Pith Number

pith:Z7ADHWX5

pith:2019:Z7ADHWX5OP4VJYBW52TVLZ76XC

not attested not anchored not stored refs pending

New Kakeya estimates using Gromov's algebraic lemma

Joshua Zahl

arxiv:1908.05314 v4 · 2019-08-14 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7ADHWX5OP4VJYBW52TVLZ76XC}

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	2026-07-05T06:43:42.583181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfc033dafd73f954e036eea755e7feb8bf01ac229d29034a00b5794b2a156ecd

Aliases

arxiv: 1908.05314 · arxiv_version: 1908.05314v4 · doi: 10.48550/arxiv.1908.05314 · pith_short_12: Z7ADHWX5OP4V · pith_short_16: Z7ADHWX5OP4VJYBW · pith_short_8: Z7ADHWX5

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/Z7ADHWX5OP4VJYBW52TVLZ76XC \
  | 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: cfc033dafd73f954e036eea755e7feb8bf01ac229d29034a00b5794b2a156ecd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83a805b006ed96fe8de9828265c75de51d8984fd7ed7febee3d9e733beddd1ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-14T19:02:15Z",
    "title_canon_sha256": "5793097cf5f829b21aad828eaf879013f1407ef78d7ba19ba2aead9eb9749edc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05314",
    "kind": "arxiv",
    "version": 4
  }
}