Pith Number

pith:NQE2B647

pith:2010:NQE2B647KRWJDFJM37F5RYQBCD

not attested not anchored not stored refs pending

Optimally Sparse Frames

Andreas Heinecke, Felix Krahmer, Gitta Kutyniok, Peter G. Casazza

arxiv:1009.3663 v3 · 2010-09-19 · math.NA · cs.IT · math.FA · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NQE2B647KRWJDFJM37F5RYQBCD}

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	2026-05-18T04:19:12.313616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c09a0fb9f546c91952cdfcbd8e20110fe0cd29935dc23254cd1e8764e883841

Aliases

arxiv: 1009.3663 · arxiv_version: 1009.3663v3 · doi: 10.48550/arxiv.1009.3663 · pith_short_12: NQE2B647KRWJ · pith_short_16: NQE2B647KRWJDFJM · pith_short_8: NQE2B647

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/NQE2B647KRWJDFJM37F5RYQBCD \
  | 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: 6c09a0fb9f546c91952cdfcbd8e20110fe0cd29935dc23254cd1e8764e883841

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2998a1a377bab45e57677b43dfd67c8f35bb6aac4ab6a551d48d19e4be78fcb9",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2010-09-19T22:00:04Z",
    "title_canon_sha256": "28e64a56890083eb7139b85e31cc038995b9b0ffb3dd27dfc310c6ccf78a5974"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3663",
    "kind": "arxiv",
    "version": 3
  }
}