Pith Number

pith:OZ3VLJBD

pith:2004:OZ3VLJBDO4ETTESIDDMMHZ2QEK

not attested not anchored not stored refs pending

Sharp asymptotics of the functional quantization problem for Gaussian processes

Gilles Pages, Harald Luschgy

arxiv:math/0410156 v1 · 2004-10-06 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZ3VLJBDO4ETTESIDDMMHZ2QEK}

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	2026-05-18T01:05:25.818355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

767755a423770939924818d8c3e75022a66265aac6741421dc4fef5ecfefe85d

Aliases

arxiv: math/0410156 · arxiv_version: math/0410156v1 · doi: 10.48550/arxiv.math/0410156 · pith_short_12: OZ3VLJBDO4ET · pith_short_16: OZ3VLJBDO4ETTESI · pith_short_8: OZ3VLJBD

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/OZ3VLJBDO4ETTESIDDMMHZ2QEK \
  | 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: 767755a423770939924818d8c3e75022a66265aac6741421dc4fef5ecfefe85d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f023366f0fded85125a6ae4c2711dee5e8e8b23567fb89ea2b6cf6e3c8c178",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-10-06T12:29:37Z",
    "title_canon_sha256": "4e30de35ce5b51b2a1087d0be6f5199de4f42d742f88083d443fb42ae9efc9b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410156",
    "kind": "arxiv",
    "version": 1
  }
}