Pith Number

pith:ZGPZSJIJ

pith:2015:ZGPZSJIJIJLMOFSVMFP6R3NAYC

not attested not anchored not stored refs pending

On the invariance principle for empirical processes of associated sequences

Vadim Demichev

arxiv:1509.07602 v1 · 2015-09-25 · 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{ZGPZSJIJIJLMOFSVMFP6R3NAYC}

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	2026-05-18T01:32:02.368487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c99f9925094256c71655615fe8eda0c09613192a1629301fb77716d25a03e2e6

Aliases

arxiv: 1509.07602 · arxiv_version: 1509.07602v1 · doi: 10.48550/arxiv.1509.07602 · pith_short_12: ZGPZSJIJIJLM · pith_short_16: ZGPZSJIJIJLMOFSV · pith_short_8: ZGPZSJIJ

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/ZGPZSJIJIJLMOFSVMFP6R3NAYC \
  | 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: c99f9925094256c71655615fe8eda0c09613192a1629301fb77716d25a03e2e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "798d4ae6a0935ffdb60484cc22ae9b91d9f0c94b1539b31ffc1317de72692130",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-25T07:15:59Z",
    "title_canon_sha256": "34b8ea7e74c865a005d5ec7ac0e6e1ede9cc00d559dcdb6b52600e87ec8f397d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07602",
    "kind": "arxiv",
    "version": 1
  }
}