Pith Number

pith:7XRFW6TA

pith:2016:7XRFW6TAGJEVQI7BG3NACXEX7O

not attested not anchored not stored refs pending

Super-Walk Formulae for Even and Odd Laplacians in Finite Graphs

Chengzheng Yu

arxiv:1612.05505 v4 · 2016-12-15 · math.CO · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XRFW6TAGJEVQI7BG3NACXEX7O}

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	2026-05-18T00:40:28.684427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde25b7a6032495823e136da015c97fb834a63f1984bcc119a14095f4f473a31

Aliases

arxiv: 1612.05505 · arxiv_version: 1612.05505v4 · doi: 10.48550/arxiv.1612.05505 · pith_short_12: 7XRFW6TAGJEV · pith_short_16: 7XRFW6TAGJEVQI7B · pith_short_8: 7XRFW6TA

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/7XRFW6TAGJEVQI7BG3NACXEX7O \
  | 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: fde25b7a6032495823e136da015c97fb834a63f1984bcc119a14095f4f473a31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca877fb96e4b2ee8cd5e9f04a76734ca06d0354134b71c01fa2ca968d96d7cb0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-15T04:02:31Z",
    "title_canon_sha256": "e2cf5f6ec992a9b32bae0dd6e1a67a58d0ed00f2ab55babc668da9db4f53f50d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05505",
    "kind": "arxiv",
    "version": 4
  }
}