Pith Number

pith:WGNQMNM2

pith:2012:WGNQMNM2LNL3QAGTA5W7L733IX

not attested not anchored not stored refs pending

On representations of positive integers by $(a+c)^{1/3}x + (b+d)y$, $(a+c)x + \bigl(k(b+d) \bigr)^{1/3} y$, and $\bigl(k(a+c) \bigr)^{1/3} x + l(b+d) y$

Mohamed El Bachraoui

arxiv:1210.3708 v3 · 2012-10-13 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WGNQMNM2LNL3QAGTA5W7L733IX}

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	2026-05-18T02:56:52.204584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b19b06359a5b57b800d3076df5ff7b45d99b7f9c91613e2e5be1b29828256bf5

Aliases

arxiv: 1210.3708 · arxiv_version: 1210.3708v3 · doi: 10.48550/arxiv.1210.3708 · pith_short_12: WGNQMNM2LNL3 · pith_short_16: WGNQMNM2LNL3QAGT · pith_short_8: WGNQMNM2

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/WGNQMNM2LNL3QAGTA5W7L733IX \
  | 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: b19b06359a5b57b800d3076df5ff7b45d99b7f9c91613e2e5be1b29828256bf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4782eedd1bf847cae8b7c036ee2fdc9d4a0d19a3e4262bd07fd76fc33770d52e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-13T13:58:06Z",
    "title_canon_sha256": "0ef77ba5a1bf3bea540363bd45e65531d654018d7bd9b18b6548037b1e798644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3708",
    "kind": "arxiv",
    "version": 3
  }
}