Pith Number

pith:VFBWIXSN

pith:2021:VFBWIXSNSJKNTDXEQA6QUINZ4N

not attested not anchored not stored refs pending

Universality of Hofstadter butterflies on hyperbolic lattices

Alexander Stegmaier, Igor Boettcher, Lavi K. Upreti, Ronny Thomale

arxiv:2111.05779 v2 · 2021-11-10 · cond-mat.mes-hall · cond-mat.other · 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{VFBWIXSNSJKNTDXEQA6QUINZ4N}

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	2026-07-05T04:19:47.590071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a943645e4d9254d98ee4803d0a21b9e363f1485627733dd4db7c45eebd9be4f4

Aliases

arxiv: 2111.05779 · arxiv_version: 2111.05779v2 · doi: 10.48550/arxiv.2111.05779 · pith_short_12: VFBWIXSNSJKN · pith_short_16: VFBWIXSNSJKNTDXE · pith_short_8: VFBWIXSN

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/VFBWIXSNSJKNTDXEQA6QUINZ4N \
  | 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: a943645e4d9254d98ee4803d0a21b9e363f1485627733dd4db7c45eebd9be4f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dac17ad39ead9f69e092b7ab15915a0e3c079eb1a2bedf98d2ab27c4eaad0123",
    "cross_cats_sorted": [
      "cond-mat.other",
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2021-11-10T16:32:06Z",
    "title_canon_sha256": "8d20ed458b1e083cb51736eba71c2708dee63f72684d70f577856215eedd3d43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.05779",
    "kind": "arxiv",
    "version": 2
  }
}