Pith Number

pith:AQU2COE5

pith:2025:AQU2COE5HN5LRGQJHETS7HJC2L

not attested not anchored not stored refs pending

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping

Shihe Liu, Yunfeng Shi, Zhifei Zhang

arxiv:2508.12714 v1 · 2025-08-18 · math-ph · math.DS · math.MP · math.PR · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AQU2COE5HN5LRGQJHETS7HJC2L}

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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

Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$

Receipt and verification

First computed	2026-07-05T11:55:25.728002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0429a1389d3b7ab89a0939272f9d22d2e4293b991b9abe3d65f68fdccdc250b1

Aliases

arxiv: 2508.12714 · arxiv_version: 2508.12714v1 · doi: 10.48550/arxiv.2508.12714 · pith_short_12: AQU2COE5HN5L · pith_short_16: AQU2COE5HN5LRGQJ · pith_short_8: AQU2COE5

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/AQU2COE5HN5LRGQJHETS7HJC2L \
  | 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: 0429a1389d3b7ab89a0939272f9d22d2e4293b991b9abe3d65f68fdccdc250b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e6a159cbc1d241cc627ff3261d9f8c1c20cbdee47a1ad05e4f723f8bd744940",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.PR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-08-18T08:25:20Z",
    "title_canon_sha256": "dd95fe97a0aa5c1806977ade48defb3805542d8709dd85fb05a7bfb9ebd2394d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.12714",
    "kind": "arxiv",
    "version": 1
  }
}