Pith Number

pith:YT6PUOG3

pith:2012:YT6PUOG35P3WQ4NISRZSWS5PEY

not attested not anchored not stored refs pending

Improved bounds for incidences between points and circles

Adam Sheffer, Joshua Zahl, Micha Sharir

arxiv:1208.0053 v3 · 2012-07-31 · 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{YT6PUOG35P3WQ4NISRZSWS5PEY}

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	2026-05-17T23:53:36.109683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4fcfa38dbebf76871a894732b4baf2624fc4a98a399f8dc2cc80b360a56271e

Aliases

arxiv: 1208.0053 · arxiv_version: 1208.0053v3 · doi: 10.48550/arxiv.1208.0053 · pith_short_12: YT6PUOG35P3W · pith_short_16: YT6PUOG35P3WQ4NI · pith_short_8: YT6PUOG3

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/YT6PUOG35P3WQ4NISRZSWS5PEY \
  | 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: c4fcfa38dbebf76871a894732b4baf2624fc4a98a399f8dc2cc80b360a56271e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a4d623bf7496b3c1ca1d904eba8e7ba143c664a705dc8c51e97176e1d76e5cd",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-31T23:20:20Z",
    "title_canon_sha256": "bc7ea7c2180dddadb9ad03490f9335f559117c63861f6e1219905d0dc6bea9ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0053",
    "kind": "arxiv",
    "version": 3
  }
}