Pith Number

pith:TF4VLLQJ

pith:2013:TF4VLLQJ6GOWD673BFMB4AFCO6

not attested not anchored not stored refs pending

A numerical study of the window condition for Chern numbers of Hofstadter Butterflies

G. Yehoshua, J. E. Avron, O. Kenneth

arxiv:1308.3334 v4 · 2013-08-15 · 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{TF4VLLQJ6GOWD673BFMB4AFCO6}

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	2026-05-18T02:53:30.108439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

997955ae09f19d61fbfb09581e00a2778dc92bb166b07119e6b36d8b365f5979

Aliases

arxiv: 1308.3334 · arxiv_version: 1308.3334v4 · doi: 10.48550/arxiv.1308.3334 · pith_short_12: TF4VLLQJ6GOW · pith_short_16: TF4VLLQJ6GOWD673 · pith_short_8: TF4VLLQJ

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/TF4VLLQJ6GOWD673BFMB4AFCO6 \
  | 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: 997955ae09f19d61fbfb09581e00a2778dc92bb166b07119e6b36d8b365f5979

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0b4cf1381a25663a3ce2074c3ad4a0a0d9419b2dd865fa181dc31257edf415f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-08-15T08:11:42Z",
    "title_canon_sha256": "17662a023d45b4d71c75c697b3694b69af395947588db03632fc635dabd8ef5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3334",
    "kind": "arxiv",
    "version": 4
  }
}