Pith Number

pith:QQTP4Y2K

pith:2008:QQTP4Y2KTR5PT3NWNEUH2UB6YO

not attested not anchored not stored refs pending

"Minesweeper" and spectrum of discrete Laplacians

Evgeny Lakshtanov, Oleg German

arxiv:0806.3480 v3 · 2008-06-20 · 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{QQTP4Y2KTR5PT3NWNEUH2UB6YO}

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	2026-05-18T04:36:51.464842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8426fe634a9c7af9edb669287d503ec384d4c59ff6b4ea33a50aeb24c6487aee

Aliases

arxiv: 0806.3480 · arxiv_version: 0806.3480v3 · doi: 10.48550/arxiv.0806.3480 · pith_short_12: QQTP4Y2KTR5P · pith_short_16: QQTP4Y2KTR5PT3NW · pith_short_8: QQTP4Y2K

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/QQTP4Y2KTR5PT3NWNEUH2UB6YO \
  | 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: 8426fe634a9c7af9edb669287d503ec384d4c59ff6b4ea33a50aeb24c6487aee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8974c41ef405d7132f846036bb4e447c932f906031e908be3e5f6967365c4b75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2008-06-20T22:00:56Z",
    "title_canon_sha256": "0f2163ccf1017753114004a008c527c9fd149a5be3f5729ed9eed7e213a38b83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.3480",
    "kind": "arxiv",
    "version": 3
  }
}