Pith Number

pith:QQKBNSVD

pith:2018:QQKBNSVDYTW54JFAAYNA57BJRJ

not attested not anchored not stored refs pending

Gradient flows for $\beta$ functions via multi-scale renormalization group equations

Ulrich Ellwanger

arxiv:1812.06751 v1 · 2018-12-17 · 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{QQKBNSVDYTW54JFAAYNA57BJRJ}

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	2026-05-17T23:50:22.379957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

841416caa3c4edde24a0061a0efc298a6712405a60cdc4dedee6717dd0263d21

Aliases

arxiv: 1812.06751 · arxiv_version: 1812.06751v1 · doi: 10.48550/arxiv.1812.06751 · pith_short_12: QQKBNSVDYTW5 · pith_short_16: QQKBNSVDYTW54JFA · pith_short_8: QQKBNSVD

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/QQKBNSVDYTW54JFAAYNA57BJRJ \
  | 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: 841416caa3c4edde24a0061a0efc298a6712405a60cdc4dedee6717dd0263d21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04deeacbb46e2287854495f87ab2db34eb54e33b2264f41a83b6d44c97d866d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2018-12-17T13:25:10Z",
    "title_canon_sha256": "83fe6b52c2b39888c8df0374f2d3f790111b92ee0dd06c5f08a26717bbfc9b86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.06751",
    "kind": "arxiv",
    "version": 1
  }
}