Pith Number

pith:VXVYC5RC

pith:2017:VXVYC5RCJCFBZNXVFAUOU7R2WE

not attested not anchored not stored refs pending

Metric discrepancy results for geometric progressions with small ratios

K. Fukuyama, M. Tscheckl, O. Shimabe, S. Sakaguchi, T. Toyoda

arxiv:1711.02839 v2 · 2017-11-08 · 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{VXVYC5RCJCFBZNXVFAUOU7R2WE}

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	2026-05-18T00:26:36.047476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39

Aliases

arxiv: 1711.02839 · arxiv_version: 1711.02839v2 · doi: 10.48550/arxiv.1711.02839 · pith_short_12: VXVYC5RCJCFB · pith_short_16: VXVYC5RCJCFBZNXV · pith_short_8: VXVYC5RC

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/VXVYC5RCJCFBZNXVFAUOU7R2WE \
  | 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: adeb817622488a1cb6f52828ea7e3ab10284091bc5667d7eef277967159f2e39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b79ab2779bdd9b819fe5da3cb2a1a75e15d886495f91f5ed7a66e0eb03ae5762",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-11-08T05:43:10Z",
    "title_canon_sha256": "713d16a5378cee536538fc09684604f5aa686c68e6db690ba97c0233c3fa81cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.02839",
    "kind": "arxiv",
    "version": 2
  }
}