Pith Number

pith:73CKRXHD

pith:2025:73CKRXHDO24SRB2QLQ74OY5ON5

not attested not anchored not stored refs pending

Entropy numbers of classes defined by integral operators

V. Temlyakov

arxiv:2505.08572 v2 · 2025-05-13 · math.NA · cs.NA · 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{73CKRXHDO24SRB2QLQ74OY5ON5}

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	2026-07-05T11:35:55.927171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fec4a8dce376b92887505c3fc763ae6f515d9697c286a0330b777fa72bff1113

Aliases

arxiv: 2505.08572 · arxiv_version: 2505.08572v2 · doi: 10.48550/arxiv.2505.08572 · pith_short_12: 73CKRXHDO24S · pith_short_16: 73CKRXHDO24SRB2Q · pith_short_8: 73CKRXHD

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/73CKRXHDO24SRB2QLQ74OY5ON5 \
  | 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: fec4a8dce376b92887505c3fc763ae6f515d9697c286a0330b777fa72bff1113

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46ab8073d067ca7ca2971bd416c97b8bdfe53945f1078d271d2bcc3789bd6102",
    "cross_cats_sorted": [
      "cs.NA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-05-13T13:46:08Z",
    "title_canon_sha256": "f7a5a74d2cd79497253e4b3e1cfc97febf5653ab145a7efe9bc3af595f1c1ccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.08572",
    "kind": "arxiv",
    "version": 2
  }
}