Pith Number

pith:ACSMKTBH

pith:2011:ACSMKTBH7RFW47YMFOWARUKXSS

not attested not anchored not stored refs pending

Weyl's Law and Connes' Trace Theorem for Noncommutative Two Tori

Farzad Fathizadeh, Masoud Khalkhali

arxiv:1111.1358 v2 · 2011-11-05 · math.QA · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ACSMKTBH7RFW47YMFOWARUKXSS}

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	2026-05-18T01:59:44.829913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00a4c54c27fc4b6e7f0c2bac08d15794b6de228b0a589eaa8f7f01b2ec9f6ddc

Aliases

arxiv: 1111.1358 · arxiv_version: 1111.1358v2 · doi: 10.48550/arxiv.1111.1358 · pith_short_12: ACSMKTBH7RFW · pith_short_16: ACSMKTBH7RFW47YM · pith_short_8: ACSMKTBH

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/ACSMKTBH7RFW47YMFOWARUKXSS \
  | 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: 00a4c54c27fc4b6e7f0c2bac08d15794b6de228b0a589eaa8f7f01b2ec9f6ddc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46ee440531719aff90dedd00aba03ba970f4ef6b936ef1743ac33803ffd4b776",
    "cross_cats_sorted": [
      "math.DG",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-11-05T22:17:39Z",
    "title_canon_sha256": "edf76820084fb35334a6c2417564f73056e045e0b3f78ead8dbb6e1f7e800a5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1358",
    "kind": "arxiv",
    "version": 2
  }
}