Pith Number

pith:7CBVBQSG

pith:2019:7CBVBQSGOJHCRMAAMJEP6JQ5SZ

not attested not anchored not stored refs pending

Flattening Karatsuba's recursion tree into a single summation

Thomas Baruchel

arxiv:1902.08982 v11 · 2019-02-24 · math.NT · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7CBVBQSGOJHCRMAAMJEP6JQ5SZ}

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

1 paper in Pith

Properties of the cumulated deficient binary digit sum

Receipt and verification

First computed	2026-07-05T00:21:32.875104Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f88350c246724e28b0006248ff261d966db8bcbecc99cfa23f4788b2a08608a2

Aliases

arxiv: 1902.08982 · arxiv_version: 1902.08982v11 · doi: 10.48550/arxiv.1902.08982 · pith_short_12: 7CBVBQSGOJHC · pith_short_16: 7CBVBQSGOJHCRMAA · pith_short_8: 7CBVBQSG

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/7CBVBQSGOJHCRMAAMJEP6JQ5SZ \
  | 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: f88350c246724e28b0006248ff261d966db8bcbecc99cfa23f4788b2a08608a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af1836ae6580064882f56e801192188fc9047853b3324124e928f9b0766cb049",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-02-24T17:22:22Z",
    "title_canon_sha256": "27b18b9f69db3559c674ccece3ce71a95fde4a1b5c2540549faebd61fdafde96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.08982",
    "kind": "arxiv",
    "version": 11
  }
}