Pith Number

pith:2APXUNVM

pith:2008:2APXUNVMXHTFPBNPFAIQR6ENFG

not attested not anchored not stored refs pending

Points in a triangle forcing small triangles

Matthew Kahle

arxiv:0811.2449 v1 · 2008-11-15 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2APXUNVMXHTFPBNPFAIQR6ENFG}

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	2026-05-18T04:40:34.156880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d01f7a36acb9e65785af281108f88d29891072296f0ea6585c2f57b696c7ae40

Aliases

arxiv: 0811.2449 · arxiv_version: 0811.2449v1 · doi: 10.48550/arxiv.0811.2449 · pith_short_12: 2APXUNVMXHTF · pith_short_16: 2APXUNVMXHTFPBNP · pith_short_8: 2APXUNVM

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/2APXUNVMXHTFPBNPFAIQR6ENFG \
  | 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: d01f7a36acb9e65785af281108f88d29891072296f0ea6585c2f57b696c7ae40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "069dc38b207af0680f716d6348aa3809af4f6231e3fc78a44d87ff50ccf23d5d",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-11-15T00:28:07Z",
    "title_canon_sha256": "51b9b648582e91b3005b7da51281e21af1ad10a0d345cba1903cea14622976aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.2449",
    "kind": "arxiv",
    "version": 1
  }
}