Pith Number

pith:6G5LJUWO

pith:2015:6G5LJUWOBW3P3Y7KYFAKLNPQTZ

not attested not anchored not stored refs pending

The stable norm on the 2-torus at irrational directions

Jan Philipp Schr\"oder, Stefan Klempnauer

arxiv:1512.02447 v1 · 2015-12-08 · math.DS · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6G5LJUWOBW3P3Y7KYFAKLNPQTZ}

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	2026-05-18T01:24:44.663716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1bab4d2ce0db6fde3eac140a5b5f09e7538f5e64d459a430905614910b588ea

Aliases

arxiv: 1512.02447 · arxiv_version: 1512.02447v1 · doi: 10.48550/arxiv.1512.02447 · pith_short_12: 6G5LJUWOBW3P · pith_short_16: 6G5LJUWOBW3P3Y7K · pith_short_8: 6G5LJUWO

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/6G5LJUWOBW3P3Y7KYFAKLNPQTZ \
  | 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: f1bab4d2ce0db6fde3eac140a5b5f09e7538f5e64d459a430905614910b588ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0da7359d054d6ac0679abe2e0ffae84bc96a54ecf68e54a1abf8f97c95e88a71",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-12-08T13:07:37Z",
    "title_canon_sha256": "8b5a329abfb11f6faae0080fe0742d09df884650cd625f2b29ff60a9b28e0764"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02447",
    "kind": "arxiv",
    "version": 1
  }
}