Pith Number

pith:VKNO42LJ

pith:2007:VKNO42LJ4S6OOJYVC77YREYMOE

not attested not anchored not stored refs pending

Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin

Erhan Bayraktar, Virginia R. Young

arxiv:math/0703862 v2 · 2007-03-29 · math.OC · math.PR · q-fin.RM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKNO42LJ4S6OOJYVC77YREYMOE}

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	2026-07-04T15:33:35.410771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa9aee6969e4bce7271517ff88930c710cec5c9199560aa684da7e51616d0e57

Aliases

arxiv: math/0703862 · arxiv_version: math/0703862v2 · doi: 10.48550/arxiv.math/0703862 · pith_short_12: VKNO42LJ4S6O · pith_short_16: VKNO42LJ4S6OOJYV · pith_short_8: VKNO42LJ

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/VKNO42LJ4S6OOJYVC77YREYMOE \
  | 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: aa9aee6969e4bce7271517ff88930c710cec5c9199560aa684da7e51616d0e57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1e3c37392c95cf7669d6bd5e7107644ba19235ce38d8cc379232b63ca9b745e",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.RM"
    ],
    "license": "",
    "primary_cat": "math.OC",
    "submitted_at": "2007-03-29T02:24:54Z",
    "title_canon_sha256": "3f02721e38ab5e68f0152838a438b87224d1711f712a53cb096d427ddbea0b70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703862",
    "kind": "arxiv",
    "version": 2
  }
}