Pith Number

pith:NJYQHB3G

pith:2017:NJYQHB3GV74EHCXNVW33BVNJ5P

not attested not anchored not stored refs pending

Some remarks on the asymmetric sum--product phenomenon

Ilya D. Shkredov

arxiv:1705.09703 v1 · 2017-05-26 · math.NT · 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{NJYQHB3GV74EHCXNVW33BVNJ5P}

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	2026-05-18T00:07:38.120632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a71038766aff8438aedadb7b0d5a9ebcdd31b4c7cdab6c1006c9b3b3529d669

Aliases

arxiv: 1705.09703 · arxiv_version: 1705.09703v1 · doi: 10.48550/arxiv.1705.09703 · pith_short_12: NJYQHB3GV74E · pith_short_16: NJYQHB3GV74EHCXN · pith_short_8: NJYQHB3G

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/NJYQHB3GV74EHCXNVW33BVNJ5P \
  | 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: 6a71038766aff8438aedadb7b0d5a9ebcdd31b4c7cdab6c1006c9b3b3529d669

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fdc2ca25365c65b864955e0199b93c2d6a0be1e73432d2948de557f3789f747",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-05-26T20:05:28Z",
    "title_canon_sha256": "9d13e962938a135f48f3ab7a312301489f5cad890a29cf7a2f67f9a19785e988"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.09703",
    "kind": "arxiv",
    "version": 1
  }
}