Pith Number

pith:2DY7T3CR

pith:2016:2DY7T3CRRDXMYJKNOBS3TYRKZ3

not attested not anchored not stored refs pending

The $K_{n+5}$ and $K_{3^2,1^n}$ families are obstructions to $n$-apex

Mike Pierce, Thomas W. Mattman

arxiv:1603.00885 v1 · 2016-03-02 · 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{2DY7T3CRRDXMYJKNOBS3TYRKZ3}

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	2026-05-18T01:19:40.160676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0f1f9ec5188eecc254d7065b9e22aceee7202639e77769c9ebe87e4213857d7

Aliases

arxiv: 1603.00885 · arxiv_version: 1603.00885v1 · doi: 10.48550/arxiv.1603.00885 · pith_short_12: 2DY7T3CRRDXM · pith_short_16: 2DY7T3CRRDXMYJKN · pith_short_8: 2DY7T3CR

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/2DY7T3CRRDXMYJKNOBS3TYRKZ3 \
  | 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: d0f1f9ec5188eecc254d7065b9e22aceee7202639e77769c9ebe87e4213857d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da56991499dae1f25eae767afdd5da1d30fae6010eba2f4d53ff9d2c3cbe1696",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-03-02T21:01:15Z",
    "title_canon_sha256": "0dba1a1a5db6f5bac28127058ae5c522dc74d2e33880242eb5a06780c3fd362c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.00885",
    "kind": "arxiv",
    "version": 1
  }
}