Pith Number

pith:X56QVOBO

pith:2015:X56QVOBOW4GXL2VEAX7RAT4D75

not attested not anchored not stored refs pending

The Chaotic Representation Property of Compensated-Covariation Stable Families of Martingales

Hans-J\"urgen Engelbert, Paolo Di Tella

arxiv:1509.08604 v1 · 2015-09-29 · 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{X56QVOBOW4GXL2VEAX7RAT4D75}

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	2026-05-18T01:31:47.526134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf7d0ab82eb70d75eaa405ff104f83ff424ac360859f59224da1ca771a4a9809

Aliases

arxiv: 1509.08604 · arxiv_version: 1509.08604v1 · doi: 10.48550/arxiv.1509.08604 · pith_short_12: X56QVOBOW4GX · pith_short_16: X56QVOBOW4GXL2VE · pith_short_8: X56QVOBO

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/X56QVOBOW4GXL2VEAX7RAT4D75 \
  | 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: bf7d0ab82eb70d75eaa405ff104f83ff424ac360859f59224da1ca771a4a9809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ab57c7f2e83cf6e3a65b91e7449e968efde5dd69223e86c5cb8de9068c12092",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-29T06:36:22Z",
    "title_canon_sha256": "8af61f3d1f0f0a1b57059de18928d0de328e068946ca91ccbfc43f4cb42c4b9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08604",
    "kind": "arxiv",
    "version": 1
  }
}