Pith Number

pith:ZMCC4E75

pith:2006:ZMCC4E75FNYIDUVVPWPZRB3LSS

not attested not anchored not stored refs pending

Laplacians on Metric Graphs: Eigenvalues, Resolvents and Semigroups

Robert Schrader, Vadim Kostrykin

arxiv:math-ph/0601041 v1 · 2006-01-20 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZMCC4E75FNYIDUVVPWPZRB3LSS}

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	2026-07-04T14:52:45.567941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb042e13fd2b7081d2b57d9f98876b94b62f2ea27c1e1a3b907ce8e5a00826bb

Aliases

arxiv: math-ph/0601041 · arxiv_version: math-ph/0601041v1 · doi: 10.48550/arxiv.math-ph/0601041 · pith_short_12: ZMCC4E75FNYI · pith_short_16: ZMCC4E75FNYIDUVV · pith_short_8: ZMCC4E75

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/ZMCC4E75FNYIDUVVPWPZRB3LSS \
  | 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: cb042e13fd2b7081d2b57d9f98876b94b62f2ea27c1e1a3b907ce8e5a00826bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57a1e41549d9a32a0e65421d2df7278015e4d4842938efad1d4209d65fbb7ded",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-01-20T12:17:09Z",
    "title_canon_sha256": "8b1b5bea03d47cf539438581b976ea8d8e776b6f42804e9ab360f60d38bd6afd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0601041",
    "kind": "arxiv",
    "version": 1
  }
}