Pith Number

pith:XPCHANJK

pith:2016:XPCHANJKFG3UVW6V5MFP66YSJ5

not attested not anchored not stored refs pending

On the entropy numbers of the mixed smoothness function classes

V. Temlyakov

arxiv:1602.08712 v1 · 2016-02-28 · math.NA · math.FA · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPCHANJKFG3UVW6V5MFP66YSJ5}

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	2026-05-18T01:19:52.126530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbc470352a29b74adbd5eb0aff7b124f4373580ae2e04bc0e384389216fcf4ec

Aliases

arxiv: 1602.08712 · arxiv_version: 1602.08712v1 · doi: 10.48550/arxiv.1602.08712 · pith_short_12: XPCHANJKFG3U · pith_short_16: XPCHANJKFG3UVW6V · pith_short_8: XPCHANJK

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/XPCHANJKFG3UVW6V5MFP66YSJ5 \
  | 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: bbc470352a29b74adbd5eb0aff7b124f4373580ae2e04bc0e384389216fcf4ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b4c04e698b97426b5ac344c6b67d6274f3ad8c70f3918430cabb468360e6cfb",
    "cross_cats_sorted": [
      "math.FA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-02-28T13:16:10Z",
    "title_canon_sha256": "1907a0285b17e3c668e634e9d0d525dc38c2a08639b2f337758cf78e02f78e6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08712",
    "kind": "arxiv",
    "version": 1
  }
}