Pith Number

pith:MT42PKSR

pith:2014:MT42PKSRUQOHOGWEDMOP4X5E7A

not attested not anchored not stored refs pending

The Sparing Number of the Cartesian Products of Certain Graphs

K. A. Germina, K. P. Chithra, N. K. Sudev

arxiv:1407.4869 v1 · 2014-07-18 · 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{MT42PKSRUQOHOGWEDMOP4X5E7A}

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	2026-05-18T02:47:22.511527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64f9a7aa51a41c771ac41b1cfe5fa4f801d7fde00d452dafa03a7ecb3be37b97

Aliases

arxiv: 1407.4869 · arxiv_version: 1407.4869v1 · doi: 10.48550/arxiv.1407.4869 · pith_short_12: MT42PKSRUQOH · pith_short_16: MT42PKSRUQOHOGWE · pith_short_8: MT42PKSR

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/MT42PKSRUQOHOGWEDMOP4X5E7A \
  | 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: 64f9a7aa51a41c771ac41b1cfe5fa4f801d7fde00d452dafa03a7ecb3be37b97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d3cb644abe9ac1d72d510566455bd8b5bcde47be1d7e55a15e904dd0ee0f67a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-07-18T02:00:10Z",
    "title_canon_sha256": "53f598cb17a71fc5969d90aa09b3217fb8f46719167286f9bab1c1e310326f8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.4869",
    "kind": "arxiv",
    "version": 1
  }
}