Pith Number

pith:3GVV6V56

pith:2013:3GVV6V56BJWPHO3HV64M2UDP4X

not attested not anchored not stored refs pending

A lower bound for the Lyapounov exponents of the random Schrodinger operator on a strip

Jean Bourgain

arxiv:1305.0176 v1 · 2013-05-01 · 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{3GVV6V56BJWPHO3HV64M2UDP4X}

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	2026-05-18T01:50:13.658429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9ab5f57be0a6cf3bb67afb8cd506fe5fdf8f3c509968269a0c335700a6b923c

Aliases

arxiv: 1305.0176 · arxiv_version: 1305.0176v1 · doi: 10.48550/arxiv.1305.0176 · pith_short_12: 3GVV6V56BJWP · pith_short_16: 3GVV6V56BJWPHO3H · pith_short_8: 3GVV6V56

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/3GVV6V56BJWPHO3HV64M2UDP4X \
  | 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: d9ab5f57be0a6cf3bb67afb8cd506fe5fdf8f3c509968269a0c335700a6b923c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9509daf0876c671764bd96eff9b9fc22644bc3efa0b35f6394c7470b56ed8b57",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-05-01T14:11:10Z",
    "title_canon_sha256": "d6624c4d35ebd7277497481778b8cd96bbe99613e38c42ee55607e032c1bfa32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0176",
    "kind": "arxiv",
    "version": 1
  }
}