Pith Number

pith:KPY5SZ2S

pith:2012:KPY5SZ2SPGEIRF7IWUBMUVSLDE

not attested not anchored not stored refs pending

Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More

Bundit Laekhanukit, Danupon Nanongkai, Parinya Chalermsook

arxiv:1212.4129 v2 · 2012-12-17 · cs.DM · cs.CC · cs.DS · 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{KPY5SZ2SPGEIRF7IWUBMUVSLDE}

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	2026-05-18T02:39:54.371705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53f1d9675279888897e8b502ca564b19219c70efa317240fd857513da8db0c06

Aliases

arxiv: 1212.4129 · arxiv_version: 1212.4129v2 · doi: 10.48550/arxiv.1212.4129 · pith_short_12: KPY5SZ2SPGEI · pith_short_16: KPY5SZ2SPGEIRF7I · pith_short_8: KPY5SZ2S

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/KPY5SZ2SPGEIRF7IWUBMUVSLDE \
  | 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: 53f1d9675279888897e8b502ca564b19219c70efa317240fd857513da8db0c06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71360493a0d73da49acb9c3b951dc08b5d952bd663599dc0b987d000e3dc107b",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DS",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-12-17T20:38:28Z",
    "title_canon_sha256": "cae1ad2addf7cb8fa920ac325eff44a8ad38dba80de1c204d2a14f5369b5cc0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4129",
    "kind": "arxiv",
    "version": 2
  }
}