Pith Number

pith:A4UQ3U37

pith:2000:A4UQ3U37NRLQWEM2MT3HARQZRX

not attested not anchored not stored refs pending

On nonperturbative localization with quasi-periodic potential

Jean Bourgain, Michael Goldstein

arxiv:math-ph/0011053 v1 · 2000-11-01 · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A4UQ3U37NRLQWEM2MT3HARQZRX}

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	2026-05-18T01:05:32.116291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07290dd37f6c570b119a64f67046198dcf7cae68ca90fe1aa55f2942b0159063

Aliases

arxiv: math-ph/0011053 · arxiv_version: math-ph/0011053v1 · doi: 10.48550/arxiv.math-ph/0011053 · pith_short_12: A4UQ3U37NRLQ · pith_short_16: A4UQ3U37NRLQWEM2 · pith_short_8: A4UQ3U37

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/A4UQ3U37NRLQWEM2MT3HARQZRX \
  | 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: 07290dd37f6c570b119a64f67046198dcf7cae68ca90fe1aa55f2942b0159063

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49dac83c90b27e326b32ebc2c314b232230e9dc89800536cd6cea7d26d46dbef",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-11-01T00:00:00Z",
    "title_canon_sha256": "0ab08e5905f2d213ec2266804dc008352f6ae6a5dafc781cc3c45bdb36258a68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0011053",
    "kind": "arxiv",
    "version": 1
  }
}