Pith Number

pith:NM76Y7MQ

pith:2025:NM76Y7MQ7HQ2YTIEXDM3SZPJPK

not attested not anchored not stored refs pending

Optimal $L^p$-approximation of convex sets by convex subsets

Enrique Zuazua, Ilias Ftouhi, Zakaria Fattah

arxiv:2501.00928 v1 · 2025-01-01 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NM76Y7MQ7HQ2YTIEXDM3SZPJPK}

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	2026-07-05T09:56:12.036585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b3fec7d90f9e1ac4d04b8d9b965e97a9e2f208ce27f7c97d676b53f7b6b0271

Aliases

arxiv: 2501.00928 · arxiv_version: 2501.00928v1 · doi: 10.48550/arxiv.2501.00928 · pith_short_12: NM76Y7MQ7HQ2 · pith_short_16: NM76Y7MQ7HQ2YTIE · pith_short_8: NM76Y7MQ

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/NM76Y7MQ7HQ2YTIEXDM3SZPJPK \
  | 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: 6b3fec7d90f9e1ac4d04b8d9b965e97a9e2f208ce27f7c97d676b53f7b6b0271

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5f6d58e6de32efdfa8b7fc6f1fbda2e3069b4c34b9e09b472a0cdca9651348b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-01-01T19:02:53Z",
    "title_canon_sha256": "ec8a70b6b80f0b96781885f09550a6339e2afc76ee07281fba55bc8f22e6fb27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.00928",
    "kind": "arxiv",
    "version": 1
  }
}