Pith Number

pith:Z57DH2LG

pith:2014:Z57DH2LGZVRQMRUV2KKANVT65E

not attested not anchored not stored refs pending

A short remark on the surjectivity of the combinatorial Laplacian on infinite graphs

Thomas Kalmes

arxiv:1412.5854 v1 · 2014-12-18 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z57DH2LGZVRQMRUV2KKANVT65E}

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	2026-05-18T00:13:53.851696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf7e33e966cd63064695d29406d67ee902991c32b61ae7d4d8cc4f55aa81e158

Aliases

arxiv: 1412.5854 · arxiv_version: 1412.5854v1 · doi: 10.48550/arxiv.1412.5854 · pith_short_12: Z57DH2LGZVRQ · pith_short_16: Z57DH2LGZVRQMRUV · pith_short_8: Z57DH2LG

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/Z57DH2LGZVRQMRUV2KKANVT65E \
  | 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: cf7e33e966cd63064695d29406d67ee902991c32b61ae7d4d8cc4f55aa81e158

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d9ad920d109802773d03e2ac81f1eede1f159fb5cb7fb66f305cbb5ec5be2cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-12-18T13:39:42Z",
    "title_canon_sha256": "3742b28e970518b397779ef81601ef62611bd0a1f6b4c559b63e61a18571f05c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.5854",
    "kind": "arxiv",
    "version": 1
  }
}