Pith Number

pith:UY2SI4BJ

pith:2012:UY2SI4BJIYDTNC5CKDXCYBV3DR

not attested not anchored not stored refs pending

Filtered Az\'ema martingales

Umut \c{C}etin

arxiv:1209.3180 v1 · 2012-09-14 · 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{UY2SI4BJIYDTNC5CKDXCYBV3DR}

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	2026-05-18T03:45:32.609013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7

Aliases

arxiv: 1209.3180 · arxiv_version: 1209.3180v1 · doi: 10.48550/arxiv.1209.3180 · pith_short_12: UY2SI4BJIYDT · pith_short_16: UY2SI4BJIYDTNC5C · pith_short_8: UY2SI4BJ

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/UY2SI4BJIYDTNC5CKDXCYBV3DR \
  | 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: a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdeaa3cb211c19c286634a5e09d251ad865e17dcf502b255479dd8f3c0bbc71e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-14T13:22:53Z",
    "title_canon_sha256": "9226f4eb339f1062fe4241f64eba5e6be0c170cb3d6d85e2e9095bb06a58757b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3180",
    "kind": "arxiv",
    "version": 1
  }
}