Pith Number

pith:37ODXGA3

pith:2013:37ODXGA3UNMUPCR5DTTSOIWYDL

not attested not anchored not stored refs pending

Spectra of sub-Dirac operators on certain nilmanifolds

Ines Kath, Oliver Ungermann

arxiv:1311.2418 v1 · 2013-11-11 · math.SP · 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{37ODXGA3UNMUPCR5DTTSOIWYDL}

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	2026-05-18T03:07:32.708257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfdc3b981ba359478a3d1ce72722d81acff704c5b05c82e5e1ac8af8a1b36483

Aliases

arxiv: 1311.2418 · arxiv_version: 1311.2418v1 · doi: 10.48550/arxiv.1311.2418 · pith_short_12: 37ODXGA3UNMU · pith_short_16: 37ODXGA3UNMUPCR5 · pith_short_8: 37ODXGA3

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/37ODXGA3UNMUPCR5DTTSOIWYDL \
  | 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: dfdc3b981ba359478a3d1ce72722d81acff704c5b05c82e5e1ac8af8a1b36483

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efbab12df07df4121997492eb8013e670c3abd21bbc181d9f1cb66f3b0af5f5f",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-11-11T11:19:45Z",
    "title_canon_sha256": "b992bab5206b9e9e1a9f4b62b01013dc19a3ca5a7c076643f87adb8c64e9e35e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2418",
    "kind": "arxiv",
    "version": 1
  }
}