Pith Number

pith:OJGAOFSL

pith:2012:OJGAOFSL5MCVPDJEKOXBQVURPX

not attested not anchored not stored refs pending

A modular Szemeredi-Trotter theorem for hyperbolas

Jean Bourgain

arxiv:1208.4008 v1 · 2012-08-20 · 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{OJGAOFSL5MCVPDJEKOXBQVURPX}

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	2026-05-18T03:48:25.490359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b

Aliases

arxiv: 1208.4008 · arxiv_version: 1208.4008v1 · doi: 10.48550/arxiv.1208.4008 · pith_short_12: OJGAOFSL5MCV · pith_short_16: OJGAOFSL5MCVPDJE · pith_short_8: OJGAOFSL

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/OJGAOFSL5MCVPDJEKOXBQVURPX \
  | 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: 724c07164beb05578d2453ae1856917dcfffa011fda9d649e2c97ae7dd87a09b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99f98b3fc472f4cb76c83fea03c294d71b9c3c94367d8b6c0c98af8df53ea975",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-20T13:52:38Z",
    "title_canon_sha256": "1fcca37f41e80ff7a77450e573aa4e2fd1194deb7a1d5f1ec55ec8eea361be84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4008",
    "kind": "arxiv",
    "version": 1
  }
}