Pith Number

pith:BXIA6MKW

pith:2019:BXIA6MKWCW5CHJPXPKTNPVEYQ6

not attested not anchored not stored refs pending

Counting critical subgraphs in $k$-critical graphs

Jie Ma, Tianchi Yang

arxiv:1906.09598 v2 · 2019-06-23 · 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{BXIA6MKWCW5CHJPXPKTNPVEYQ6}

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	2026-05-17T23:41:52.778556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0dd00f315615ba23a5f77aa6d7d49887b8ef195f001b606286d99655d1ac1bac

Aliases

arxiv: 1906.09598 · arxiv_version: 1906.09598v2 · doi: 10.48550/arxiv.1906.09598 · pith_short_12: BXIA6MKWCW5C · pith_short_16: BXIA6MKWCW5CHJPX · pith_short_8: BXIA6MKW

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/BXIA6MKWCW5CHJPXPKTNPVEYQ6 \
  | 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: 0dd00f315615ba23a5f77aa6d7d49887b8ef195f001b606286d99655d1ac1bac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "785fa4a8934c33c1990712dd3751e0654115ec5611254b62d5fc8947a79e8ff4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-06-23T15:44:56Z",
    "title_canon_sha256": "5002885badb52fb4bd73353ce093cc8d2144584a62a0eb9e49feae7357161bb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.09598",
    "kind": "arxiv",
    "version": 2
  }
}