Pith Number

pith:55NGKUMH

pith:2026:55NGKUMHHH4Z7GDD2DGPT5Y7X4

not attested not anchored not stored refs pending

Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results

D. Kotlorz, S. V. Mikhailov

arxiv:2606.31592 v1 · 2026-06-30 · hep-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{55NGKUMHHH4Z7GDD2DGPT5Y7X4}

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	2026-07-01T01:18:08.567625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef5a65518739f99f9863d0ccf9f71fbf327fdd0aa2cefbbf54b4d4cc17b3df16

Aliases

arxiv: 2606.31592 · arxiv_version: 2606.31592v1 · doi: 10.48550/arxiv.2606.31592 · pith_short_12: 55NGKUMHHH4Z · pith_short_16: 55NGKUMHHH4Z7GDD · pith_short_8: 55NGKUMH

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/55NGKUMHHH4Z7GDD2DGPT5Y7X4 \
  | 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: ef5a65518739f99f9863d0ccf9f71fbf327fdd0aa2cefbbf54b4d4cc17b3df16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2b86875b8d05756d016ae2675d54d7dddf2cc68a875bee47e0224afd005b548",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-06-30T12:42:45Z",
    "title_canon_sha256": "73a7fb9e79572e2ee86b4918334b448427f3acbd3597cc8c1219b00f743f4d4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31592",
    "kind": "arxiv",
    "version": 1
  }
}