Pith Number

pith:M3GQKJD5

pith:2011:M3GQKJD5NBCW533MTNZTNTH3KT

not attested not anchored not stored refs pending

Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance

Claus Griessler, Martin Keller-Ressel

arxiv:1103.2310 v2 · 2011-03-11 · q-fin.PR · 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{M3GQKJD5NBCW533MTNZTNTH3KT}

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	2026-05-18T03:44:15.650600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66cd05247d68456eef6c9b7336ccfb54c0e80c71ecb81f9c7927b08eb6edf7b4

Aliases

arxiv: 1103.2310 · arxiv_version: 1103.2310v2 · doi: 10.48550/arxiv.1103.2310 · pith_short_12: M3GQKJD5NBCW · pith_short_16: M3GQKJD5NBCW533M · pith_short_8: M3GQKJD5

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/M3GQKJD5NBCW533MTNZTNTH3KT \
  | 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: 66cd05247d68456eef6c9b7336ccfb54c0e80c71ecb81f9c7927b08eb6edf7b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba02c6cf43d7bd9606accf7816340b8c24f364a71893cab7e22583fc6931c109",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.PR",
    "submitted_at": "2011-03-11T16:30:13Z",
    "title_canon_sha256": "db2fc4e1d4006024a96b6cfe821bfccb9e52297bcd20c90f0545b2940893aee7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2310",
    "kind": "arxiv",
    "version": 2
  }
}