Pith Number

pith:44HA2ILP

pith:2013:44HA2ILP2ITEPHJKSKP3WITYQL

not attested not anchored not stored refs pending

Spectral Gaps of Almost Mathieu Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

arxiv:1311.0658 v1 · 2013-11-04 · 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{44HA2ILP2ITEPHJKSKP3WITYQL}

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	2026-05-18T00:17:55.685824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e70e0d216fd226479d2a929fbb227882d33789366941ae406c5745e7a85ce41d

Aliases

arxiv: 1311.0658 · arxiv_version: 1311.0658v1 · doi: 10.48550/arxiv.1311.0658 · pith_short_12: 44HA2ILP2ITE · pith_short_16: 44HA2ILP2ITEPHJK · pith_short_8: 44HA2ILP

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/44HA2ILP2ITEPHJKSKP3WITYQL \
  | 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: e70e0d216fd226479d2a929fbb227882d33789366941ae406c5745e7a85ce41d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "606ba99d0aeca628c7c1a56fb526c021ea34ebc8494517773b5100a97fcc467a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-11-04T12:00:07Z",
    "title_canon_sha256": "3140e759f3a6e1d1f290daf284809fcd70296f177a310c4554cafc1852c42bd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0658",
    "kind": "arxiv",
    "version": 1
  }
}