Pith Number

pith:3KXH2XVD

pith:2011:3KXH2XVDN276DCCZ6FYPDM2VKW

not attested not anchored not stored refs pending

Strict local martingales and bubbles

Ashkan Nikeghbali, Constantinos Kardaras, D\"orte Kreher

arxiv:1108.4177 v3 · 2011-08-21 · 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{3KXH2XVDN276DCCZ6FYPDM2VKW}

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	2026-05-18T01:09:25.319250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daae7d5ea36ebfe18859f170f1b35555b565b18c3215209c7d4db542018d0fb6

Aliases

arxiv: 1108.4177 · arxiv_version: 1108.4177v3 · doi: 10.48550/arxiv.1108.4177 · pith_short_12: 3KXH2XVDN276 · pith_short_16: 3KXH2XVDN276DCCZ · pith_short_8: 3KXH2XVD

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/3KXH2XVDN276DCCZ6FYPDM2VKW \
  | 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: daae7d5ea36ebfe18859f170f1b35555b565b18c3215209c7d4db542018d0fb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbe9e67fbec6d892f1c20e4b3c0bc3a7a32712ffa38d093cc4b1e2d2e9918f96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-21T10:29:42Z",
    "title_canon_sha256": "7ff49e42984e158f4832422364bce2763059424b9a279883748f3b086e2534f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4177",
    "kind": "arxiv",
    "version": 3
  }
}