Pith Number

pith:76WJOU23

pith:2015:76WJOU23UWHMTIT5EB7SIBYSAY

not attested not anchored not stored refs pending

New bounds on curve tangencies and orthogonalities

Jordan S. Ellenberg, Joshua Zahl, Jozsef Solymosi

arxiv:1509.05821 v4 · 2015-09-18 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{76WJOU23UWHMTIT5EB7SIBYSAY}

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	2026-05-18T00:11:19.491476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffac97535ba58ec9a27d207f24071206209e5a04e475994670c74c8afb990268

Aliases

arxiv: 1509.05821 · arxiv_version: 1509.05821v4 · doi: 10.48550/arxiv.1509.05821 · pith_short_12: 76WJOU23UWHM · pith_short_16: 76WJOU23UWHMTIT5 · pith_short_8: 76WJOU23

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/76WJOU23UWHMTIT5EB7SIBYSAY \
  | 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: ffac97535ba58ec9a27d207f24071206209e5a04e475994670c74c8afb990268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "beda324879eb7d5dd27a3a6bfb5c0319a8479faf6a72e2470662b1967d64cbfb",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-18T23:49:40Z",
    "title_canon_sha256": "4fbb0ecae6dbc3b26bc050cd5825d140ec0177b20098937e6db1e80c4e9d3ec1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05821",
    "kind": "arxiv",
    "version": 4
  }
}