Pith Number

pith:U5THHFNM

pith:2017:U5THHFNMWT5CS3KXGS6UZQZIAI

not attested not anchored not stored refs pending

Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency

Xiaoping Yuan, Yunfeng Shi

arxiv:1708.01762 v4 · 2017-08-05 · 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{U5THHFNMWT5CS3KXGS6UZQZIAI}

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	2026-05-18T00:27:00.346777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7667395acb4fa296d5734bd4cc3280224ce118a03802dbd321a20123cb40374

Aliases

arxiv: 1708.01762 · arxiv_version: 1708.01762v4 · doi: 10.48550/arxiv.1708.01762 · pith_short_12: U5THHFNMWT5C · pith_short_16: U5THHFNMWT5CS3KX · pith_short_8: U5THHFNM

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/U5THHFNMWT5CS3KXGS6UZQZIAI \
  | 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: a7667395acb4fa296d5734bd4cc3280224ce118a03802dbd321a20123cb40374

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "461e05419929aef4c725f2355bec8f58ba232a52be391c44edd71d115c3141ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2017-08-05T12:49:13Z",
    "title_canon_sha256": "a9762cd74e5b4a073f960eb4136d6e1d55dd0373e46a4d5f1857c1694f282608"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01762",
    "kind": "arxiv",
    "version": 4
  }
}