Pith Number

pith:E7MIXH4P

pith:2015:E7MIXH4PCU2KM5FDZX4WWJQITF

not attested not anchored not stored refs pending

Improved Upper Bounds on $a'(G\Box H)$

Devanshi Vyas, Gaurav Patel, Om Thakkar, Punit Mehta, Rahul Muthu

arxiv:1507.01818 v1 · 2015-07-07 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E7MIXH4PCU2KM5FDZX4WWJQITF}

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	2026-05-18T01:37:12.309135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27d88b9f8f1534a674a3cdf96b26089964b4863dd48d2a1f48dfe2638a8a177e

Aliases

arxiv: 1507.01818 · arxiv_version: 1507.01818v1 · doi: 10.48550/arxiv.1507.01818 · pith_short_12: E7MIXH4PCU2K · pith_short_16: E7MIXH4PCU2KM5FD · pith_short_8: E7MIXH4P

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/E7MIXH4PCU2KM5FDZX4WWJQITF \
  | 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: 27d88b9f8f1534a674a3cdf96b26089964b4863dd48d2a1f48dfe2638a8a177e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da9ecc38bc2f20da4fb6cdfde0630d37fc16ded55f35a26b476f884a5db562d9",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-07T14:08:08Z",
    "title_canon_sha256": "56f4205c501cacbbc6a0ad6fc15dc6a5e96ef403962ca03677b8f5573125bdd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01818",
    "kind": "arxiv",
    "version": 1
  }
}