Pith Number

pith:MTRWVO4D

pith:2019:MTRWVO4DM5VPMNEZ72IYCIZ4J7

not attested not anchored not stored refs pending

On the number of pairs of positive integers $\mathbf{x, y \leq H}$ such that $\mathbf{x^2+y^2+1}$, $\mathbf{x^2+y^2+2}$ are square-free

S. I. Dimitrov

arxiv:1901.04838 v2 · 2019-01-05 · 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{MTRWVO4DM5VPMNEZ72IYCIZ4J7}

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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	2026-05-17T23:39:36.942685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64e36abb83676af63499fe9181233c4ffeaf5c88d4da05e9b46f6b0527d22754

Aliases

arxiv: 1901.04838 · arxiv_version: 1901.04838v2 · doi: 10.48550/arxiv.1901.04838 · pith_short_12: MTRWVO4DM5VP · pith_short_16: MTRWVO4DM5VPMNEZ · pith_short_8: MTRWVO4D

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/MTRWVO4DM5VPMNEZ72IYCIZ4J7 \
  | 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: 64e36abb83676af63499fe9181233c4ffeaf5c88d4da05e9b46f6b0527d22754

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b96e1bf5295468851271a0b93ad5a3f772b944c7adc83b547e9a1ee7884177f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-01-05T15:38:52Z",
    "title_canon_sha256": "75a07ff0eba3b64f6181dd31bca03c6adc916c29192cd26597ccd785c6f98a50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.04838",
    "kind": "arxiv",
    "version": 2
  }
}