Pith Number

pith:IMJ6YPCF

pith:2025:IMJ6YPCF5OC3KPNREDDDKHEEK5

not attested not anchored not stored refs pending

On Loops in critical high-dimensional percolation

Amelia Carpenter, Wendelin Werner

arxiv:2507.02676 v3 · 2025-07-03 · 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{IMJ6YPCF5OC3KPNREDDDKHEEK5}

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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

On reversing the Simon-Lieb inequality in high-dimensional percolation

Receipt and verification

First computed	2026-06-30T02:16:52.986301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4313ec3c45eb85b53db120c6351c845769c010c9620388197f1f179fefe2fe11

Aliases

arxiv: 2507.02676 · arxiv_version: 2507.02676v3 · doi: 10.48550/arxiv.2507.02676 · pith_short_12: IMJ6YPCF5OC3 · pith_short_16: IMJ6YPCF5OC3KPNR · pith_short_8: IMJ6YPCF

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/IMJ6YPCF5OC3KPNREDDDKHEEK5 \
  | 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: 4313ec3c45eb85b53db120c6351c845769c010c9620388197f1f179fefe2fe11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe78fcdc837051f4e74d28dc0d444fd3739f834bc2c2957c9947429da5ac6e6a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-03T14:38:47Z",
    "title_canon_sha256": "20e33ee82339da3e4c4be4100cec74fc2b0c408d91a6b4f9eb3c06ed95cc48f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02676",
    "kind": "arxiv",
    "version": 3
  }
}