Pith Number

pith:PGPUFT52

pith:2014:PGPUFT5275A34RCAX2ZXTPJGLA

not attested not anchored not stored refs pending

A Simple Proof of a Martingale Representation Theorem Using Nonstandard Analysis

Tristram de Piro

arxiv:1405.2725 v2 · 2014-05-12 · math.PR · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGPUFT5275A34RCAX2ZXTPJGLA}

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	2026-05-18T00:14:07.148736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

799f42cfbaff41be4440beb379bd2658295aa54f3b58fdf32ea86224c3c480c0

Aliases

arxiv: 1405.2725 · arxiv_version: 1405.2725v2 · doi: 10.48550/arxiv.1405.2725 · pith_short_12: PGPUFT5275A3 · pith_short_16: PGPUFT5275A34RCA · pith_short_8: PGPUFT52

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/PGPUFT5275A34RCAX2ZXTPJGLA \
  | 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: 799f42cfbaff41be4440beb379bd2658295aa54f3b58fdf32ea86224c3c480c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73230502e2d94ac8b720e7cba918f38d272770f247941e69866fd9e1534ae49d",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-05-12T12:22:07Z",
    "title_canon_sha256": "83597a33966eb44f764ce66e6fe181a91d0c9f7347cccc361fc6075698d76a3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.2725",
    "kind": "arxiv",
    "version": 2
  }
}