Pith Number

pith:GZZYKDFM

pith:2007:GZZYKDFMAFL3MRFP7RIF7O3TWF

not attested not anchored not stored refs pending

Homogenized spectral problems for exactly solvable operators: asymptotics of polynomial eigenfunctions

Boris Shapiro, Julius Borcea, Rikard B{\o}gvad

arxiv:0705.2822 v3 · 2007-05-19 · math.CA · math.CV · 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{GZZYKDFMAFL3MRFP7RIF7O3TWF}

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	2026-05-18T04:40:45.545817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3673850cac0157b644affc505fbb73b14a802c70e1276037795d77d980d488bc

Aliases

arxiv: 0705.2822 · arxiv_version: 0705.2822v3 · doi: 10.48550/arxiv.0705.2822 · pith_short_12: GZZYKDFMAFL3 · pith_short_16: GZZYKDFMAFL3MRFP · pith_short_8: GZZYKDFM

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/GZZYKDFMAFL3MRFP7RIF7O3TWF \
  | 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: 3673850cac0157b644affc505fbb73b14a802c70e1276037795d77d980d488bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "619df3d9160a36a64435a57664d729171c4f33be6fa0338e9c4f41f7f23d55f3",
    "cross_cats_sorted": [
      "math.CV",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2007-05-19T15:45:55Z",
    "title_canon_sha256": "b98b0998715dd47dc54d004e22b0834445b96e6601313df9ad3800558ddbe844"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.2822",
    "kind": "arxiv",
    "version": 3
  }
}