Pith Number

pith:CTC4N74J

pith:2007:CTC4N74JYJHCEZZEQ4EG3L7SWE

not attested not anchored not stored refs pending

Minimizing the Lifetime Shortfall or Shortfall at Death

Erhan Bayraktar

arxiv:math/0703824 v1 · 2007-03-28 · 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{CTC4N74JYJHCEZZEQ4EG3L7SWE}

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	2026-07-04T15:33:35.366489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14c5c6ff89c24e22672487086daff2b107e34029e7d6d7b3d0a19155c70ce28c

Aliases

arxiv: math/0703824 · arxiv_version: math/0703824v1 · doi: 10.48550/arxiv.math/0703824 · pith_short_12: CTC4N74JYJHC · pith_short_16: CTC4N74JYJHCEZZE · pith_short_8: CTC4N74J

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/CTC4N74JYJHCEZZEQ4EG3L7SWE \
  | 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: 14c5c6ff89c24e22672487086daff2b107e34029e7d6d7b3d0a19155c70ce28c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27979c779ac8f69b8b458837fbffff780d94cc8f4624ec7cf886aa4bd91bab45",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.RM"
    ],
    "license": "",
    "primary_cat": "math.OC",
    "submitted_at": "2007-03-28T01:00:35Z",
    "title_canon_sha256": "24acaeaf0dfa8c1df3f604f0b67ef9551e7f5e0842876ac232b34bf0f155aff7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703824",
    "kind": "arxiv",
    "version": 1
  }
}