Pith Number

pith:HAKKIT6I

pith:2019:HAKKIT6ILAPT2XECOI4ZHKN24N

not attested not anchored not stored refs pending

On the Simple Quasi Crossing Number of $K_{11}$

Arjun Pitchanathan, Saswata Shannigrahi

arxiv:1908.07851 v1 · 2019-08-19 · 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{HAKKIT6ILAPT2XECOI4ZHKN24N}

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	2026-07-05T00:23:06.889066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3814a44fc8581f3d5c82723993a9bae341d12a41617b08edb8daf4f72d492e72

Aliases

arxiv: 1908.07851 · arxiv_version: 1908.07851v1 · doi: 10.48550/arxiv.1908.07851 · pith_short_12: HAKKIT6ILAPT · pith_short_16: HAKKIT6ILAPT2XEC · pith_short_8: HAKKIT6I

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/HAKKIT6ILAPT2XECOI4ZHKN24N \
  | 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: 3814a44fc8581f3d5c82723993a9bae341d12a41617b08edb8daf4f72d492e72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e334b67f1f1b38e47e59cae482fb559493361e77a1efc89fd6e17dd1b7bda084",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-19T20:39:38Z",
    "title_canon_sha256": "85a9e2af044893422a07e28de0d7ec5c4ee26fc6d375bb60d40b52aaec660aaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07851",
    "kind": "arxiv",
    "version": 1
  }
}