Pith Number

pith:I2BR3QVW

pith:2021:I2BR3QVWPU7SBZZ3HM7I3M5CRZ

not attested not anchored not stored refs pending

Asymptotics for the number of directions determined by $[n] \times [n]$ in $\mathbb{F}_p^2$

Chi Hoi Yip, Ethan Patrick White, Greg Martin

arxiv:2107.01311 v1 · 2021-07-03 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I2BR3QVWPU7SBZZ3HM7I3M5CRZ}

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	2026-07-05T04:15:09.552302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46831dc2b67d3f20e73b3b3e8db3a28e4db659f2638b6cf21dbe9b6910e6007c

Aliases

arxiv: 2107.01311 · arxiv_version: 2107.01311v1 · doi: 10.48550/arxiv.2107.01311 · pith_short_12: I2BR3QVWPU7S · pith_short_16: I2BR3QVWPU7SBZZ3 · pith_short_8: I2BR3QVW

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/I2BR3QVWPU7SBZZ3HM7I3M5CRZ \
  | 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: 46831dc2b67d3f20e73b3b3e8db3a28e4db659f2638b6cf21dbe9b6910e6007c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fe7bae23a0d0de04e9583d0647cbffb5814b7e3df41955c2020198639eb2534",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-07-03T00:20:34Z",
    "title_canon_sha256": "45c032c1900bd4cd02dd04899c53d778023f084b8637707cbed79c7f4404394b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.01311",
    "kind": "arxiv",
    "version": 1
  }
}