Pith Number

pith:TZHWXXGS

pith:2014:TZHWXXGSCLIPKWR5R76HB5TIAW

not attested not anchored not stored refs pending

Gaussian integrability of distance function under the Lyapunov condition

Yuan Liu

arxiv:1409.8496 v2 · 2014-09-30 · 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{TZHWXXGSCLIPKWR5R76HB5TIAW}

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	2026-05-18T02:27:05.215487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e4f6bdcd212d0f55a3d8ffc70f668059bb423a6f76efd13db3e773c5712e075

Aliases

arxiv: 1409.8496 · arxiv_version: 1409.8496v2 · doi: 10.48550/arxiv.1409.8496 · pith_short_12: TZHWXXGSCLIP · pith_short_16: TZHWXXGSCLIPKWR5 · pith_short_8: TZHWXXGS

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/TZHWXXGSCLIPKWR5R76HB5TIAW \
  | 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: 9e4f6bdcd212d0f55a3d8ffc70f668059bb423a6f76efd13db3e773c5712e075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2faaaf823954b154a018fd1bb263c7d49197053d465148fa7ad12383aea8eaa8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-09-30T11:35:09Z",
    "title_canon_sha256": "2fbe8bd7d6f932df44ee676ab3b2e1af910d31ca3524e2544afdcd4155eb064f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8496",
    "kind": "arxiv",
    "version": 2
  }
}