Pith Number

pith:BSHGTKR5

pith:2017:BSHGTKR5DCABWCRGOW3XCXMZ2I

not attested not anchored not stored refs pending

An application of kissing numbers in sum-product estimates

Ching Wong, Jozsef Solymosi

arxiv:1709.08758 v1 · 2017-09-26 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BSHGTKR5DCABWCRGOW3XCXMZ2I}

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	2026-05-18T00:34:21.943947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c8e69aa3d18801b0a2675b7715d99d2035552ce85f40e1428c634fcb6a896d4

Aliases

arxiv: 1709.08758 · arxiv_version: 1709.08758v1 · doi: 10.48550/arxiv.1709.08758 · pith_short_12: BSHGTKR5DCAB · pith_short_16: BSHGTKR5DCABWCRG · pith_short_8: BSHGTKR5

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/BSHGTKR5DCABWCRGOW3XCXMZ2I \
  | 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: 0c8e69aa3d18801b0a2675b7715d99d2035552ce85f40e1428c634fcb6a896d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e91cc97ca7c6b8a5b2157cc231443162a082cc2b11df8b29103bb3140a1ae46d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-09-26T00:10:24Z",
    "title_canon_sha256": "b7886d2e6a83d04956945779d18c49d16ad467c0a7f4ebad65afd50395af7ac3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.08758",
    "kind": "arxiv",
    "version": 1
  }
}