Pith Number

pith:H5U5IFB2

pith:2022:H5U5IFB2EY5ZACJ4BXHJPFCJXI

not attested not anchored not stored refs pending

Integers expressible as the sum of two rational cubes

Ari Shnidman (with an appendix by Ashay Burungale, Christopher Skinner), Levent Alp\"oge, Manjul Bhargava

arxiv:2210.10730 v3 · 2022-10-19 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H5U5IFB2EY5ZACJ4BXHJPFCJXI}

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

4 papers in Pith

Gross-Zagier formula for the $4, 7$ cases of Sylvester's conjecture

Tamagawa ratios and unbounded Selmer moments

A proof of the $4,7$ cases of Sylvester's conjecture on cube sums

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two

Receipt and verification

First computed	2026-07-05T09:22:36.117463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f69d4143a263b90093c0dce979449ba1976d68c500e1a4637f0d9c3992fbb1b

Aliases

arxiv: 2210.10730 · arxiv_version: 2210.10730v3 · doi: 10.48550/arxiv.2210.10730 · pith_short_12: H5U5IFB2EY5Z · pith_short_16: H5U5IFB2EY5ZACJ4 · pith_short_8: H5U5IFB2

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/H5U5IFB2EY5ZACJ4BXHJPFCJXI \
  | 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: 3f69d4143a263b90093c0dce979449ba1976d68c500e1a4637f0d9c3992fbb1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b318e14219c87baab5d250ed68b3946794d193c52e560af07b82498a51feeaa",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-10-19T17:14:03Z",
    "title_canon_sha256": "d4d5f900d82957e21c6750e00b34e1d8d43c776a5d601abcdd96f994b6624bf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.10730",
    "kind": "arxiv",
    "version": 3
  }
}