Pith Number

pith:KLCHR5RV

pith:2015:KLCHR5RVY2RR4CF4OIIOHA3JBB

not attested not anchored not stored refs pending

A Szemer\'edi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Craig Timmons, Le Anh Vinh, Michael Tait, Thang Pham

arxiv:1505.07308 v4 · 2015-05-27 · 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{KLCHR5RVY2RR4CF4OIIOHA3JBB}

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	2026-05-18T01:01:52.271890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52c478f635c6a31e08bc7210e38369085e6cd88ca2ac2d3d9bfd40b37a05be98

Aliases

arxiv: 1505.07308 · arxiv_version: 1505.07308v4 · doi: 10.48550/arxiv.1505.07308 · pith_short_12: KLCHR5RVY2RR · pith_short_16: KLCHR5RVY2RR4CF4 · pith_short_8: KLCHR5RV

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/KLCHR5RVY2RR4CF4OIIOHA3JBB \
  | 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: 52c478f635c6a31e08bc7210e38369085e6cd88ca2ac2d3d9bfd40b37a05be98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9aa0b406141781568a440223fc1c1c516ae038dce93df2b05b5e52bc23803e34",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-27T13:33:21Z",
    "title_canon_sha256": "15ba546fabcf30a1c058230af770e57c38ead62cedda669bde5b14be8e98bf8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07308",
    "kind": "arxiv",
    "version": 4
  }
}