Pith Number

pith:R4LAMR2R

pith:2026:R4LAMR2RSD46IJ3F5ZZZPZQAJ2

not attested not anchored not stored refs pending

Lower bounds on expressions depending on the functions {\boldmath$\varphi(n)$}, {\boldmath$\psi(n)$} and {\boldmath$\sigma(n)$}, III

S. I. Dimitrov

arxiv:2606.12484 v1 · 2026-06-10 · 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{R4LAMR2RSD46IJ3F5ZZZPZQAJ2}

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	2026-06-12T00:07:51.816301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f1606475190f9e42765ee7397e6004ebb2c2d770b04046d27abfc857284ed0f

Aliases

arxiv: 2606.12484 · arxiv_version: 2606.12484v1 · doi: 10.48550/arxiv.2606.12484 · pith_short_12: R4LAMR2RSD46 · pith_short_16: R4LAMR2RSD46IJ3F · pith_short_8: R4LAMR2R

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/R4LAMR2RSD46IJ3F5ZZZPZQAJ2 \
  | 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: 8f1606475190f9e42765ee7397e6004ebb2c2d770b04046d27abfc857284ed0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "885e928b21325c9753ad05bbcf219e83fe7cbbb557e4b36f1457083e58798fb5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-10T08:16:39Z",
    "title_canon_sha256": "0f3ebc41dfec095395a4b06f6e5bc6ec64786393a0190b5ba8828b39b6cfe7af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12484",
    "kind": "arxiv",
    "version": 1
  }
}