Pith Number

pith:YQE4JR2N

pith:2011:YQE4JR2NMCJCAVQSCB7VIW43TL

not attested not anchored not stored refs pending

Gabor frames with rational density

Preben Gr{\aa}berg Nes, Yurii Lyubarskii

arxiv:1108.2684 v1 · 2011-08-12 · 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{YQE4JR2NMCJCAVQSCB7VIW43TL}

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	2026-05-18T04:15:36.418389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c409c4c74d6092205612107f545b9b9ac46c7292e270b3ca77361cf5d4c5c29c

Aliases

arxiv: 1108.2684 · arxiv_version: 1108.2684v1 · doi: 10.48550/arxiv.1108.2684 · pith_short_12: YQE4JR2NMCJC · pith_short_16: YQE4JR2NMCJCAVQS · pith_short_8: YQE4JR2N

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/YQE4JR2NMCJCAVQSCB7VIW43TL \
  | 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: c409c4c74d6092205612107f545b9b9ac46c7292e270b3ca77361cf5d4c5c29c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27273aa8e1e8eaa34d8bda0b9bbdcd6c03fca16c7526dece26ea1fc33e31f0bf",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-08-12T18:34:06Z",
    "title_canon_sha256": "53c15ce8cd578a5a4a0b441bd71ca5937da0b881ce5bd172b4ebcd3517afaf0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2684",
    "kind": "arxiv",
    "version": 1
  }
}