Pith Number

pith:GRJ5XSCO

pith:2010:GRJ5XSCOY545DY4RLC2FHMIBTR

not attested not anchored not stored refs pending

Extended States in a Lifshitz Tail Regime for Random Schr\"odinger Operators on Trees

Michael Aizenman, Simone Warzel

arxiv:1010.2673 v3 · 2010-10-13 · cond-mat.dis-nn · math-ph · 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{GRJ5XSCOY545DY4RLC2FHMIBTR}

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.

Receipt and verification

First computed	2026-05-18T04:24:54.276174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3453dbc84ec779d1e39158b453b1019c67612a72ada945885e4c569a111f5c3c

Aliases

arxiv: 1010.2673 · arxiv_version: 1010.2673v3 · doi: 10.48550/arxiv.1010.2673 · pith_short_12: GRJ5XSCOY545 · pith_short_16: GRJ5XSCOY545DY4R · pith_short_8: GRJ5XSCO

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/GRJ5XSCOY545DY4RLC2FHMIBTR \
  | 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: 3453dbc84ec779d1e39158b453b1019c67612a72ada945885e4c569a111f5c3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c37b02b70645d3489844d78ac2b5f330487a3288add99cdb909945913d6d2de",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2010-10-13T14:41:34Z",
    "title_canon_sha256": "b613a8113a80cc55fd9da03c34e02cf253b79f56db8feaa53e2057332f8d0222"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2673",
    "kind": "arxiv",
    "version": 3
  }
}