Pith Number

pith:QJFN34FD

pith:2024:QJFN34FDQUJZR5HYE6PHY4PAOQ

not attested not anchored not stored refs pending

Percolation at the uniqueness threshold via subgroup relativization

Minghao Pan, Tom Hutchcroft

arxiv:2409.12283 v1 · 2024-09-18 · math.PR · math.GR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJFN34FDQUJZR5HYE6PHY4PAOQ}

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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

Dimension jump at the uniqueness threshold for percolation in $\infty+d$ dimensions

Receipt and verification

First computed	2026-07-05T09:08:51.072796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

824addf0a3851398f4f8279e7c71e07412154fdcefd858a74b516fbb39089ffd

Aliases

arxiv: 2409.12283 · arxiv_version: 2409.12283v1 · doi: 10.48550/arxiv.2409.12283 · pith_short_12: QJFN34FDQUJZ · pith_short_16: QJFN34FDQUJZR5HY · pith_short_8: QJFN34FD

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/QJFN34FDQUJZR5HYE6PHY4PAOQ \
  | 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: 824addf0a3851398f4f8279e7c71e07412154fdcefd858a74b516fbb39089ffd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16c1fe56a9ff55117341d05bf198048d11563e57e89e028a2f8e32539fbbee00",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-09-18T19:36:51Z",
    "title_canon_sha256": "74c3e85b0ab559d14f98494d8c5015a3516e4cda14d9029022251ef4677e6bdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.12283",
    "kind": "arxiv",
    "version": 1
  }
}