Pith Number

pith:3QQHL6GS

pith:2009:3QQHL6GSZB56VKGYFJ7KFIL4PC

not attested not anchored not stored refs pending

Opening Gaps in the Spectrum of Strictly Ergodic Schr\"odinger Operators

Artur Avila, David Damanik, Jairo Bochi

arxiv:0903.2281 v1 · 2009-03-12 · math.DS · 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{3QQHL6GSZB56VKGYFJ7KFIL4PC}

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	2026-05-18T02:30:16.177301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc2075f8d2c87beaa8d82a7ea2a17c7880fccf143d6ac44e8aefb3c2488c5894

Aliases

arxiv: 0903.2281 · arxiv_version: 0903.2281v1 · doi: 10.48550/arxiv.0903.2281 · pith_short_12: 3QQHL6GSZB56 · pith_short_16: 3QQHL6GSZB56VKGY · pith_short_8: 3QQHL6GS

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/3QQHL6GSZB56VKGYFJ7KFIL4PC \
  | 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: dc2075f8d2c87beaa8d82a7ea2a17c7880fccf143d6ac44e8aefb3c2488c5894

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5aa1e5e48182a3cacf0af816e4d66700e119231fc5b635e5ecad745bc72a308d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-03-12T21:52:55Z",
    "title_canon_sha256": "9ab1cfac4141f59a088f73c14b520e964d9bf4fb83433bb17ef1452b6b6d00bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2281",
    "kind": "arxiv",
    "version": 1
  }
}