Pith Number

pith:YDZMMFBP

pith:2011:YDZMMFBPPK2DYVFUIENTQ6VP6G

not attested not anchored not stored refs pending

On an Inclusion of the Essential Spectrum of Laplacians under Non-Compact Change of Metric

Jun Masamune

arxiv:1103.2163 v1 · 2011-03-10 · 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{YDZMMFBPPK2DYVFUIENTQ6VP6G}

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	2026-05-18T04:26:56.061383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0f2c6142f7ab43c54b4411b387aaff1bf2871e049f08525fd1575976a56ce4e

Aliases

arxiv: 1103.2163 · arxiv_version: 1103.2163v1 · doi: 10.48550/arxiv.1103.2163 · pith_short_12: YDZMMFBPPK2D · pith_short_16: YDZMMFBPPK2DYVFU · pith_short_8: YDZMMFBP

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/YDZMMFBPPK2DYVFUIENTQ6VP6G \
  | 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: c0f2c6142f7ab43c54b4411b387aaff1bf2871e049f08525fd1575976a56ce4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff538ff95129fabff5404845f2c8f53400d039858073251fe6185d793f442c9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-03-10T23:12:31Z",
    "title_canon_sha256": "0b948b2e6e4bf88551d02f0df58e04d65996dcf1d85ddb3d81e7f275ea2a38c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2163",
    "kind": "arxiv",
    "version": 1
  }
}