Pith Number

pith:7FMZZTTU

pith:2012:7FMZZTTUTG243MJLAMMCSMMWFC

not attested not anchored not stored refs pending

Cram\'er large deviation expansions for martingales under Bernstein's condition

Ion Grama, Quansheng Liu, Xiequan Fan

arxiv:1210.2198 v3 · 2012-10-08 · 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{7FMZZTTUTG243MJLAMMCSMMWFC}

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	2026-05-18T02:42:54.236083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9599cce7499b5cdb12b031829319628864ca5b694a97e914083c0e3fafd6ef6

Aliases

arxiv: 1210.2198 · arxiv_version: 1210.2198v3 · doi: 10.48550/arxiv.1210.2198 · pith_short_12: 7FMZZTTUTG24 · pith_short_16: 7FMZZTTUTG243MJL · pith_short_8: 7FMZZTTU

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/7FMZZTTUTG243MJLAMMCSMMWFC \
  | 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: f9599cce7499b5cdb12b031829319628864ca5b694a97e914083c0e3fafd6ef6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c00100548f2c742a2ee6ebfc0a96ab0d870e7f7143fcd65947d2c8ed8102a3ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-08T09:28:52Z",
    "title_canon_sha256": "d93e7816eb249f2536e5b61aa8770b81b3b3198ec97b08e7eece228ac77f563a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2198",
    "kind": "arxiv",
    "version": 3
  }
}