Pith Number

pith:D77O3ALF

pith:2010:D77O3ALFQGAKMQULD6ONA3WJ74

not attested not anchored not stored refs pending

On Products and Line Graphs of Signed Graphs, their Eigenvalues and Energy

K.A. Germina, Shahul Hameed K, Thomas Zaslavsky

arxiv:1010.3884 v1 · 2010-10-19 · 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{D77O3ALFQGAKMQULD6ONA3WJ74}

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	2026-05-18T01:02:14.535535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ffeed81658180a6428b1f9cd06ec9ff2f6c8823d1b3027717c3ae8d42f4c889

Aliases

arxiv: 1010.3884 · arxiv_version: 1010.3884v1 · doi: 10.48550/arxiv.1010.3884 · pith_short_12: D77O3ALFQGAK · pith_short_16: D77O3ALFQGAKMQUL · pith_short_8: D77O3ALF

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/D77O3ALFQGAKMQULD6ONA3WJ74 \
  | 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: 1ffeed81658180a6428b1f9cd06ec9ff2f6c8823d1b3027717c3ae8d42f4c889

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1246a826967e2c22e91f266cdad41a8041f4bc76158b132057e064922c13e497",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-19T12:47:19Z",
    "title_canon_sha256": "905368c3b3a3dd8382ef9ec3f17fcdfeeec38c1752451dc31f1f65cb3920f165"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3884",
    "kind": "arxiv",
    "version": 1
  }
}