Pith Number

pith:27D47RB2

pith:2016:27D47RB2PJ3DCPHTS6BVVI3AUW

not attested not anchored not stored refs pending

Hofstadter's Butterfly in Quantum Geometry

Hosho Katsura, Yasuyuki Hatsuda, Yuji Tachikawa

arxiv:1606.01894 v2 · 2016-06-06 · hep-th · cond-mat.mes-hall · cond-mat.stat-mech · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27D47RB2PJ3DCPHTS6BVVI3AUW}

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	2026-05-18T00:57:30.778721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7c7cfc43a7a76313cf397835aa360a5bfcca8a714f815f1a8239fcd9e60872e

Aliases

arxiv: 1606.01894 · arxiv_version: 1606.01894v2 · doi: 10.48550/arxiv.1606.01894 · pith_short_12: 27D47RB2PJ3D · pith_short_16: 27D47RB2PJ3DCPHT · pith_short_8: 27D47RB2

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/27D47RB2PJ3DCPHTS6BVVI3AUW \
  | 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: d7c7cfc43a7a76313cf397835aa360a5bfcca8a714f815f1a8239fcd9e60872e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "658f3dfbe904f369b5a35cc20a54ad95bf786b171809a76b741af0de92847b9e",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2016-06-06T20:00:01Z",
    "title_canon_sha256": "1afb5d55cd51e9b17aa08fcbbcabbcb5a26057d8270d0ec77dec38213156243a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01894",
    "kind": "arxiv",
    "version": 2
  }
}