Pith Number

pith:XCZV2GRK

pith:2015:XCZV2GRKNRJEKGNNZHVBOWN4GO

not attested not anchored not stored refs pending

Sums of reciprocals of fractional parts and multiplicative Diophantine approximation

Alan Haynes, Sanju Velani, Victor Beresnevich

arxiv:1511.06862 v2 · 2015-11-21 · 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{XCZV2GRKNRJEKGNNZHVBOWN4GO}

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	2026-05-18T00:47:29.447784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8b35d1a2a6c524519adc9ea1759bc3383d1bcf1d08bda66cfe3614b433bf2f6

Aliases

arxiv: 1511.06862 · arxiv_version: 1511.06862v2 · doi: 10.48550/arxiv.1511.06862 · pith_short_12: XCZV2GRKNRJE · pith_short_16: XCZV2GRKNRJEKGNN · pith_short_8: XCZV2GRK

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/XCZV2GRKNRJEKGNNZHVBOWN4GO \
  | 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: b8b35d1a2a6c524519adc9ea1759bc3383d1bcf1d08bda66cfe3614b433bf2f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0ab03c13ecc40b7f29e06f538fa9b8da34be4f141e7c0e599743dd654e511b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-21T09:50:08Z",
    "title_canon_sha256": "5a0380d5290d7dd5616580be140e81457a46f3be47b36b4f8902d2103fc48e52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06862",
    "kind": "arxiv",
    "version": 2
  }
}