Pith Number

pith:K5O37C25

pith:2010:K5O37C25OSIODX2HGYLQKRI6FD

not attested not anchored not stored refs pending

Tight lower bounds for the size of epsilon-nets

G\'abor Tardos, J\'anos Pach

arxiv:1012.1240 v1 · 2010-12-06 · cs.DM · 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{K5O37C25OSIODX2HGYLQKRI6FD}

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	2026-05-18T04:34:01.677057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

575dbf8b5d7490e1df47361705451e28df275fc21ffcc37688e23b560fd4a85f

Aliases

arxiv: 1012.1240 · arxiv_version: 1012.1240v1 · doi: 10.48550/arxiv.1012.1240 · pith_short_12: K5O37C25OSIO · pith_short_16: K5O37C25OSIODX2H · pith_short_8: K5O37C25

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/K5O37C25OSIODX2HGYLQKRI6FD \
  | 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: 575dbf8b5d7490e1df47361705451e28df275fc21ffcc37688e23b560fd4a85f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61590f320bc21e28e17fe7bb2b6a7205ff94f8820f91208609e4c12874581a1d",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-12-06T16:46:45Z",
    "title_canon_sha256": "576fb7d4f39f9eab9fb940bb8d4dbf7d6b129c38282ab6941aeb834963e3bb7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1240",
    "kind": "arxiv",
    "version": 1
  }
}