Pith Number

pith:6P2PI3OJ

pith:2010:6P2PI3OJB3DLMEPPCA5ICBAQ7H

not attested not anchored not stored refs pending

The Sparsity Gap: Uncertainty Principles Proportional to Dimension

Joel A. Tropp

arxiv:1003.0415 v1 · 2010-03-01 · cs.IT · 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{6P2PI3OJB3DLMEPPCA5ICBAQ7H}

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	2026-05-18T00:57:57.882335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3f4f46dc90ec6b611ef103a810410f9d88b20b1c4b515d15d7a9422bc6abf32

Aliases

arxiv: 1003.0415 · arxiv_version: 1003.0415v1 · doi: 10.48550/arxiv.1003.0415 · pith_short_12: 6P2PI3OJB3DL · pith_short_16: 6P2PI3OJB3DLMEPP · pith_short_8: 6P2PI3OJ

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/6P2PI3OJB3DLMEPPCA5ICBAQ7H \
  | 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: f3f4f46dc90ec6b611ef103a810410f9d88b20b1c4b515d15d7a9422bc6abf32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "730bf0bbb615572be39088a2824e108521674e4842496c68d8cbe5205e971958",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2010-03-01T18:28:33Z",
    "title_canon_sha256": "e40473c9140a2e860fba4f451e5ee7ac9699644fd10687fcc6b1bacad91f6ac7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0415",
    "kind": "arxiv",
    "version": 1
  }
}