Pith Number

pith:APGZTLE6

pith:2022:APGZTLE6TBRILO5R6T3OM4XC7D

not attested not anchored not stored refs pending

Efficient Concentration with Gaussian Approximation

Lester Mackey, Morgane Austern

arxiv:2208.09922 v9 · 2022-08-21 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APGZTLE6TBRILO5R6T3OM4XC7D}

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.

Cited by

1 paper in Pith

Computable Bounds for Strong Approximations with Applications

Receipt and verification

First computed	2026-06-01T02:03:17.012872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03cd99ac9e986285bbb1f4f6e672e2f8c0fcf5787bc68b2c50af9a44746b9bac

Aliases

arxiv: 2208.09922 · arxiv_version: 2208.09922v9 · doi: 10.48550/arxiv.2208.09922 · pith_short_12: APGZTLE6TBRI · pith_short_16: APGZTLE6TBRILO5R · pith_short_8: APGZTLE6

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/APGZTLE6TBRILO5R6T3OM4XC7D \
  | 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: 03cd99ac9e986285bbb1f4f6e672e2f8c0fcf5787bc68b2c50af9a44746b9bac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fa860095fad3da78efdc3ec54410aabc0e0aab9eb0581d5ce66f868a61d5b54",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-08-21T17:03:09Z",
    "title_canon_sha256": "30fe4c8ae5be6d41d33ff9bd7652c2e7b3be91e8eaffc5928bdc768bb3cb29dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.09922",
    "kind": "arxiv",
    "version": 9
  }
}