Pith Number

pith:BGMFFBJ5

pith:2015:BGMFFBJ5K45HDA22OCYPBRDDVI

not attested not anchored not stored refs pending

On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori

Ali Fathi, Masoud Khalkhali

arxiv:1504.01174 v1 · 2015-04-05 · math.QA · 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{BGMFFBJ5K45HDA22OCYPBRDDVI}

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	2026-05-18T02:19:34.997823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

099852853d573a71835a70b0f0c463aa355a2fe000ffe5f3b54362a921404804

Aliases

arxiv: 1504.01174 · arxiv_version: 1504.01174v1 · doi: 10.48550/arxiv.1504.01174 · pith_short_12: BGMFFBJ5K45H · pith_short_16: BGMFFBJ5K45HDA22 · pith_short_8: BGMFFBJ5

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/BGMFFBJ5K45HDA22OCYPBRDDVI \
  | 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: 099852853d573a71835a70b0f0c463aa355a2fe000ffe5f3b54362a921404804

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef6f90f118467271664b6c3ec651d35f3f18711f5d73c82a5dfc0c75fbcf8e7d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-04-05T23:53:02Z",
    "title_canon_sha256": "496a35c47fc54b69228dad1aa7cfbe44ba6976451f1bd8cfbddb4976ac448344"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01174",
    "kind": "arxiv",
    "version": 1
  }
}