Pith Number

pith:BP2LFJO5

pith:2010:BP2LFJO5D2AH6ZZJ4KE6XCBCHW

not attested not anchored not stored refs pending

On three point configurations determined by subsets of the Euclidean plane, the associated bilinear operator and applications to discrete geometry

Alex Iosevich, Allan Greenleaf

arxiv:1009.2471 v4 · 2010-09-13 · math.CA · 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{BP2LFJO5D2AH6ZZJ4KE6XCBCHW}

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	2026-05-18T04:09:45.870541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bf4b2a5dd1e807f6729e289eb88223d91c9e10133d807a7d7cbbd17c0084973

Aliases

arxiv: 1009.2471 · arxiv_version: 1009.2471v4 · doi: 10.48550/arxiv.1009.2471 · pith_short_12: BP2LFJO5D2AH · pith_short_16: BP2LFJO5D2AH6ZZJ · pith_short_8: BP2LFJO5

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/BP2LFJO5D2AH6ZZJ4KE6XCBCHW \
  | 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: 0bf4b2a5dd1e807f6729e289eb88223d91c9e10133d807a7d7cbbd17c0084973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f2e81989663fbd3ff65a8d9489e910b922007cba6d412a372e306192ee7594a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-09-13T18:27:38Z",
    "title_canon_sha256": "cdcdb58cf7fb66600b377d942071a417c8e3172674982914910bd05352ae378c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2471",
    "kind": "arxiv",
    "version": 4
  }
}