Pith Number

pith:JL6XW5JU

pith:2026:JL6XW5JUOPPMTEWHOZQKPAGNJ4

not attested not anchored not stored refs pending

On the number of directions formed by Cartesian products in $\mathbb{F}_{p^2}^2$

Ali Mohammadi

arxiv:2605.15727 v1 · 2026-05-15 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JL6XW5JUOPPMTEWHOZQKPAGNJ4}

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	2026-05-20T00:01:15.120463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4afd7b753473dec992c77660a780cd4f187dcff53c0aa1772170b64ad2e6400e

Aliases

arxiv: 2605.15727 · arxiv_version: 2605.15727v1 · doi: 10.48550/arxiv.2605.15727 · pith_short_12: JL6XW5JUOPPM · pith_short_16: JL6XW5JUOPPMTEWH · pith_short_8: JL6XW5JU

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/JL6XW5JUOPPMTEWHOZQKPAGNJ4 \
  | 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: 4afd7b753473dec992c77660a780cd4f187dcff53c0aa1772170b64ad2e6400e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5a983ddf48d4e0f40b6af2432aceb3da3f63066043356b0bca29c24adbf3a82",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-15T08:23:42Z",
    "title_canon_sha256": "16fdb686a0622c7cf75ed5173035949dbecb1b02353e479bb8a59e1f6d9329c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15727",
    "kind": "arxiv",
    "version": 1
  }
}