Pith Number

pith:MZ5IDJEF

pith:2009:MZ5IDJEFP7C6PSQLM5VD3C3WJ3

not attested not anchored not stored refs pending

Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers

Richard J. Mathar

arxiv:0903.2514 v2 · 2009-03-13 · 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{MZ5IDJEFP7C6PSQLM5VD3C3WJ3}

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	2026-05-18T04:31:51.250496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

667a81a4857fc5e7ca0b676a3d8b764ec6ea771d0072f2f992e2d3413375e603

Aliases

arxiv: 0903.2514 · arxiv_version: 0903.2514v2 · doi: 10.48550/arxiv.0903.2514 · pith_short_12: MZ5IDJEFP7C6 · pith_short_16: MZ5IDJEFP7C6PSQL · pith_short_8: MZ5IDJEF

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/MZ5IDJEFP7C6PSQLM5VD3C3WJ3 \
  | 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: 667a81a4857fc5e7ca0b676a3d8b764ec6ea771d0072f2f992e2d3413375e603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5df2f4169016ee2bd5201adaf17cfd89344525c1d0f73c0c89f99ca654772e8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-03-13T23:03:20Z",
    "title_canon_sha256": "a96c0c5067506994a4569ac9047ed94b89fc17c0d806a654565f66c66cb05fdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2514",
    "kind": "arxiv",
    "version": 2
  }
}