Pith Number

pith:EENOVKG7

pith:2018:EENOVKG7BCGHENOM5NHJZMFVQW

not attested not anchored not stored refs pending

Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator

Bernard Helffer, Qinghui Liu, Qi Zhou, Yanhui Qu

arxiv:1804.01658 v1 · 2018-04-05 · 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{EENOVKG7BCGHENOM5NHJZMFVQW}

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	2026-05-18T00:00:56.607344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

211aeaa8df088c7235cceb4e9cb0b585965eab6dc9987e06fa9b2288457f93a6

Aliases

arxiv: 1804.01658 · arxiv_version: 1804.01658v1 · doi: 10.48550/arxiv.1804.01658 · pith_short_12: EENOVKG7BCGH · pith_short_16: EENOVKG7BCGHENOM · pith_short_8: EENOVKG7

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/EENOVKG7BCGHENOM5NHJZMFVQW \
  | 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: 211aeaa8df088c7235cceb4e9cb0b585965eab6dc9987e06fa9b2288457f93a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dac1ded7f702ec52bee50082ff2cd2523c7691ff147df5096a3bc23824fa1dd6",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-04-05T03:00:31Z",
    "title_canon_sha256": "7f497331825fc99f02882f403023895a1eed9078d8d84f8111d9fca5f94f31fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.01658",
    "kind": "arxiv",
    "version": 1
  }
}