Pith Number

pith:BHKZ4U5J

pith:2026:BHKZ4U5JFL7LGSAZNVQXGAPNGI

not attested not anchored not stored refs pending

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem

Danqing He, Xinyu Zhu

arxiv:2607.05124 v1 · 2026-07-06 · 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{BHKZ4U5JFL7LGSAZNVQXGAPNGI}

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	2026-07-07T03:19:16.891154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09d59e53a92afeb348196d617301ed322f1bedc33047e5a17634baf87ae9e34f

Aliases

arxiv: 2607.05124 · arxiv_version: 2607.05124v1 · doi: 10.48550/arxiv.2607.05124 · pith_short_12: BHKZ4U5JFL7L · pith_short_16: BHKZ4U5JFL7LGSAZ · pith_short_8: BHKZ4U5J

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/BHKZ4U5JFL7LGSAZNVQXGAPNGI \
  | 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: 09d59e53a92afeb348196d617301ed322f1bedc33047e5a17634baf87ae9e34f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e9ccdbfafb54eae5a895082dbb40f33c4a339b5d64a81c2c5293c4e6e1fefd4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-07-06T14:12:33Z",
    "title_canon_sha256": "32b8e8165833e09ff8209402cbad8d4aa81d0aadfb1435f0c6fd5be577d2fe9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05124",
    "kind": "arxiv",
    "version": 1
  }
}