Pith Number

pith:DGAMHXRZ

pith:2011:DGAMHXRZVNPEMW7SVKMN2VMGCH

not attested not anchored not stored refs pending

The absence of QCD $\beta$-function factorization property of the generalized Crewther relation in the 't Hooft $\bar{MS}$-based scheme

A.L. Kataev (INR, A.V. Garkusha (Physics Dep., Moscow), Moscow State Univ)

arxiv:1108.5909 v2 · 2011-08-30 · hep-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DGAMHXRZVNPEMW7SVKMN2VMGCH}

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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	2026-05-18T02:00:44.791706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1980c3de39ab5e465bf2aa98dd558611f77100d7bb889ff2771dfbf9ef0da0f0

Aliases

arxiv: 1108.5909 · arxiv_version: 1108.5909v2 · doi: 10.48550/arxiv.1108.5909 · pith_short_12: DGAMHXRZVNPE · pith_short_16: DGAMHXRZVNPEMW7S · pith_short_8: DGAMHXRZ

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/DGAMHXRZVNPEMW7SVKMN2VMGCH \
  | 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: 1980c3de39ab5e465bf2aa98dd558611f77100d7bb889ff2771dfbf9ef0da0f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "665596f40de03607a63ceaae37b92b3aeac06c612612d262c8942daf4d9a8c7d",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2011-08-30T10:31:17Z",
    "title_canon_sha256": "19135d66a8aaa1afdfffdb86dd7369ff5d90fac40a0879909fcfa172c5b777e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5909",
    "kind": "arxiv",
    "version": 2
  }
}