Pith Number

pith:BZW2C3U5

pith:2009:BZW2C3U5OD4H2HAZHYWU5JIKRD

not attested not anchored not stored refs pending

The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II

Hironori Kumura

arxiv:0905.1451 v3 · 2009-05-10 · 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{BZW2C3U5OD4H2HAZHYWU5JIKRD}

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	2026-05-18T02:58:03.189505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e6da16e9d70f87d1c193e2d4ea50a88efa84d6a3837b2bc65bd2d9e8e3b8eb1

Aliases

arxiv: 0905.1451 · arxiv_version: 0905.1451v3 · doi: 10.48550/arxiv.0905.1451 · pith_short_12: BZW2C3U5OD4H · pith_short_16: BZW2C3U5OD4H2HAZ · pith_short_8: BZW2C3U5

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/BZW2C3U5OD4H2HAZHYWU5JIKRD \
  | 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: 0e6da16e9d70f87d1c193e2d4ea50a88efa84d6a3837b2bc65bd2d9e8e3b8eb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "076646616f1aa8da6d3cc96f788b35c4667122bae0e6c64acbf8de828c65b039",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-05-10T06:33:36Z",
    "title_canon_sha256": "4bc028ccda8208fb04ef047ac45a2dca7d027d96bf5a028517e17cd70e9ecbc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.1451",
    "kind": "arxiv",
    "version": 3
  }
}