Pith Number

pith:4DKJCOON

pith:2019:4DKJCOONEWTEALIXYQ6WCWSQ67

not attested not anchored not stored refs pending

Two Examples of COM Bounds using Spectral Gaps: Length of the LIS in a Random Permutation and Lipschitz Functions of 1d Markov Chains

Michael Froehlich, Shannon Starr

arxiv:1901.08410 v1 · 2019-01-24 · 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{4DKJCOONEWTEALIXYQ6WCWSQ67}

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	2026-05-17T23:55:35.538218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0d49139cd25a6402d17c43d615a50f7f566005b74b53fee759c1c73cbfe55d2

Aliases

arxiv: 1901.08410 · arxiv_version: 1901.08410v1 · doi: 10.48550/arxiv.1901.08410 · pith_short_12: 4DKJCOONEWTE · pith_short_16: 4DKJCOONEWTEALIX · pith_short_8: 4DKJCOON

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/4DKJCOONEWTEALIXYQ6WCWSQ67 \
  | 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: e0d49139cd25a6402d17c43d615a50f7f566005b74b53fee759c1c73cbfe55d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6b70224e2b3091ba18bcf127014d990d4f4d02f858f3ca51683a377821031a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-01-24T13:55:10Z",
    "title_canon_sha256": "5b5cb38d2e8985954fec6822964240071d78b3a8bfa62ca65949e1cf06b86a2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.08410",
    "kind": "arxiv",
    "version": 1
  }
}