Pith Number

pith:BTCXKXPD

pith:2008:BTCXKXPD4RUDCV6PBNW5Q2Z3AF

not attested not anchored not stored refs pending

Stochastic integrals and conditional full support

Mikko S. Pakkanen

arxiv:0811.1847 v3 · 2008-11-12 · 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{BTCXKXPD4RUDCV6PBNW5Q2Z3AF}

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	2026-05-18T04:32:20.117416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cc5755de3e4683157cf0b6dd86b3b016692d7f1656b950303c2889ab04dad12

Aliases

arxiv: 0811.1847 · arxiv_version: 0811.1847v3 · doi: 10.48550/arxiv.0811.1847 · pith_short_12: BTCXKXPD4RUD · pith_short_16: BTCXKXPD4RUDCV6P · pith_short_8: BTCXKXPD

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/BTCXKXPD4RUDCV6PBNW5Q2Z3AF \
  | 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: 0cc5755de3e4683157cf0b6dd86b3b016692d7f1656b950303c2889ab04dad12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82389c0f7f685142a7ff096e94d94ba63905624380c30944dd4a13adfade39cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-11-12T09:36:26Z",
    "title_canon_sha256": "d58834e3e49c8335ab0e205c440249e6d287c0c8b086ad6066fbe38e56318e60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.1847",
    "kind": "arxiv",
    "version": 3
  }
}