Pith Number

pith:MWRKB3CM

pith:2011:MWRKB3CM4ISYATXZENZ2GNVHGJ

not attested not anchored not stored refs pending

Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential

Boris Vainberg, Stanislav Molchanov, Yuri Godin

arxiv:1104.3150 v3 · 2011-04-15 · 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{MWRKB3CM4ISYATXZENZ2GNVHGJ}

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	2026-05-17T23:54:37.228048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65a2a0ec4ce225804ef92373a336a7326345ebde51d37fbedea5ea832a22aee9

Aliases

arxiv: 1104.3150 · arxiv_version: 1104.3150v3 · doi: 10.48550/arxiv.1104.3150 · pith_short_12: MWRKB3CM4ISY · pith_short_16: MWRKB3CM4ISYATXZ · pith_short_8: MWRKB3CM

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/MWRKB3CM4ISYATXZENZ2GNVHGJ \
  | 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: 65a2a0ec4ce225804ef92373a336a7326345ebde51d37fbedea5ea832a22aee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e07de4f8fcfa5264177dcdf4d0d2ac1801ba05ba13e570d24e432ce73046575",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-04-15T20:18:53Z",
    "title_canon_sha256": "eb0d7a59adf73b92dde3993db601911b8285f019a593e231cf80be6b3301a848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3150",
    "kind": "arxiv",
    "version": 3
  }
}