Pith Number

pith:HPW6ZM7S

pith:2009:HPW6ZM7SRJNWMUENFZ3VQP4RKJ

not attested not anchored not stored refs pending

The lower bound of the Ricci curvature that yields the infinite number of the discrete spectrum of the Laplacian

Hironori Kumura

arxiv:0902.1919 v7 · 2009-02-11 · math.DG · 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{HPW6ZM7SRJNWMUENFZ3VQP4RKJ}

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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	2026-05-18T04:32:43.756326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bedecb3f28a5b66508d2e77583f91527e985b10a8856912ccea3f27e0359603

Aliases

arxiv: 0902.1919 · arxiv_version: 0902.1919v7 · doi: 10.48550/arxiv.0902.1919 · pith_short_12: HPW6ZM7SRJNW · pith_short_16: HPW6ZM7SRJNWMUEN · pith_short_8: HPW6ZM7S

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/HPW6ZM7SRJNWMUENFZ3VQP4RKJ \
  | 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: 3bedecb3f28a5b66508d2e77583f91527e985b10a8856912ccea3f27e0359603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73afbf9cd0d33a31b180448a4323bb92889ef54a2b8c0e5dad094f60c336a64f",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-02-11T16:18:57Z",
    "title_canon_sha256": "d4c9a8524f7bf7da5e18a39034008496c998898a355cec9248c89133cafb70ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1919",
    "kind": "arxiv",
    "version": 7
  }
}