Pith Number

pith:6X76W7WR

pith:2026:6X76W7WRZT5EDCTDAJ7IJHKOD5

not attested not anchored not stored refs pending

Full Gabor frames, its existence problem, and a non-uniform Balian-Low type theorem

Rui Liu, Xin Ma, Yuxuan Zheng

arxiv:2606.19800 v1 · 2026-06-18 · math.FA · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6X76W7WRZT5EDCTDAJ7IJHKOD5}

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	2026-06-19T16:12:35.610868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5ffeb7ed1ccfa418a63027e849d4e1f6a977e35648ba4bf3ee9140d3cfb9624

Aliases

arxiv: 2606.19800 · arxiv_version: 2606.19800v1 · doi: 10.48550/arxiv.2606.19800 · pith_short_12: 6X76W7WRZT5E · pith_short_16: 6X76W7WRZT5EDCTD · pith_short_8: 6X76W7WR

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/6X76W7WRZT5EDCTDAJ7IJHKOD5 \
  | 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: f5ffeb7ed1ccfa418a63027e849d4e1f6a977e35648ba4bf3ee9140d3cfb9624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "237003a00cd3a66cae356fd71a5d2093d775c1aa0fdae217a81203607afc20bc",
    "cross_cats_sorted": [
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-18T05:11:00Z",
    "title_canon_sha256": "cb9409a25ae03e2be73d9c18b2ad916a16feef5c84f16bc7fdd2e8e564c669c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19800",
    "kind": "arxiv",
    "version": 1
  }
}