Pith Number

pith:TSCKQ7KS

pith:2011:TSCKQ7KSEJHAUQ6CPYTKFRKKOW

not attested not anchored not stored refs pending

Resonant delocalization for random Schr\"odinger operators on tree graphs

Michael Aizenman, Simone Warzel

arxiv:1104.0969 v3 · 2011-04-05 · 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{TSCKQ7KSEJHAUQ6CPYTKFRKKOW}

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	2026-05-18T03:19:11.921984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c84a87d52224e0a43c27e26a2c54a75a3a3ec5dea09d590c4e87c3f54d6e078

Aliases

arxiv: 1104.0969 · arxiv_version: 1104.0969v3 · doi: 10.48550/arxiv.1104.0969 · pith_short_12: TSCKQ7KSEJHA · pith_short_16: TSCKQ7KSEJHAUQ6C · pith_short_8: TSCKQ7KS

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/TSCKQ7KSEJHAUQ6CPYTKFRKKOW \
  | 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: 9c84a87d52224e0a43c27e26a2c54a75a3a3ec5dea09d590c4e87c3f54d6e078

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b24d34e97d40c4aefb5838db1d424ce46c8768eedf346263b4d9be8293a0cf9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-04-05T22:00:49Z",
    "title_canon_sha256": "2318fb48fe9c81df0e194745e9754db2a53721043872686fe333432f6dbc2a6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0969",
    "kind": "arxiv",
    "version": 3
  }
}