Pith Number

pith:2CD7MQFJ

pith:2001:2CD7MQFJTCMPE53TARK3K3BCYV

not attested not anchored not stored refs pending

Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential

J. Bourgain, S. Jitomirskaya

arxiv:math-ph/0110040 v1 · 2001-10-31 · math-ph · math.DS · 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{2CD7MQFJTCMPE53TARK3K3BCYV}

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.

Cited by

1 paper in Pith

Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results

Receipt and verification

First computed	2026-07-04T14:33:40.571168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d087f640a99898f277730455b56c22c5458ebd7adb2c5a43b26252beded20667

Aliases

arxiv: math-ph/0110040 · arxiv_version: math-ph/0110040v1 · doi: 10.48550/arxiv.math-ph/0110040 · pith_short_12: 2CD7MQFJTCMP · pith_short_16: 2CD7MQFJTCMPE53T · pith_short_8: 2CD7MQFJ

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/2CD7MQFJTCMPE53TARK3K3BCYV \
  | 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: d087f640a99898f277730455b56c22c5458ebd7adb2c5a43b26252beded20667

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c8cfce9bb6ee3b5215ad6b2417b68932549b46bb24eb53ea6331a95bf784dbb",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2001-10-31T18:32:54Z",
    "title_canon_sha256": "d5cd029b682f8ea26914677edff1db7e299c6790fc61a55e9f1189df074a3664"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0110040",
    "kind": "arxiv",
    "version": 1
  }
}