Pith Number

pith:TG4GN6N3

pith:2014:TG4GN6N3WK22QD4HCS2PAHXWBT

not attested not anchored not stored refs pending

Existence of Invariant Measures of Stochastic Systems with Delay in the Highest Order Partial Derivatives

Kai Liu

arxiv:1402.2157 v1 · 2014-02-10 · 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{TG4GN6N3WK22QD4HCS2PAHXWBT}

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	2026-05-18T02:59:32.128370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99b866f9bbb2b5a80f8714b4f01ef60ceee2830ce0e9930623491429272817ee

Aliases

arxiv: 1402.2157 · arxiv_version: 1402.2157v1 · doi: 10.48550/arxiv.1402.2157 · pith_short_12: TG4GN6N3WK22 · pith_short_16: TG4GN6N3WK22QD4H · pith_short_8: TG4GN6N3

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/TG4GN6N3WK22QD4HCS2PAHXWBT \
  | 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: 99b866f9bbb2b5a80f8714b4f01ef60ceee2830ce0e9930623491429272817ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5780beb349d933c192462fe77969088ac7b6f1d6940a8eac49746f360ac4cdf7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-02-10T14:26:38Z",
    "title_canon_sha256": "c4dd409123e40c000da9b552b940f2112c6f62f00fa06070d1a2849f9b045e43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.2157",
    "kind": "arxiv",
    "version": 1
  }
}