Pith Number

pith:ZRAB2TLU

pith:2018:ZRAB2TLUCLZCBAU3NRLLB6KGPZ

not attested not anchored not stored refs pending

Topological Poincar\'e type inequalities and lower bounds on the infimum of the spectrum for graphs

Daniel Lenz, Marcel Schmidt, Peter Stollmann

arxiv:1801.09279 v1 · 2018-01-28 · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZRAB2TLUCLZCBAU3NRLLB6KGPZ}

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	2026-05-18T00:24:57.966600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc401d4d7412f220829b6c56b0f9467e40eff78133f411f07a59ca8ccfc9bc1d

Aliases

arxiv: 1801.09279 · arxiv_version: 1801.09279v1 · doi: 10.48550/arxiv.1801.09279 · pith_short_12: ZRAB2TLUCLZC · pith_short_16: ZRAB2TLUCLZCBAU3 · pith_short_8: ZRAB2TLU

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/ZRAB2TLUCLZCBAU3NRLLB6KGPZ \
  | 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: cc401d4d7412f220829b6c56b0f9467e40eff78133f411f07a59ca8ccfc9bc1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dafc33c33165c5fbe7e05f955cadd35d424849d6a538cf5e6ceadebea3a289cc",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-01-28T20:23:22Z",
    "title_canon_sha256": "4e71cec2e2b7ca1553830910096de54a38603758a2e22e60f199abf83687ac77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09279",
    "kind": "arxiv",
    "version": 1
  }
}