Pith Number

pith:BCZRSOCA

pith:2026:BCZRSOCAUVA56XD5OEYYNKGROO

not attested not anchored not stored refs pending

The Minimum Cardinality of a Dependent Finite Gabor System Is Four

Tailin Wu, Wenhao Deng, Xinan Dai, Yingdong Shi, Yuchen Yang

arxiv:2608.08190 v1 · 2026-08-08 · math.FA · math.CA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BCZRSOCAUVA56XD5OEYYNKGROO}

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	2026-08-11T01:21:55.816582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08b3193840a541df5c7d713186a8d1738b2f4c1199709260864a99e8c9680919

Aliases

arxiv: 2608.08190 · arxiv_version: 2608.08190v1 · doi: 10.48550/arxiv.2608.08190 · pith_short_12: BCZRSOCAUVA5 · pith_short_16: BCZRSOCAUVA56XD5 · pith_short_8: BCZRSOCA

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/BCZRSOCAUVA56XD5OEYYNKGROO \
  | 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: 08b3193840a541df5c7d713186a8d1738b2f4c1199709260864a99e8c9680919

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "335c739f8459ea88731bab33c6b70129d48cefd4b723d42917bafc03a22948c9",
    "cross_cats_sorted": [
      "math.CA",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-08T15:32:24Z",
    "title_canon_sha256": "3217f77eb851f091594d0f65d37ecee8c4b4cfde4d1f50865c62905fe13daa4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08190",
    "kind": "arxiv",
    "version": 1
  }
}