Pith Number

pith:NAALTTC7

pith:2019:NAALTTC7NNXMLKHERDJM2N2FRA

not attested not anchored not stored refs pending

The Fourier transform on harmonic manifolds of purely exponential volume growth

Gerhard Knieper, Kingshook Biswas, Norbert Peyerimhoff

arxiv:1905.04112 v1 · 2019-05-08 · math.DG · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NAALTTC7NNXMLKHERDJM2N2FRA}

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	2026-05-17T23:46:34.519586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6800b9cc5f6b6ec5a8e488d2cd3745881be6df7476f0e23909a8bee5834cf580

Aliases

arxiv: 1905.04112 · arxiv_version: 1905.04112v1 · doi: 10.48550/arxiv.1905.04112 · pith_short_12: NAALTTC7NNXM · pith_short_16: NAALTTC7NNXMLKHE · pith_short_8: NAALTTC7

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/NAALTTC7NNXMLKHERDJM2N2FRA \
  | 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: 6800b9cc5f6b6ec5a8e488d2cd3745881be6df7476f0e23909a8bee5834cf580

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f004c8ba3f48273cb29a4a56da9e2a9791cf4ca321e4d27c0d95e170c41cf1e",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-05-08T19:07:47Z",
    "title_canon_sha256": "68b578d103d0a7cb4d7b97717a444d5076e3939f848464cf7624d23de6cdb15b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.04112",
    "kind": "arxiv",
    "version": 1
  }
}