Pith Number

pith:M62LOXVU

pith:2018:M62LOXVU2TJLFHDX7SDKLSLF2L

not attested not anchored not stored refs pending

Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves

Jie Gu, Tin Sulejmanpasic, Yasuyuki Hatsuda, Zhihao Duan

arxiv:1806.11092 v2 · 2018-06-28 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M62LOXVU2TJLFHDX7SDKLSLF2L}

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.

Cited by

3 papers in Pith

Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics

Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence

Receipt and verification

First computed	2026-05-17T23:55:14.228348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67b4b75eb4d4d2b29c77fc86a5c965d2df460326400bab900f1cd93f2b107ef4

Aliases

arxiv: 1806.11092 · arxiv_version: 1806.11092v2 · doi: 10.48550/arxiv.1806.11092 · pith_short_12: M62LOXVU2TJL · pith_short_16: M62LOXVU2TJLFHDX · pith_short_8: M62LOXVU

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/M62LOXVU2TJLFHDX7SDKLSLF2L \
  | 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: 67b4b75eb4d4d2b29c77fc86a5c965d2df460326400bab900f1cd93f2b107ef4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b7223a8cc5cbcde6b5b2f2626842b5998b3b355f3ce271b86a7e865c54cc40f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2018-06-28T17:32:03Z",
    "title_canon_sha256": "d74db9f41ff075629f39b15a36e775997ca60c26378d0cc5cec128163634dcfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.11092",
    "kind": "arxiv",
    "version": 2
  }
}