Pith Number

pith:TFMVIJLF

pith:2025:TFMVIJLF2NCCHJWPB5S43WDJ6P

not attested not anchored not stored refs pending

The One-Loop QCD $\beta$-Function as an Index

Kevin Costello, Roland Bittleston

arxiv:2510.26764 v3 · 2025-10-30 · hep-th · gr-qc · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TFMVIJLF2NCCHJWPB5S43WDJ6P}

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.

Cited by

1 paper in Pith

Non-Abelian and Type-A Conformal Anomalies from Euler Descent

Receipt and verification

First computed	2026-06-09T02:08:34.383638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9959542565d34423a6cf0f65cdd869f3cd7b7088dc20acf863d38fb17641bd68

Aliases

arxiv: 2510.26764 · arxiv_version: 2510.26764v3 · doi: 10.48550/arxiv.2510.26764 · pith_short_12: TFMVIJLF2NCC · pith_short_16: TFMVIJLF2NCCHJWP · pith_short_8: TFMVIJLF

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/TFMVIJLF2NCCHJWPB5S43WDJ6P \
  | 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: 9959542565d34423a6cf0f65cdd869f3cd7b7088dc20acf863d38fb17641bd68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf3d1a88b46a1127dec507df74b8c4810c253b12030ce0f7abd28523b50505a3",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2025-10-30T17:50:45Z",
    "title_canon_sha256": "ac25b72bb5eb2ad777268bc3428f81495f25798686698f45d85450b67dd00023"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.26764",
    "kind": "arxiv",
    "version": 3
  }
}