXDX6RIFC · pith_short_16: IBMFXDX6RIFCEXV7 · pith_short_8: IBMFXDX6

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/IBMFXDX6RIFCEXV7T3NJ4NON4M \
  | 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: 40585b8efe8a0a225ebf9eda9e35cde33fc09d847e8ff759547958c9727aaa15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83933bf5819cb6e893feed25b08076e5c31d92f24838785531483accff6a4183",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-10-07T05:49:34Z",
    "title_canon_sha256": "b47f5ced56d86b57fb048de76bb397959431390333c855a4f7e4fa991babac36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.04767",
    "kind": "arxiv",
    "version": 2
  }
}