Pith Number

pith:FJJKBJJ6

pith:2000:FJJKBJJ66IHHVQCBGIFUXITWT2

not attested not anchored not stored refs pending

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

Robert Schrader, Vadim Kostrykin

arxiv:math-ph/0005017 v1 · 2000-05-15 · 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{FJJKBJJ66IHHVQCBGIFUXITWT2}

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	2026-07-04T14:33:35.493560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a52a0a53ef20e7ac041320b4ba2769e814600efa711b20bc9b6fffe059dfc84

Aliases

arxiv: math-ph/0005017 · arxiv_version: math-ph/0005017v1 · doi: 10.48550/arxiv.math-ph/0005017 · pith_short_12: FJJKBJJ66IHH · pith_short_16: FJJKBJJ66IHHVQCB · pith_short_8: FJJKBJJ6

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/FJJKBJJ66IHHVQCBGIFUXITWT2 \
  | 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: 2a52a0a53ef20e7ac041320b4ba2769e814600efa711b20bc9b6fffe059dfc84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b7ce41e242eb6ff026b55f3eb53cffc4ff4379c876843134cbc9438d56d309a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-05-15T21:03:52Z",
    "title_canon_sha256": "af4dd61087554f2948017b7ee72801362692ef34f6a6c212d4ee3c9db58b6a29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0005017",
    "kind": "arxiv",
    "version": 1
  }
}