Pith Number

pith:7FZXHGPU

pith:2013:7FZXHGPUZ43F5S3IF2DXZT5LF4

not attested not anchored not stored refs pending

Strong supermartingales and limits of nonnegative martingales

Christoph Czichowsky, Walter Schachermayer

arxiv:1312.2024 v4 · 2013-12-06 · 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{7FZXHGPUZ43F5S3IF2DXZT5LF4}

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.

Cited by

2 papers in Pith

Interpreting Manifolds and Graph Neural Embeddings from Internet of Things Traffic Flows

Fast-Food Intimacy: How Chinese Women Navigate Soul's AI Boyfriend

Receipt and verification

First computed	2026-05-18T01:20:17.905380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9737399f4cf365ecb682e877ccfab2f2a4233814fec5e4c6fe536baa21475c5

Aliases

arxiv: 1312.2024 · arxiv_version: 1312.2024v4 · doi: 10.48550/arxiv.1312.2024 · pith_short_12: 7FZXHGPUZ43F · pith_short_16: 7FZXHGPUZ43F5S3I · pith_short_8: 7FZXHGPU

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/7FZXHGPUZ43F5S3IF2DXZT5LF4 \
  | 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: f9737399f4cf365ecb682e877ccfab2f2a4233814fec5e4c6fe536baa21475c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49f1b5034ee9d4fe77c466afd0c3edf3a0ca4aac3edcb4c637005d8f7aba4642",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-06T21:57:09Z",
    "title_canon_sha256": "e6474e5a84d3574f6c470d1a6896ce9f29906ecdf10f619eed5fe629a85c83e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2024",
    "kind": "arxiv",
    "version": 4
  }
}