Pith Number

pith:4KITTLHD

pith:2015:4KITTLHDXEEOJC34S5B2TYGYKN

not attested not anchored not stored refs pending

Lower bounds for independence and $k$-independence number of graphs using the concept of degenerate degrees

Manouchehr Zaker

arxiv:1507.07194 v1 · 2015-07-26 · 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{4KITTLHDXEEOJC34S5B2TYGYKN}

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	2026-05-18T01:36:16.956652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e29139ace3b908e48b7c9743a9e0d8534ebabca0ecda0b3acdb2a8471a8f4543

Aliases

arxiv: 1507.07194 · arxiv_version: 1507.07194v1 · doi: 10.48550/arxiv.1507.07194 · pith_short_12: 4KITTLHDXEEO · pith_short_16: 4KITTLHDXEEOJC34 · pith_short_8: 4KITTLHD

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/4KITTLHDXEEOJC34S5B2TYGYKN \
  | 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: e29139ace3b908e48b7c9743a9e0d8534ebabca0ecda0b3acdb2a8471a8f4543

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f5e792224495103a815a46db6d5ecb51e9611328529227f15d61b8a7b8b1413",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-26T12:32:34Z",
    "title_canon_sha256": "84e92fe9963036964244602377887e6e2985bd75ad4243d14289aa34cf34f500"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07194",
    "kind": "arxiv",
    "version": 1
  }
}