Pith Number

pith:XA4CTO2K

pith:2005:XA4CTO2KGKN52PHKI3B7PTVGKB

not attested not anchored not stored refs pending

Asymptotic behavior of $L^2$-normalized eigenfunctions of the Laplace-Beltrami operator on a closed Riemannian manifold

Bin Xu

arxiv:math/0509061 v2 · 2005-09-04 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XA4CTO2KGKN52PHKI3B7PTVGKB}

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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.

Cited by

1 paper in Pith

How well behaved is finite dimensional Diffusion Maps?

Receipt and verification

First computed	2026-07-04T15:42:16.748142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b83829bb4a329bdd3cea46c3f7cea65073356a538680a530a839fba2a5c89f78

Aliases

arxiv: math/0509061 · arxiv_version: math/0509061v2 · doi: 10.48550/arxiv.math/0509061 · pith_short_12: XA4CTO2KGKN5 · pith_short_16: XA4CTO2KGKN52PHK · pith_short_8: XA4CTO2K

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/XA4CTO2KGKN52PHKI3B7PTVGKB \
  | 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: b83829bb4a329bdd3cea46c3f7cea65073356a538680a530a839fba2a5c89f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9add0c40178a3cc0d0c9747001a5e91d15ffb7b8d284f5f0ec66448fcd6ff146",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2005-09-04T11:50:45Z",
    "title_canon_sha256": "39090526aded3f0940c5ce0b63d6d60ff5e7c93247514586ed53485fcd16b0bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509061",
    "kind": "arxiv",
    "version": 2
  }
}