Pith Number

pith:6DWBNQK6

pith:2025:6DWBNQK6JNJGK5MYG5ECEVK6SD

not attested not anchored not stored refs pending

Spectral Barron spaces of vector-valued functions on compact groups

Isiaka Aremua, Yaogan Mensah

arxiv:2512.12382 v3 · 2025-12-13 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6DWBNQK6JNJGK5MYG5ECEVK6SD}

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	2026-05-22T01:03:16.444096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0ec16c15e4b52657598374822555e90f39cd8c7fc61ef2547ab2eb5576573b6

Aliases

arxiv: 2512.12382 · arxiv_version: 2512.12382v3 · doi: 10.48550/arxiv.2512.12382 · pith_short_12: 6DWBNQK6JNJG · pith_short_16: 6DWBNQK6JNJGK5MY · pith_short_8: 6DWBNQK6

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/6DWBNQK6JNJGK5MYG5ECEVK6SD \
  | 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: f0ec16c15e4b52657598374822555e90f39cd8c7fc61ef2547ab2eb5576573b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45c7294af80a43700fd9e21cb99e4750e57d8cb1d3bf92ed0602b8edb36e03fa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-12-13T16:17:32Z",
    "title_canon_sha256": "200328845b5b4ea95f2279ac6afb69b68ef4423bd5c2c6fd03dfd1c839307d38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12382",
    "kind": "arxiv",
    "version": 3
  }
}