Pith Number

pith:W4YS44XI

pith:2007:W4YS44XIZGBGOLHCCBDEILV4TP

not attested not anchored not stored refs pending

On the linear independence of spikes and sines

Joel A. Tropp

arxiv:0709.0517 v2 · 2007-09-04 · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4YS44XIZGBGOLHCCBDEILV4TP}

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	2026-05-18T02:53:16.133564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7312e72e8c982672ce21046442ebc9bea558247c74be6b256b45fe07dae5754

Aliases

arxiv: 0709.0517 · arxiv_version: 0709.0517v2 · doi: 10.48550/arxiv.0709.0517 · pith_short_12: W4YS44XIZGBG · pith_short_16: W4YS44XIZGBGOLHC · pith_short_8: W4YS44XI

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/W4YS44XIZGBGOLHCCBDEILV4TP \
  | 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: b7312e72e8c982672ce21046442ebc9bea558247c74be6b256b45fe07dae5754

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b58cd71f1b4503aae368b7a590bbc9890d4d1aad7119b1e02598deb11d64e0e2",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2007-09-04T19:48:10Z",
    "title_canon_sha256": "ec3c2b7e24213ba49fb8d1f313d0fd6f0259b0b2cc3e42607d00a0a7f4907518"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0517",
    "kind": "arxiv",
    "version": 2
  }
}