Pith Number

pith:CSLWISXL

pith:2017:CSLWISXLYDFANTCMEA2DHFMYJM

not attested not anchored not stored refs pending

Density of the set of probability measures with the martingale representation property

Dmitry Kramkov, Sergio Pulido

arxiv:1709.07329 v2 · 2017-09-21 · math.PR · q-fin.GN · q-fin.MF

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CSLWISXLYDFANTCMEA2DHFMYJM}

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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	2026-05-17T23:41:01.455393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1497644aebc0ca06cc4c20343395984b075421ed274940fa673fc1d96a1980c3

Aliases

arxiv: 1709.07329 · arxiv_version: 1709.07329v2 · doi: 10.48550/arxiv.1709.07329 · pith_short_12: CSLWISXLYDFA · pith_short_16: CSLWISXLYDFANTCM · pith_short_8: CSLWISXL

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/CSLWISXLYDFANTCMEA2DHFMYJM \
  | 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: 1497644aebc0ca06cc4c20343395984b075421ed274940fa673fc1d96a1980c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c317d101d2a3a76960a72f97b43aa1a123081fb5b43bb064d741f4b2b9fb57a",
    "cross_cats_sorted": [
      "q-fin.GN",
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-09-21T13:54:19Z",
    "title_canon_sha256": "d612c9fd6b315f5598e8fd5496cb49632ebca2c3cec1887a618ec24c0289c9df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07329",
    "kind": "arxiv",
    "version": 2
  }
}