Pith Number

pith:JSMZ4QBA

pith:2011:JSMZ4QBAZRDHLNYKBD7JP3F6H2

not attested not anchored not stored refs pending

The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

Chao Chen, Junfeng Liu, Litan Yan

arxiv:1106.2302 v2 · 2011-06-12 · 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{JSMZ4QBAZRDHLNYKBD7JP3F6H2}

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	2026-05-18T04:19:42.817725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c999e4020cc4675b70a08fe97ecbe3eb30463390143ba342963e2532b0351a9

Aliases

arxiv: 1106.2302 · arxiv_version: 1106.2302v2 · doi: 10.48550/arxiv.1106.2302 · pith_short_12: JSMZ4QBAZRDH · pith_short_16: JSMZ4QBAZRDHLNYK · pith_short_8: JSMZ4QBA

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/JSMZ4QBAZRDHLNYKBD7JP3F6H2 \
  | 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: 4c999e4020cc4675b70a08fe97ecbe3eb30463390143ba342963e2532b0351a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d79fba5b1a690323aa16dde50f04a2f436c04d0bd45b1492d06af08803af73f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-06-12T10:53:28Z",
    "title_canon_sha256": "5bb6d8ed9b1c50a1c2318f3776fd8798c6e36a1c0989785da4dc56f0b7e016a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2302",
    "kind": "arxiv",
    "version": 2
  }
}